Two-dimensional wave-current numerical flume based on ISPH method with added damping zone and its application

Abstract

The application discloses a two-dimensional wave-current numerical flume construction method based on an ISPH method and addition of a wave absorbing area and application. k-ε The method combines the ISPH method, the "sponge layer" wave absorbing theory and a modified k-ε turbulence model to construct a two-dimensional numerical flume model of wave-current interaction, and verifies the accuracy and applicability of the two-dimensional numerical flume model through the wave propagation process on the coral reef profile, the wave height change along the reef and the variation of the hydrodynamic characteristics of the horizontal flow velocity, and is used for analyzing the change of the hydrodynamic characteristics of the coral reef area after composite engineering activities, and / or used for analyzing the influence of the construction of a breakwater on the hydrodynamic environment of the coral reef topography under the condition of the coupling action of regular waves and water flow. The simulation result of the numerical model after the wave absorbing theory is improved and coupled with the modified k-ε turbulence model is in good agreement with the experimental result of the physical model, and the problem of the exponential growth of the turbulence kinetic energy index in the potential flow area before wave breaking is obviously improved compared with traditional methods.

Description

Technical Field

[0001] This invention belongs to the field of coral reef hydrodynamics research, and in particular relates to a method and application for constructing a two-dimensional wave-flow numerical flume with a "sponge layer" wave-dissipating zone. Background Technology

[0002] Coral reef areas represent a unique ecological environment. Through long-term observation and analysis of coral reef topography, numerous researchers have summarized that a typical coral reef topography usually consists of three parts: a steep foreshore slope connecting the reef to the deep seabed, a nearly horizontal reef flat extending towards the shore, and a raised reef crown connecting the foreshore slope and the reef flat. In the transition zone between the reef flat and the shore, there may be a relatively deep lagoon. This area has relatively calm waters, providing habitats and breeding grounds for many marine organisms. The morphology and structure of coral reefs exert a powerful regulatory influence on ocean dynamic processes (such as waves and tides). Their hydrodynamic characteristics play a crucial role in maintaining ecological balance, promoting biodiversity, predicting coastline evolution, disaster prevention and mitigation, and marine engineering construction. In recent years, with the continuous advancement of marine exploration and the increasingly profound impact of human activities on marine areas, coupled with the more frequent natural disasters disrupting marine ecosystems, the hydrodynamic characteristics surrounding coral reef topography have become a key research focus for scholars both domestically and internationally. Revealing the hydrodynamic characteristics and regulatory mechanisms surrounding marine coral reefs is not only crucial for understanding the healthy maintenance of marine ecosystems, but also a core scientific issue in areas such as marine resource development, ecological restoration engineering, and coastal disaster prevention. In marine science and engineering, physical model experiments and field observation methods are widely used as two important research tools in many key areas such as coastal hydrodynamics, marine engineering construction, and marine disaster early warning. These two methods each have their advantages and complement each other, providing rich and reliable data support and theoretical basis for related research. However, with the rapid development of computer technology, numerical simulation methods are increasingly becoming an important tool for studying the hydrodynamics of shallow marine reefs, breaking through the limitations of previous research methods in studying coral reef topography and hydrodynamics. This method can reproduce complex and changing marine environments without requiring huge financial and material resources, greatly improving the efficiency of scientific research.

[0003] In 2017, Zhao Qinyang's dissertation at Dalian University of Technology, "SPH Analysis of Wave Propagation and Flow Field Characteristics on Reef Flat Topography," used the Navier-Stokes equations as the hydrodynamic control equations and constructed a two-dimensional numerical wave flume based on the Smooth Particle Hydrodynamics (SPH) method. It simulated wave propagation on coral reef topography with different slopes and analyzed the wave surface, water movement, and flow field variation patterns. Wen Hongjie et al., in their SPH simulation of random wave propagation on coral reef topography published in *Research and Progress in Hydrodynamics (Series A)* (2018, 33(06):706-713), combined momentum source wave generation theory with artificial velocity decay functions in the SPH hydrodynamic model to achieve stable generation of conventional and random waves and efficient wave absorption. By setting the wave generation zone, it was made applicable to any depth of sea area. Then, the established numerical model was used to study wave evolution problems on islands and reefs. Studies have shown that the constructed SPH numerical model can effectively represent hydrodynamic problems such as wave rolling and breaking on steep reef foreslopes and wave surge on reef flats. However, the traditional SPH method has certain shortcomings when dealing with incompressible fluids, such as density fluctuations and numerical noise, which affect the accuracy and stability of the simulation results.

[0004] Wang Dong et al., in their research published in Coastal Engineering (Wang D, Liu PL F. An ISPH with k-ε closure for simulating turbulence under solitary waves[J].CoastalEngineering,2020,157:103657-103657.), constructed an ISPH method to solve the closed two-dimensional RANS equations of the k-ε turbulence model. At the same time, they adopted the adaptive wall condition of the k-ε turbulence model to solve the problem of unrealistic turbulence generated near the wall. Subsequently, the model was further optimized in the research results published in the journal in 2022 (Wang D, Liu P LF. An ISPH with modified k–ε closure for simulating breaking periodic waves[J]. Coastal Engineering, 2022, 178: 104191.). The modified k-ε turbulence model was used to solve the two-dimensional RANS equations in a closed loop, enabling the model to accurately simulate long-term periodic wave motion. The model was applied to three experimental examples, and the applicability of the model was verified by comparing it with experimental data in terms of free surface profile, mean velocity field, and turbulent kinetic energy.

[0005] Currently, research on simulating the hydrodynamic characteristics around marine coral reefs using the ISPH method focuses primarily on the effects of single waves or currents, with limited research on the combined effects of waves and currents. However, the complex hydrodynamic environment in reality involves more than just the individual effects of waves or currents; it often exhibits the combined effects of both. Furthermore, previous studies on turbulent kinetic energy changes in coral reef areas have often overlooked the exponential increase in turbulent kinetic energy in the potential current region before wave breaking. Therefore, conducting numerical simulation studies on the topographic and hydrodynamic characteristics of coral reefs under the combined effects of waves and currents is of significant practical value, both for deepening our understanding of coral reef topographic and hydrodynamic theory and for promoting the steady progress of practical engineering projects. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a method and application for constructing a two-dimensional wave-flow numerical flume based on the ISPH method to add a wave-dissipating region. The method combines the ISPH method with the "sponge layer" wave-dissipating theory and a modified k-ε turbulence model to construct a two-dimensional wave-flow numerical flume model, improving the simulation accuracy for complex coral reef topography. Furthermore, it provides an analytical method for the changes in hydrodynamic characteristics after complex engineering activities in coral reef areas and the impact of breakwater construction on the hydrodynamic environment of coral reef topography.

[0007] This invention is implemented as follows:

[0008] One approach is a two-dimensional wave-flow numerical flume construction method based on the ISPH method to add wave-dissipating regions. This method combines the ISPH method with the "sponge layer" wave-dissipating theory and a modified k-ε turbulence model, including:

[0009] S1, based on the ISPH method, adds a damping term to the momentum conservation equation in the basic governing equations to absorb waves, constructing a two-dimensional wave-flow numerical flume model with wave-damping effect, expressed as:

[0010]

[0011] In the formula, ρ is the fluid density; t is time; u is the velocity vector; P is the pressure; g is the volume force vector per unit mass; ν is the viscosity coefficient; D / Dt represents the total derivative over time; ▽· is the divergence operator; q d,u Represents the damping term.

