Multi-scale numerical simulation method and system for wave evolution and effect of wave evolution on ocean structure

Abstract

The invention discloses a multi-scale numerical simulation method and system for wave evolution and the effect of the wave evolution on an ocean structure. The method comprises the steps that a high-order Boussinesq equation is solved through a finite difference method, a B-FD sub-model is constructed, a Navier-Stokes equation is solved through a smoothed particle fluid dynamics method, and an NS-SPH sub-model is constructed; the B-FD sub-model and the NS-SPH sub-model are subjected to multi-time-step coupling through a two-way boundary opening method, the wave propagation form of the offshore waves propagating to the offshore and the physical quantity interacting with the offshore structure are obtained, the wave propagation form is used for analyzing the evolution characteristics of the wave surface, and the physical quantity is used for analyzing nonlinear flow caused by the waves. According to the method, the efficiency of large-range wave propagation calculation can be ensured, and high-precision nonlinear simulation of the local wave breaking process is also considered.

Description

Technical Field

[0001] This invention relates to the field of wave evolution technology, specifically to a multi-scale numerical simulation method for wave evolution and its effects on marine structures. Background Technology

[0002] The propagation of waves from the open ocean to the nearshore exhibits complex dynamic characteristics influenced by water depth, topography, and structures. In deeper open waters, waves propagate over a wide area with minimal waveform variation. In shallow nearshore waters, waves are affected by topography and nearshore structures, resulting in nonlinear wave deformation and breaking. Analyzing the complete wave evolution from the open ocean to the nearshore is crucial for the scientific planning and structural safety design of coastal engineering. Existing research methods include field observation, physical model experiments, and numerical simulation. Among these, numerical simulation has become the primary technical approach for studying this problem due to its high controllability and low cost. The NS-SPH model, established by solving the Navier-Stokes equations using the Smoothed Particle Hydrodynamics (SPH) method, can naturally handle large deformations of free surfaces and wave breaking processes. It is suitable for simulating strong nonlinear deformations of nearshore waves in local areas, but its low computational efficiency makes it unsuitable for simulating large-scale wave propagation in offshore areas. The B-FD numerical model, established by solving the higher-order Boussinesq equations using the Finite Difference Method (FDM), can efficiently simulate wave propagation processes in large-scale ocean areas. However, the Boussinesq equations, based on potential flow theory, cannot directly calculate turbulent dissipation and vortex motion caused by wave breaking in nearshore areas.

[0003] The complete wave evolution process from the open ocean to the nearshore involves large-scale, long-term wave propagation and locally strongly nonlinear evolution, making it difficult for a single numerical model to simultaneously meet the requirements of computational efficiency and accuracy. Currently, various coupled models have been proposed, but most rely on open-source or commercial software interfaces, supporting only unidirectional transfer of physical quantities between sub-models at the surface level, and failing to achieve real-time bidirectional exchange of intermediate variables such as pressure and velocity. Furthermore, existing coupled models generally suffer from the following problems:

[0004] (1) The coupled boundary pressure field is unstable and easily causes numerical oscillations;

[0005] (2) It is difficult to guarantee the mass conservation of the coupling region;

[0006] (3) Physical quantities cannot achieve a smooth transition between different models.

[0007] Currently, there is a lack of a highly robust numerical model that can both efficiently simulate large-scale wave propagation and accurately calculate wave deformation and breaking in nearshore areas. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a coupled numerical model for analyzing the complete wave evolution process from the open sea to the nearshore. The coupled model combines the efficiency of the B-FD model in large-scale wave propagation simulation with the advantages of the NS-SPH model in high-precision simulation of locally strong nonlinear waves, providing a scientific and effective technical approach for analyzing the complete wave evolution process from the open sea to the nearshore.

[0009] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0010] A multi-scale numerical simulation method for wave evolution and its effects on marine structures:

[0011] In the computer, based on Fortran programming, the higher-order Boussinesq equations are solved by the finite difference method to construct the B-FD sub-model, and the Navier-Stokes equations are solved by the smoothed particle hydrodynamics method to construct the NS-SPH sub-model.

[0012] Using the two-way open boundary method, the B-FD sub-model and the NS-SPH sub-model are coupled in multiple time steps to obtain the wave propagation morphology of offshore waves to nearshore and the physical quantities of their interaction with nearshore structures. The wave propagation morphology includes wave height, wave shape, and free surface motion state. The physical quantities of the wave interaction with nearshore structures include pressure field, velocity field, density, vorticity field, turbulent motion, and turbulent viscosity field.

[0013] In each time step, the coupling process is as follows: the depth-averaged velocity ū and free surface height calculated by the NS-SPH sub-model are provided as boundary conditions to the B-FD sub-model; in the governing equations of the B-FD sub-model, time t is taken as one time step ∆t. B Calculate up to t n+1 At time; the B-FD sub-model provides the open boundary particles of the NS-SPH sub-model with the free surface elevation, velocity vector u, and pressure field p; the governing equations of the NS-SPH sub-model calculate multiple time steps ∆t. N Until t is reached n+1 time.

[0014] Furthermore, during coupling, the spatial computational domain is divided through the following interface: the leftmost boundary Γ of the NS-SPH sub-model computational domain. O The interface between open boundary particles and relaxed particles Γ I The interface between relaxation particles and computational particles Γ R The interface Γ between the computational domain and the open boundary region in the B-FD sub-model B .

[0015] Furthermore, to ensure mass conservation at the boundary of the NS-SPH sub-model, open boundary particles