[0012] q d,u (x)=γb(x0)(-u)

[0013] In the formula, γ is the absorption intensity, x0 represents the x-coordinate of the particle's position at this moment, b(x0) is the mixing function, and u represents the horizontal velocity of the particle at this moment.

[0014] S2, Verify and debug the wave-flow numerical flume model with wave-damping effect constructed in step S1;

[0015] S3. The optimized wave-flow numerical flume model with wave-damping effect is coupled with the modified k-ε turbulence model. A turbulent eddy viscosity term is added to its momentum conservation equation. A gradient correction-dynamic stabilization scheme is used to reduce numerical dissipation. A two-dimensional wave-current-coral reef topography numerical flume model is established. The expression of the coupled momentum conservation equation is:

[0016]

[0017] In the formula, Let Reynolds stress tensor be the stress tensor.

[0018] S4 verifies the accuracy and applicability of the two-dimensional numerical flume model in step S3 by analyzing the wave propagation process, wave height variation along the reef, and horizontal velocity variation on the coral reef profile, and provides the distribution of turbulent kinetic energy along the reef.

[0019] Furthermore, the wave-absorbing effect was verified by comparing the wave-absorbing effects of different absorption intensities γ to determine the wave-absorbing intensity value of the model. The verification numerical water tank was set to a size of 12×1m. The verification numerical water tank was composed of wall particles, wave-generating plate particles and water particles. The wave-absorbing area was set to 9.06-11.8m. Ten wave height measuring points were set along the entire water area in the water tank to capture the change of the free surface elevation of each section over time. Some of the measuring points were set in the wave-absorbing area.

[0020] Furthermore, the wave-damping effect was verified by setting the wave-damping area of ​​the water tank within a range of 1-2 times the wavelength.

[0021] Furthermore, the hybrid function b(x0) described in S1 uses an exponential function, and its expression is as follows:

[0022]

[0023] In the formula, x0 represents the x-coordinate of the particle's position at this moment; x sd The x-coordinate represents the starting position of the wave-damping area; ed The x-coordinate represents the position of the end of the wave-damping area.

[0024] Furthermore, the two-dimensional wave-flow numerical flume model is 25m long, 1.25m high, and 0.3m deep. A wave-generating plate is set at the left end of the numerical flume model, and the travel path of the wave-generating plate is generated according to the preset wave height and period. A wave-dissipating area with a length twice the characteristic wavelength is set at the right end. Inflow and outflow areas with a width of 0.2m are set on the left and right sides of the bottom wall, respectively. The total number of particles in the model is approximately 140,000, and the particle segmentation diameter is 0.01m. A cross-sectional measurement position is selected at a distance of 14m from the wave-generating plate. Starting from the liquid surface, a velocity measurement point is set at a depth of 0.015m, for a total of 20 measurement points. The flow velocity at different depths is measured over time, and the average flow velocity of the cross-section is calculated.

[0025] Furthermore, the numerical calculation area of ​​the two-dimensional wave-current-coral reef topography numerical flume model is 22m long and 1m high. A wave-generating plate is set at the left end of the model to generate regular waves, with the positive x-direction being the direction of regular wave propagation. A wave-dissipating zone with a length of 3m is set at the right end. The length l of the reef flat is 6m, and the height hr is 0.35m. The slope of the reef-front slope is 1:5, and the distance from the toe of the reef-front slope to the right boundary of the wave-generating plate is 5.05m. The slope of the reef-back slope is 1:6, and the distance from the toe of the reef-back slope to the left boundary of the wave-dissipating zone is 3.8m. The wave-dissipating zone is 18.9-21.9m deep, the water depth h in the wave-generating zone is 0.45m, and the water depth hc at the top of the reef flat is 0.1m. The flow conditions are achieved by setting the flow velocities in the inflow and outflow areas at the bottom of the flume.

[0026] Furthermore, the diameter of the particles in the computational domain is 0.01m, and the total number of particles is 145215. To ensure the stability of the waves and water flow, the simulation time is set to 100s. The verification of the numerical model focuses on testing three different working conditions: waves acting alone, waves and water flow acting in the same direction, and waves and water flow acting in opposite directions. During the model calculation, wave height measuring points G1-G16 along the x-direction will measure the change in the elevation of the free surface during the simulation, and flow velocity measuring points L1-L14 will measure the change in flow velocity at the water depth position in the middle of each cross section.

[0027] In another aspect, this invention provides an application of a two-dimensional wave-flow numerical flume construction method based on the ISPH method for adding wave-dissipating areas. This method is used for analyzing changes in hydrodynamic characteristics after complex engineering activities in coral reef areas, or for analyzing the impact of breakwater construction on the topographic and hydrodynamic environment of coral reefs under the coupling effect of regular waves and currents, and / or for analyzing the impact of breakwater construction on the topographic and hydrodynamic environment of coral reefs under the coupling effect of regular waves and currents.

[0028] Furthermore, the application involves analyzing the changes in hydrodynamic characteristics following complex engineering activities in coral reef areas, including the analysis of wave propagation characteristics, velocity field distribution, and energy dissipation under different sand pit depths. The method steps are as follows:

[0029] (1) Three different sand pit conditions with different depths were set up in the wave-current-coral reef two-dimensional numerical flume: hs = 0.15m, 0.25m and 0.35m, where hs represents the depth, and the original topography without sand pit (hs = 0m) was used as the control group.

[0030] (2) The sand mining pit adopts a centrally symmetrical trapezoidal cross-section layout. The geometric parameters of the sand mining pit are set as follows: center position coordinate x s = 9.5m, upstream starting position x t =8.0m, downstream termination position x e =11.0m, total horizontal width w s =3m, the front and rear slopes of the sand pit are designed with a gentle slope of 1:3; wave conditions include: regular wave height H = 0.14m, period T = 1.5s, water flow conditions include water flow in the same direction as the wave and in the opposite direction, with initial flow velocities of 0.1m / s and -0.12m / s respectively;

[0031] (3) The setting of measuring points for free surface elevation and flow velocity under the three different sand pit conditions is completely consistent with the above-mentioned original coral reef topography without sand pits.

[0032] (4) Under the combined action of waves and water flow, measure the average flow velocity of the intermediate water depth section of the coral reef topography in sand pits of different depths, and obtain relevant data on the elevation and flow velocity of the free surface of the entire water tank.

[0033] (5) Analyze the acquired data.

[0034] Furthermore, the application analyzes the impact of breakwater construction on the topographic and hydrodynamic environment of coral reefs under the coupling effect of regular waves and currents. The method and steps are as follows:

[0035] (1) In the two-dimensional numerical flume of wave-current-coral reef, the three-dimensional triangular block structure of the breakwater is simplified into a two-dimensional triangular submerged breakwater and set on the reef flat. Four breakwater construction conditions are designed at different locations, namely d / l=1 / 6, d / l=1 / 3, d / l=1 / 2 and d / l=2 / 3. The original topography without a breakwater (d / l=0) is used as the control group. d represents the distance from the reef crown to the center of the breakwater, l represents the length of the reef flat, and d / l represents the location of the breakwater.

[0036] (2) Set the wave height H = 0.14m, period T = 1.5s, the velocity of the wave and current in the same direction is 0.1m / s, and the velocity of the wave and current in opposite directions is -0.12m / s. Statistically analyze the average velocity data and analyze the influence of the breakwater layout on the spatial distribution characteristics of the average velocity in the middle water depth of the reef flat under the wave-current interaction condition.

[0037] (3) Analyze the influence of the breakwater layout location (d / l) on the spatial distribution characteristics of turbulent kinetic energy (k) in the reef flat area under wave-current interaction conditions.

[0038] The beneficial effects of this invention are: the numerical simulation results of the k-ε turbulence model, improved and coupled with wave-damping theory, show good agreement with the experimental results of the physical model, and significantly improve the problem of exponential growth of turbulent kinetic energy in the potential flow region before wave breaking compared to traditional methods. Specifically, this is reflected in the following aspects:

[0039] (1) A two-dimensional wave-flow numerical flume was constructed by combining the ISPH method with the "sponge layer" wave attenuation theory. Comparative analysis of numerical simulation results and experimental data before and after the introduction of the wave attenuation theory verified the accuracy of the waveform and cross-sectional average velocity simulation under wave-flow coupling. The addition of the wave attenuation theory significantly improved the simulation accuracy of the waveform and cross-sectional average velocity, and the numerical simulation results showed good agreement with the experimental data, demonstrating that the improved ISPH model has excellent applicability in reproducing the flow field distribution characteristics under wave-flow coupling.

[0040] (2) The improved ISPH model was coupled with the modified k-ε turbulence model to conduct a numerical simulation study of the wave-current hydrodynamic environment around marine coral reefs. The accuracy and applicability of the coupled model in the simulation of coral reef topography and hydrodynamics were verified. The model successfully reproduced the entire process of wave propagation and deformation, including nearshore wave generation, steepening of the reef foreshore slope waveform, sawtooth breaking waves at the reef flat front, and prediction of transmitted wave height. In particular, regarding the wave height evolution along the reef, the influence mechanism of the reef crown on waves was revealed: under three conditions (waves alone, wave and current in the same direction, and wave and current in opposite directions), the wave height reached its peak and decreased after the reef crown effect, but the wave-current interaction changed the peak position—in the same direction, it shifted towards the wave propagation direction, and in the opposite direction, it moved towards the opposite wave propagation direction and the peak value was higher. The flow field simulation results further confirmed the model's ability to accurately reproduce the complex hydrodynamics of coral reef topography.

[0041] (3) In terms of turbulent kinetic energy simulation, the model overcomes the limitations of the traditional k-ε model: it achieves a physically reasonable representation of the turbulent kinetic energy in the potential current region before wave breaking tends to zero, solving the problem of spurious growth of turbulent kinetic energy in the potential current region in traditional methods. Comparative studies show that wave-current interaction significantly changes turbulence characteristics—the same-direction condition weakens the instantaneous turbulence during breaking but enhances the intensity in the post-breaking region, while the opposite-direction condition greatly increases the turbulent kinetic energy throughout the breaking process. This improvement provides a more reliable theoretical tool for the study of key processes such as material transport and energy dissipation in marine ecosystems.

[0042] (4) Based on a validated two-dimensional wave-current-coral reef topography numerical model, the impact mechanism of sand dredging pits and breakwater projects on the hydrodynamic environment of marine coral reefs was systematically studied. The study found that sand dredging pits significantly weaken wave breaking intensity by altering the topography, leading to a general increase in wave height within the pit and downstream, while simultaneously forming a distinct low-turbulence zone, potentially hindering material exchange within the ecosystem. Breakwaters exhibit significant nonlinear effects: when the wave and current are in the same direction, the overall flow velocity increases by 20%-26%, while when they are in opposite directions, the upstream flow velocity decreases by 35%-53%. Regarding turbulence reorganization, under the same-direction condition, an asymmetric characteristic of weakening upstream and strengthening downstream is observed, while under opposite-direction conditions, a unique pattern of overall suppression and only local strengthening at the breakwater crest is observed. These findings reveal the complex feedback mechanism between engineering intervention and marine coral reef structure, providing important scientific basis for regional engineering planning in marine coral reefs, and emphasizing the need to consider both hydrodynamic impacts and ecological protection requirements in engineering design. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the two-dimensional wave-flow numerical water tank of the present invention;

[0044] Figure 2 This is a comparison diagram of different γ wave attenuation effects of the present invention.

[0045] Figure 3 This is a schematic diagram of the two-dimensional wave-flow numerical water tank of the present invention;

[0046] Figure 4 This is a comparison between the waveform simulation results of this invention and experimental data;

[0047] Figure 5 This invention compares numerical simulations and experimental data of U under the action of waves alone.

[0048] Figure 6 This is a comparison between numerical simulation and experimental results of U under the combined action of wave and current according to the present invention;

[0049] Figure 7 This is a schematic diagram of the computational region of the numerical model of this invention;

[0050] Figure 8 This is a verification of the free surface elevation change under wave-only conditions of the present invention;

[0051] Figure 9 This invention verifies the change in free surface elevation under the condition of wave and current in the same direction;

[0052] Figure 10 This invention verifies the change in free surface elevation under wave-current reversal conditions.

[0053] Figure 11 This is a comparison between the numerical model of wave height variation along the reef and experimental results of this invention;

[0054] Figure 12 This is a verification of the instantaneous change in flow velocity under the condition of waves alone in this invention;

[0055] Figure 13 This is a verification of the instantaneous change in flow velocity under the condition of wave and current in the same direction in this invention;

[0056] Figure 14 This is a verification of the instantaneous change in flow velocity under the reverse wave-flow condition of the present invention;

[0057] Figure 15 This invention relates to the variation of turbulent kinetic energy along a reef under wave-only conditions.

[0058] Figure 16 The present invention describes the variation of turbulent kinetic energy along the reef under the condition that the wave and current are in the same direction;

[0059] Figure 17 The present invention describes the variation of turbulent kinetic energy along the reef under the condition of reverse wave flow.

[0060] Figure 18 This invention is a numerical flume model of coral reef topography with sand mining pits;

[0061] Figure 19 This is a diagram showing the wave height variation along the reef at different sand pit depths according to the present invention;

[0062] Figure 20 This invention provides vorticity and streamline diagrams under the condition of wave-current co-directionality.

[0063] Figure 21 This is a diagram of vorticity and streamlines under the reverse wave-current condition of the present invention;

[0064] Figure 22 This is a graph showing the variation of average flow velocity along the reef at different sand pit depths according to the present invention;

[0065] Figure 23 This invention describes the instantaneous flow velocity field distribution at different sand pit depths.

[0066] Figure 24 This is a diagram showing the distribution of turbulent kinetic energy (k) under the condition of wave and current in the same direction, as described in this invention.

[0067] Figure 25 This is a diagram of turbulent kinetic energy distribution under wave-current reversal conditions according to the present invention;

[0068] Figure 26 This is a schematic diagram of the numerical simulation of coral reef dike construction according to the present invention;

[0069] Figure 27 This is a diagram showing the variation of u along the reef under the condition of wave and current in the same direction, as described in this invention;

[0070] Figure 28 This is a diagram showing the variation of u along the reef under the reverse wave-current condition of the present invention;

[0071] Figure 29 This invention describes the distribution characteristics of turbulent kinetic energy along the reef under the condition of wave and current in the same direction.

[0072] Figure 30 This invention describes the distribution characteristics of turbulent kinetic energy along the reef under wave-current reversal conditions. Detailed Implementation

[0073] The present invention will be further explained in detail below with reference to the accompanying drawings and specific embodiments.

[0074] It should be noted that the physical model of Yao Yu mentioned in this invention comes from the literature: Yao Y, Li Z, Xu C, et al. A study of wave-driven flow characteristics across a reef under the effect of tidal current[J]. Applied Ocean Research, 2023, 130:103430.

[0075] One embodiment of the present invention is a method for constructing a two-dimensional wave-flow numerical flume based on the ISPH method to add a wave-dissipating region. This method combines the ISPH method with the "sponge layer" wave-dissipating theory and a modified k-ε turbulence model, and includes:

[0076] S1, based on the ISPH method, adds a damping term to the momentum conservation equation in the basic control equation to achieve wave absorption, and constructs a two-dimensional wave-flow numerical flume model with wave-damping effect.

[0077] In numerical wave flumes, to prevent waves from propagating to the flume boundary and being reflected, thus interfering with the incident wave, a wave-damping region is set at the end of the flume. This method is called the "sponge layer" wave-damping method. This is achieved by introducing a damping term into the momentum conservation equation, namely:

[0078]

[0079] In the formula, ρ is the fluid density; t is time; u is the velocity vector; P is the pressure; g is the volume force vector per unit mass; ν is the viscosity coefficient; D / Dt represents the total derivative over time; ▽· is the divergence operator; q d,u This represents the damping term, which gradually reduces the velocity of the fluid entering the wave-dissipating zone during propagation, thereby dissipating the wave's energy. The formula for calculating the damping term can be expressed as:

[0080] q d,u (x)=γb(x0)(-u)

[0081] In the formula, γ is the absorption intensity, x0 represents the x-coordinate of the particle's position at this moment, b(x0) is the mixing function, and u represents the horizontal velocity of the particle at this moment. The equation of the mixing function b(x0) has multiple types, including constant type, linear type, quadratic type, cosine type, and exponential type. Studies have shown that higher-order mixing functions generally have better wave-damping effects. This embodiment uses the exponential function, and the expression is as follows:

[0082]

[0083] In the formula, x0 represents the x-coordinate of the particle's position at this moment; x sd The x-coordinate represents the starting position of the wave-damping area; ed The x-coordinate represents the position of the end of the wave-damping area.

[0084] S2, Verify and debug the wave-flow numerical flume model with wave-damping effect constructed in step S1;

[0085] S3. The optimized wave-flow numerical flume model with wave-damping effect is coupled with the modified k-ε turbulence model. A turbulent eddy viscosity term is added to its momentum conservation equation. A gradient correction-dynamic stabilization scheme is used to reduce numerical dissipation. A two-dimensional wave-current-coral reef topography numerical flume model is established. The expression of the coupled momentum conservation equation is:

[0086]

[0087] In the formula, Let Reynolds stress tensor be the stress tensor.

[0088] S4. The accuracy and applicability of the two-dimensional numerical flume model in step S3 are verified by the wave propagation process, wave height variation along the reef, and horizontal flow velocity variation hydrodynamic characteristics on the coral reef profile.

[0089] 1. Wave attenuation effect verification

[0090] To preliminarily verify the coupling effect between the ISPH numerical model and the "sponge layer" wave absorption theory, and to determine the wave absorption intensity value of this model by comparing the wave absorption effects of different absorption intensities γ, a simple two-dimensional wave numerical flume was established, such as... Figure 1As shown, the numerical cooling tank measures 12×1m and consists of wall particles, wave-generating plate particles, and water particles. The wall particles are neatly arranged and stationary. The wave-generating plate particles generate a linear incident wave with a wave height of 0.023m and a period of 1.0s based on a given path file. The water particles move under external force. The initial water depth is 0.3m. The optimal wave-damping effect is achieved when the wave-damping area length is controlled within the range of 1-2 times the wavelength. This length range effectively dissipates wave energy propagating to the end of the tank, significantly suppressing the interference of reflected waves on the test area, thereby ensuring the stability of the wave field within the test area. In this embodiment, the wave-damping area is set to 9.06-11.8m, approximately twice the wavelength. In subsequent experiments, the wave-damping area was also set to twice the wavelength length.

[0091] Ten wave height measurement points (WG1-WG10) were set up along the entire water area in the numerical wave flume to capture the change of free surface elevation of each section over time. Among them, three measurement points (WG8-WG10) are located in the wave-dissipating area. The left boundary of the numerical flume wall was used as the reference zero point in the horizontal x-direction, i.e., x=0. The arrangement of the wave height measurement points in the x-direction is listed in Table 1.

[0092] Table 1 Horizontal Position Layout of Wave Height Measurement Points

[0093]

[0094] Under the same conditions, simulations were conducted for test conditions with two different absorption intensity parameters: γ = 10 and γ = 100. The free surface elevation (η) data within a relatively stable 30 seconds at each measurement location were averaged, and the resulting periodic waveforms at each location were arranged to obtain the following... Figure 2 The diagram shows the wave-damping effect. It can be seen from the diagram that both absorption intensities can achieve wave-damping, but the absorption effect is better when γ = 100. Therefore, subsequent experiments will use an absorption intensity of 100.

[0095] When constructing a two-dimensional wave-current numerical flume model, precise region setting and parameter configuration are crucial. In this embodiment, the numerical model region is set to a length of 25m, a height of 1.25m, and a water depth of 0.3m. The 25m length provides sufficient space for wave development and propagation, while the 1.25m height and 0.3m depth conform to common flume experiment depth ratios, ensuring that the flow characteristics are realistically represented in the simulation. The two-dimensional wave-current numerical flume model is as follows: Figure 3As shown, the numerical flume model has a wave-generating plate at the left end, which generates the linear waves required for the experiment by predicting the wave height and period. A wave-dissipating zone with a length approximately twice the characteristic wavelength is located at the right end. Inflow and outflow zones with a width of 0.2m are located on the left and right sides of the bottom wall, respectively. Water circulation within the flume is achieved by setting the inflow and outflow velocities. This water circulation simulation not only reproduces the actual flow conditions in experiments but also allows for precise control of key parameters such as flow velocity distribution and flow rate changes, providing a stable flow field for studying wave-current interactions. Regarding the numerical accuracy of the model, the particle segmentation diameter is set to 0.01m, and the total number of particles in the model is approximately 140,000. This precise setting ensures computational efficiency while accurately capturing the microscopic characteristics of water flow and waves. These particles, as discrete units of the numerical model, simulate the motion of water flow and waves by solving the governing equations using a numerical discretization scheme, providing a data source for subsequent data analysis.

[0096] During the simulation, the focus was on validating the waveform and cross-sectional average velocity data within one cycle of the experiment. To obtain data on the change in free surface elevation, precise data was captured at a distance of 14m from the wavemaker along the water flow direction. For obtaining the cross-sectional average velocity, the cross-section at a distance of 14m from the wavemaker was selected as the key measurement location. Regarding the measurement depth, starting from the liquid surface (z=0), a velocity measurement point was set at every 0.015m depth, for a total of 20 measurement points. This dense arrangement of measurement points on the cross-section allowed for comprehensive and detailed measurement of the velocity changes over time at different depths, thus enabling accurate calculation of the cross-sectional average velocity.

[0097] This embodiment uses a two-dimensional wave-flow numerical flume model to simulate two operating conditions, W2 and WC2, in the Umeyama experiment:

[0098] Table 2 Experimental conditions and parameters

[0099]

[0100] 2. Waveform Verification

[0101] In the verification process of the two-dimensional numerical model of wave-current, the verification of free surface elevation is the first and crucial step. Free surface elevation directly reflects the morphology and propagation characteristics of waves, and accurate verification helps to evaluate the accuracy of the numerical model in simulating wave motion. To ensure the reliability and stability of the data, this embodiment experimentally collected free surface elevation data for 30 cycles at a horizontal distance of 14m from the wavemaker. These 30 cycles of data were then averaged. Figure 4Figures (a) and (b) show the comparison between numerical simulation results and experimental data of one-cycle waveforms before and after applying the "sponge layer" wave attenuation theory, under the effects of wave action alone and wave-current combined action, respectively. The numerical simulation results before wave attenuation are represented by solid blue lines and dashed blue lines, respectively; the numerical simulation results after applying the wave attenuation theory are represented by solid red lines and dashed red lines, respectively. The experimental results of the physical model under wave action alone are represented by hollow circles, while the experimental results under wave-current combined action are represented by black × signs. The data in the figures show that the numerical simulation results after introducing the wave attenuation theory match the experimental results better, and better reproduce the characteristics of wave propagation in the direction of water flow. Under wave action alone, the wave crests and troughs obtained from the numerical simulation are relatively symmetrical, conforming to the basic characteristics of pure wave propagation in theory, indicating that under this condition, the numerical model can simulate the natural propagation pattern of waves well. However, under the combined action of wave and current, the wave crests are clearly wider than the troughs, and the wave height decreases.

[0102] 3. Cross-sectional horizontal velocity verification

[0103] Horizontal velocity at the cross-section, as a key parameter of wave motion, can intuitively and effectively reflect the morphological characteristics and propagation properties of waves. In the data processing stage, the flow velocity data exhibiting a periodic variation pattern within 30 seconds were averaged to extract the horizontal velocity at different times within one cycle (1 second). To more comprehensively verify the accuracy of the model, the horizontal velocities at five representative times—t=0.0s, t=0.25s, t=0.5s, t=0.75s, and t=1.0s—were selected for comparative verification. These five times cover different phases of wave motion and can fully reflect the wave's motion changes within one cycle.

[0104] Figure 5 This paper presents a comparison between simulation results and experimental data of the horizontal velocity at different depths (z) under wave-only action at different times, before and after incorporating the "sponge layer" wave-damping theory. It can be seen that the horizontal velocity changes with depth according to a clear pattern at different times, and the simulation data and experimental data before and after wave-damping are basically consistent in their trends. This indicates that under wave-only action, both the numerical models before and after introducing the wave-damping theory can intuitively reflect the true flow field characteristics.

[0105] Figure 6This figure shows a comparison between simulation results and experimental data for the horizontal velocity at different depths (z) at different times under the combined action of waves and current, before and after incorporating the "sponge layer" wave attenuation theory. As can be observed from the figure, the black "×" symbols representing experimental data are more dispersed, indicating a significantly increased degree of dispersion. The variation of horizontal velocity with depth has also become more complex, differing drastically from the velocity-depth relationship when waves act alone. This is mainly due to the intervention of water flow, which greatly increases the complexity of wave motion, leading to a significant increase in the uncertainty of the results. This also affects the accuracy of the numerical simulation, resulting in increased errors. However, the numerical simulation results after introducing the wave attenuation theory show a relative improvement at the bottom of the tank compared to the results without it.

[0106] 4. Numerical simulations were conducted to verify the flow fields of the ISPH wave-current numerical flume model and the wave-monopile numerical flume model. By comparing the numerical simulation results with experimental data, it was found that the ISPH model with the addition of the "sponge layer" wave attenuation theory can accurately reproduce the flow field of the physical model experiment. To avoid the exponential growth of eddy viscosity and the unavoidable wave attenuation in the standard turbulent closed model, and to further improve the performance and accuracy of the model, the ISPH model with the introduction of wave attenuation theory was coupled with a modified k-ε turbulence model. A gradient correction-dynamic stabilization scheme was adopted to reduce numerical dissipation, and the model was further optimized. The expression of the momentum conservation equation after coupling is as follows:

[0107]

[0108] In the formula, Let be the Reynolds stress tensor.

[0109] By conducting numerical simulation studies and verifications on the hydrodynamic characteristics around marine coral reefs, we can further evaluate the accuracy and reliability of the coupled model in simulating the interaction between coral reef topography and complex marine dynamics.

[0110] Figure 7As shown, the numerical model calculation area is set to be 22m long and 1m high. A wave-generating plate is set at the left end of the model to generate regular waves, with the positive x-direction being the direction of regular wave propagation. A 3m long wave-dissipating zone is set at the right end to effectively reduce wave reflection. The length (l) of the reef flat is 6m, the height (hr) is 0.35m, the slope of the foreshore slope is 1:5, and the distance from the toe of the foreshore slope to the right boundary of the wave-generating plate is 5.05m. The slope of the aft slope is 1:6, and the distance from the toe of the aft slope to the left boundary of the wave-dissipating zone is 3.8m. The wave-dissipating zone is 18.9-21.9m deep. The water depth (h) in the wave-generating zone is 0.45m, and the water depth (hc) at the top of the reef flat is 0.1m. The flow conditions are achieved by setting the flow velocities in the inflow and outflow areas at the bottom of the channel, which can simulate flow conditions with different directions and velocities. The diameter of the particles in the computational domain segmentation was 0.01 m, and the total number of particles was 145215. To ensure the stability of the waves and water flow, the simulation time was set to 100 s. The verification of the numerical model focused on testing three different working conditions: wave action alone, wave and water flow in the same direction (referred to as "wave-current in the same direction"), and wave and water flow in opposite directions (referred to as "wave-current in opposite directions"). The specific parameter values ​​for the verification working conditions are shown in Table 3.

[0111] During the model calculations, the measurement points for wave height and flow velocity were located at the same positions as in the experimental setup. Figure 7 As can be seen, wave height measuring points G1-G16 along the x-direction measure the change in free surface elevation during the simulation, while velocity measuring points L1-L14 measure the change in flow velocity at the mid-depth position of each cross-section. Table 4 shows the exact locations of the wave height and velocity measuring points under the verification condition (with the lower left corner of the numerical flume as the reference zero point). However, the measurement of free surface elevation and mid-depth flow velocity in this model is not limited to these 16 locations; numerical simulation can obtain more comprehensive data on the free surface elevation and flow velocity of the entire flume.

[0112] Table 3 Parameter settings for verification conditions

[0113]

[0114] Table 4. Locations of wave height and flow velocity measuring points.

[0115]

[0116] 5. Verification and Analysis of Wave Propagation and Deformation Characteristics

[0117] In wave characteristic verification analysis, the instantaneous change of free surface elevation and the change of wave height along the reef are two key indicators for evaluating wave propagation and deformation characteristics. Figure 8 , Figure 9 and Figure 10The simulation and experimental results of the free surface elevation (η) time series at six characteristic measuring points are presented under three conditions: wave action alone, wave and current action in the same direction, and wave and current action in opposite directions. The blue solid line represents the simulation results of the improved ISPH model, the black solid dots represent the experimental measurement data from Yao Yu's physical model, and the magenta solid line represents the simulation results of Yao Yu's numerical model.

[0118] Comparative analysis of numerical model data and experimental data reveals that, for most measurement points under the three operating conditions, the instantaneous changes in free surface elevation of the ISPH numerical model show good consistency with the results of the physical model. Although the simulation accuracy is slightly lower at individual locations, the overall agreement is high. Specifically, at the incident wave measurement point (G1) in the nearshore area, the model accurately generated the wave characteristics set in the experiment; at the measurement point (G3) in the foreshore slope area, the model successfully simulated the waveform steepening phenomenon caused by the shallow water effect; at the measurement points (G6 and G11) in the frontal area of ​​the reef flat, the model accurately captured the sawtooth waveform characteristics formed by the wave breaking process; and it also performed well in simulating the transmitted wave height at the central location of the reef flat (G14 and G16).

[0119] Regarding wave height variations along the reef Figure 11 Figures (a), (b), and (c) respectively illustrate the distribution characteristics of wave height (H) along the reef (x direction) under the conditions of wave action alone, wave-current action in the same direction, and wave-current action in opposite directions. The Skill number of the simulation accuracy is also given, and the figures also show schematic diagrams of the interaction between wave-current and coral reef under the three conditions.

[0120] Regarding the instantaneous change in the elevation of the free surface, Figures 12 to 14 The ISPH simulation results for the instantaneous change of u under three operating conditions are presented. Figures 15 to 17 This describes the distribution of turbulent kinetic energy (k) within one wave cycle in the foreshore slope, reef crown, and front area of ​​the reef flat (key observation area) under three working conditions.

[0121] Another embodiment of the present invention is the application of a two-dimensional wave-flow numerical flume construction method based on the ISPH method to add wave-dissipating areas. This method is used for analyzing changes in hydrodynamic characteristics after composite engineering activities in coral reef areas, and / or for analyzing the impact of breakwater construction on the topographic and hydrodynamic environment of coral reefs under the coupling effect of regular waves and currents.

[0122] In analyzing wave propagation characteristics, velocity field distribution, and energy dissipation under different sand pit depths, this study focuses on the influence mechanism of the sand pit depth (hs) on the hydrodynamic environment. Numerical simulation experiments are used to analyze the variation characteristics of wave propagation characteristics, velocity field distribution, and energy dissipation under different sand pit depths. Figure 18 As shown, the method steps are as follows:

[0123] (1) Three different sand pit depths were set up in the two-dimensional wave-current-coral reef numerical flume: hs = 0.15m, 0.25m, and 0.35m, where hs represents the depth. The original topography without sand pits (hs = 0m) was used as the control group. That is, the calculation area of ​​the two-dimensional wave-current-coral reef topography numerical flume model was 22m long and 1m high. A wave-generating plate was set at the left end of the model, and a wave-dissipating zone with a length of 3m was set at the right end. The length l of the reef flat was... The reef is 6m high with a height of hr of 0.35m. The slope of the foreshore slope is 1:5, and the distance from the toe of the foreshore slope to the right boundary of the wave-making plate is 5.05m. The slope of the aft slope is 1:6, and the distance from the toe of the aft slope to the left boundary of the wave-dissipating area is 3.8m. The wave-dissipating area is 18.9-21.9m deep, the water depth h in the wave-making area is 0.45m, and the water depth hc above the reef flat is 0.1m. The flow conditions are achieved by setting the flow velocities in the inflow and outflow areas at the bottom of the channel.

[0124] (2) The sand mining pit adopts a centrally symmetrical trapezoidal cross-section layout. The geometric parameters of the sand mining pit are set as follows: center position coordinate x s = 9.5m, upstream starting position x t =8.0m, downstream termination position x e =11.0m, total horizontal width w s =3m, the front and rear slopes of the sand pit are designed with a gentle slope of 1:3; wave conditions include: regular wave height H = 0.14m, period T = 1.5s, water flow conditions include water flow in the same direction as the wave and in the opposite direction, with initial flow velocities of 0.1m / s and -0.12m / s respectively.

[0125] (3) Set up measuring points with the lower left corner of the numerical water tank as the reference zero point. Set up measuring point G1 on the left side at a distance of 1.65m from the center of the pile. Set up measuring points G2, G3 and G4 in front, on the side and behind the center of the pile at a distance of 0.45m from the center of the pile, respectively.

[0126] (4) Under the combined action of waves and water flow, measure the average flow velocity of the intermediate water depth section of the coral reef topography in sand pits of different depths, and obtain relevant data on the elevation and flow velocity of the free surface of the entire water tank.

[0127] (5) Analyze the acquired data.

[0128] Table 5. Design of Test Conditions for Sand Mining Pit

[0129]

[0130] Figure 20 (a) to Figure 20(d) shows the synchronous vorticity field (voz) and streamline distribution for four sand pit conditions (hs = 0m, hs = 0.15m, 0.25m and 0.35m) under the condition of wave and current in the same direction.

[0131] exist Figure 21 (a) to Figure 21 (d) Under the condition of reverse wave and current, vortex phenomena were also observed in the synchronous vorticity field and streamline distribution of the four sand pit conditions (hs = 0m, hs = 0.15m, 0.25m, and 0.35m), leading to a significant increase in wave height in the sand pit area. However, unlike under the condition of co-current, vortices also exist on the back slope of the reef without sand pit conditions, although the vortex shapes are slightly different. This reduces the difference in the influence of sand pits of different depths on the back wave height, which is consistent with... Figure 19 The distribution characteristics of the medium wave are consistent.

[0132] Figure 22 The distribution of average flow velocity along the reef flat at intermediate water depths is shown under different sand pit depths (hs = 0 m, 0.15 m, 0.25 m, 0.35 m). The horizontal axis represents the spatial position of the measuring point in the x-direction (m), and the vertical axis represents the average flow velocity at the intermediate water depth (m / s).

[0133] Figure 23 Instantaneous velocity field distribution at different sand pit depths Figure 24 The distribution characteristics of turbulent kinetic energy along the reef topography under four sand pit depth conditions (hs = 0m, 0.15m, 0.25m and 0.35m) under the condition of wave-current propagation in the same direction.

[0134] Figure 24 This paper describes the distribution characteristics of turbulent kinetic energy along the reef topography under four different sand pit depth conditions (hs = 0 m, 0.15 m, 0.25 m, and 0.35 m) under the condition of wave-current propagation in the same direction. Under the condition without a sand pit (hs = 0 m), such as... Figure 24 As shown in (a), when waves and currents interact with the foreshore slope, an enhancement of turbulent kinetic energy (k) occurs along the slope surface, and the k value increases with decreasing water depth. When the waves break up with the reef crown, wave energy is converted into turbulent kinetic energy, causing the k value in this area to increase significantly to its peak value. Subsequently, the broken waves and currents continue to propagate along the reef flat, and the k value gradually decreases to 0.006m. 2 / s 2 Due to the significant water level difference between the reef slope and the reef flat, a strong turbulent mixing zone is formed in the area behind the reef flat, resulting in a second sharp increase in the k value, with its influence extending up to 3m.

[0135] Figure 25This illustrates the influence of different pit depths on the distribution of turbulent kinetic energy (k) under conditions of wave and water flow propagation in opposite directions. In the baseline condition without pits, Figure 25 As shown in (a), the complex interaction between waves and the foreshore slope, reef crown, and reverse current results in a large area of ​​high k-values ​​around the reef crown. As the waves continue to propagate along the reef flat after breaking up, the k-value gradually decreases. A comparative analysis of the case including the sand mining pit... Figure 25 (b) to Figure 25 (d) It can be observed that when the depth of the sand pit varies within the range of 0.15-0.35m, the distribution characteristics of the k-value in the foreshore slope and the reef flat area in front of the sand pit remain basically consistent with the no-pit condition. However, a significant k-value suppression effect is observed in the sand pit area, with the k-value almost dropping to 0 throughout the entire pit. This phenomenon may be related to the flow separation and energy dissipation caused by the sand pit. When the wave propagates to the second reef flat area, although the interaction with the slope and reef crown still causes an increase in the k-value, the increase is significantly smaller than that of the first interaction due to the influence of the previous energy dissipation.

[0136] Since turbulence plays a crucial role in maintaining the ecological function of reef areas, the existence of sand pits significantly alters the distribution characteristics of turbulent kinetic energy under wave-current interaction, forming a distinct low-turbulence zone in the pit area. This change may have a significant impact on the marine ecosystem.

[0137] This study analyzes the impact of breakwater construction on the topographic and hydrodynamic environment of coral reefs under the coupling effect of regular waves and currents. The focus is on the influence mechanism of the breakwater location (d / l) on the hydrodynamic environment. Numerical simulations are used to analyze the impact of the breakwater location on the flow field distribution and turbulent kinetic energy changes in the coral reef flat area under two conditions: wave-current in the same direction and wave-current in opposite directions. Triangular block breakwaters are widely used in special marine areas such as coral reef zones due to their good structural stability, adaptability to complex environments, and eco-friendliness. This embodiment simplifies the three-dimensional triangular block structure into a two-dimensional triangular submerged breakwater placed on the coral reef flat. Figure 26 This is a numerical simulation diagram of breakwater construction on a coral reef. Where d is the distance from the reef crown to the centerline of the breakwater, and l is the length of the reef flat. This embodiment designs four breakwater construction scenarios at different locations: d / l = 1 / 6, d / l = 1 / 3, d / l = 1 / 2, and d / l = 2 / 3, with the original topography without a breakwater (d / l = 0) serving as a control group. Simultaneously, the regular wave height H = 0.14 m, period T = 1.5 s, wave-current velocity in the same direction is 0.1 m / s, and wave-current velocity in the same direction is -0.12 m / s. Sufficient simulation time is ensured for each set of experiments to guarantee stable statistical data.

[0138] The specific conditions for the control group were as follows: the computational area of ​​the two-dimensional wave-current-coral reef topography numerical flume model was 22m long and 1m high. A wave-generating plate was set at the left end of the model, and a wave-dissipating zone with a length of 3m was set at the right end. The length l of the reef flat was 6m, the height hr was 0.35m, the slope of the foreshore slope was 1:5, the distance from the toe of the foreshore slope to the right boundary of the wave-generating plate was 5.05m, the slope of the aft slope was 1:6, the distance from the toe of the aft slope to the left boundary of the wave-dissipating zone was 3.8m, the wave-dissipating zone was 18.9-21.9m, the water depth h in the wave-generating zone was 0.45m, the water depth hc above the reef flat was 0.1m, and the flow conditions were achieved by setting the flow velocities in the inflow and outflow areas at the bottom of the flume.

[0139] Figure 27 and Figure 28 The lateral evolution of the average flow velocity at the mid-depth of the reef flat profile and its response characteristics to changes in the breakwater position were compared and analyzed under two typical working conditions: wave-current in the same direction and wave-current in opposite directions.

[0140] Table 6 Comparison of flow velocity variations caused by different breakwater locations

[0141]

[0142] Under reverse wave-current propagation conditions, the impact mechanism of submerged breakwaters on the hydrodynamic environment of reef flats exhibits significantly different characteristics compared to the co-current propagation condition, displaying a more complex interaction. Numerical simulation results show that when waves and currents act in opposite directions, the submerged breakwater structure alters the original wave-current equilibrium, triggering a more pronounced flow field reorganization phenomenon. In the upstream region of the breakwater, due to the mutual cancellation of wave breaking and reverse current, the velocity field exhibits a stabilizing effect, resulting in a significantly lower reverse velocity compared to the unbreakwater condition, as detailed in Table 6. This phenomenon reveals the unique regulatory mechanism of submerged breakwaters on the hydrodynamic environment under reverse wave-current propagation conditions. Furthermore, unlike the homogenization effect under the co-current propagation condition, the velocity changes under reverse conditions exhibit spatial dependence.

[0143] Figure 29 (a) to Figure 29 (e) illustrates the distribution characteristics and evolution of k along the reef flat profile under the condition of wave and current in the same direction, at different deployment locations of the submerged breakwater. The figure shows that compared to the case without a breakwater (d / l=0), the construction of the breakwater will create more obvious turbulence control zones, namely the upstream suppression zone and the downstream enhancement zone. Figure 30 (a) to Figure 30(e) reveals the moderating effect of submersible breakwaters on the reef flat turbulence field at different deployment locations under wave-current reversal conditions. The figure shows that, unlike the wave-current reversal condition, the breakwater exhibits unique bidirectional turbulence suppression characteristics under wave-current reversal conditions. Specifically, the breakwater's presence can both reduce upstream turbulence k and lower downstream turbulence k. Near the apex of the triangular breakwater, there exists a small local turbulence enhancement zone. This pattern suggests that the breakwater crest can be designed with a circular arc shape.

[0144] A systematic study of the impact mechanisms of sand dredging pits and breakwater projects on the hydrodynamic environment of coral reefs revealed that sand dredging pits significantly weaken wave breaking intensity by altering the topography, leading to a general increase in wave height within the pit and downstream, while simultaneously creating a distinct low-turbulence zone that may hinder the exchange of matter within the ecosystem. Breakwaters, on the other hand, exhibited significant nonlinear effects: when waves and currents flowed in the same direction, the overall flow velocity increased by 20%-26%, while when they flowed in opposite directions, the upstream flow velocity decreased by 35%-53%. Regarding turbulence remodeling, under the same-direction conditions, an asymmetric characteristic of weakening upstream and strengthening downstream was observed, while under opposite-direction conditions, a unique pattern of overall suppression with only localized strengthening at the breakwater crest was observed. These findings reveal a complex feedback mechanism between engineering intervention and coral reef structure, providing important scientific basis for regional engineering planning in coral reef areas, and emphasizing the need to consider both hydrodynamic impacts and ecological protection requirements in engineering design.

[0145] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and an explanation of the technical principles employed, and is not intended to limit the scope of the claimed invention, but merely to illustrate preferred embodiments of the invention. Those skilled in the art should understand that the scope of the invention is not limited to the specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A two-dimensional wave-current numerical flume construction method based on the ISPH method adding a wave-breaking region, characterized in that, The ISPH method is combined with the "sponge layer" wave absorbing theory and the modified k-ε turbulence model, including: S1, based on the ISPH method, a damping term is added to the momentum conservation equation in the basic control equation to realize the absorption of waves, and a two-dimensional wave-current numerical tank model with wave absorbing effect is constructed, and the expression is: wherein is the fluid density; is time; is the flow velocity vector; p is the pressure; is the volume force vector per unit mass; is the viscosity coefficient; denotes the total derivative with respect to time; is the divergence operator, represents the damping term, wherein is the absorption intensity, denotes the horizontal coordinate of the position of the particle at this moment, is the mixing function, u is the horizontal flow velocity of the particle at this moment, and the mixing function is expressed as follows: In the formula, represents the horizontal coordinate of the start position of the wave-damping region; represents the horizontal coordinate of the end position of the wave-damping region; S2, verifying the wave-current numerical tank model with wave-absorbing effect built in step S1, the verification of wave-absorbing effect is determined by comparing the wave-absorbing effect of different wave-absorbing intensity The verification numerical tank is 12*1m in size, and is composed of wall particles, wave-making plate particles and water particles. The wave-absorbing area is set to 9.06-11.8m. Ten wave height measuring points are set in the whole water area of the tank to capture the change of free surface elevation of each section with time, and some measuring points are set in the wave-absorbing area. S3, the debugged two-dimensional wave-current numerical tank model with wave absorbing effect is coupled with the modified k-ε turbulence model, and a turbulence eddy viscosity term is added to the momentum conservation equation, and a gradient correction-dynamic stabilization scheme is used to reduce numerical dissipation, and a two-dimensional wave-current numerical tank model with wave absorbing effect is established, and the coupled momentum conservation equation is expressed as: wherein is the Reynolds stress tensor; S4, the accuracy and applicability of the two-dimensional numerical tank model of step S3 are verified by the wave propagation process on the coral profile, the change of wave height along the reef, and the hydrodynamic characteristics of the horizontal flow velocity, and the distribution of turbulent kinetic energy along the reef is given.

2. The two-dimensional wave-curren numerical flume setup method based on ISPH method with added damping zone according to claim 1, wherein, The wave absorbing area of the wave absorbing effect verification numerical tank is set to 1-2 times the wavelength.

3. The method according to claim 1, wherein, The two-dimensional wave-current numerical tank model has a length of 25m, a height of 1.25m, and a water depth of 0.3m, a wave board is arranged at the left end of the numerical tank model, the wave board travels according to the preset wave height and period, a wave absorbing area with a length of 2 times the characteristic wavelength is arranged at the right end, and an inflow and outflow area with a width of 0.2m is arranged on the left and right sides of the bottom wall respectively, the total number of particles in the model is 140,000, the particle segmentation diameter is 0.01m, the cross-section measurement position 14m away from the wave board is selected, the liquid surface is taken as the starting point, a velocity measurement point is arranged every 0.015m in depth, a total of 20 measurement points are arranged, the flow velocity at different depths is measured, and the cross-section average flow velocity is calculated.

4. The method according to claim 1, wherein, The two-dimensional wave-current numerical tank model of step S3 has a calculation area with a length of 22m and a height of 1m, a wave board is arranged at the left end of the model, and a wave absorbing area with a length of 3m is arranged at the right end, the length of the reef flat l is 6m, the height of the reef flat hr is 0.35m, the slope of the front slope of the reef is 1:5, the front slope of the reef is 5.05m away from the right boundary of the wave board, the slope of the back slope of the reef is 1:6, the back slope of the reef is 3.8m away from the left boundary of the wave absorbing area, the wave absorbing area is 18.9-21.9m, the water depth h of the wave area is 0.45m, the water depth hc of the upper part of the reef flat is 0.1m, and the flow condition is realized by setting the flow velocity of the inflow and outflow areas at the bottom of the tank.

5. The method according to claim 4, wherein, The diameter of the segmented particles in the calculation area is 0.01m, the total number of particles is 145,215, the simulation time is set to 100s, and the verification of the numerical model focuses on testing three different working conditions, namely wave alone, wave and current in the same direction, and wave and current in opposite directions. During the model calculation process, the wave height measurement points G1-G16 will measure the free surface elevation change during the simulation process, and the flow velocity measurement points L1-L14 will measure the flow velocity change at the middle water depth position of each cross section.

6. The application of the two-dimensional wave-curren numerical flume construction method based on the ISPH method with added damping zone according to any one of claims 1-5, characterized in that, The application is used for analyzing the change of water dynamic characteristics after the composite engineering activities in the coral reef area, and / or used for analyzing the influence of the breakwater construction on the water dynamic environment of the coral reef topography under the condition of the coupling action of regular waves and water flow.

7. Use according to claim 6, characterized in that, The application is used for analyzing the change of water dynamic characteristics after the composite engineering activities in the coral reef area, including the analysis of the wave propagation characteristics, the flow velocity field distribution and the energy dissipation under the condition of different sand mining pit depths, and the method steps are as follows: (1) three different depth sand mining pit working conditions are set in the wave flow-coral reef two-dimensional numerical flume: hs = 0.15 m, 0.25 m and 0.35 m, hs represents the depth, and the original topography without sand mining pit hs = 0 m is taken as the control group; (2) The sand mining pit is arranged in a center-symmetrical trapezoidal section, and geometric parameters of the sand mining pit are set as follows: a center position coordinate x s = 9.5 m, an upstream starting position x t = 8.0 m, a downstream terminal position x e = 11.0 m, a total horizontal width w s = 3 m, and a 1:3 gentle slope is designed for the front and rear slopes of the sand mining pit; wave conditions include a regular wave height H = 0.14 m and a period T = 1.5 s, and flow conditions include the same direction and the opposite direction of the flow and the wave, and initial flow velocities are 0.1 m / s and-0.12 m / s respectively; (3) the measuring points of the free surface elevation and the flow velocity under the three different depth sand mining pit working conditions are set to be completely consistent with the original coral reef topography without sand mining pit; (4) under the action of waves and water flow, the average flow velocity of the middle water depth section of the coral reef topography under different depth sand mining pits is measured, and the related data of the free surface elevation and the flow velocity of the entire flume are obtained; (5) the obtained data are analyzed.

8. Use according to claim 6, characterized in that, The application is used for analyzing the influence of the breakwater construction on the water dynamic environment of the coral reef topography under the condition of the coupling action of regular waves and water flow, and the method steps are as follows: (1) In the two-dimensional numerical wave tank of wave-coral reef, the three-dimensional triangular block structure breakwater is simplified to two-dimensional triangular shape submerged breakwater, which is set on the coral reef flat. Four positions of breakwater conditions are designed, which are , , and , and the original topography without breakwater is taken as the control group. d represents the distance from the reef crown to the center line of the breakwater, l represents the length of the reef flat, represents the breakwater layout position; (2) the regular wave height H = 0.14 m, the period T = 1.5 s, the water flow velocity in the same direction is 0.1 m / s, the water flow velocity in the opposite direction is-0.12 m / s, the average flow velocity data are counted, and the influence of the breakwater setting position on the average flow velocity spatial distribution characteristics at the middle water depth of the reef flat under the condition of the wave flow interaction is analyzed; (3) Analysis of the wave-dike interaction condition under the wave-dike interaction condition The influence on the spatial distribution characteristics of the turbulent kinetic energy k in the reef flat area.

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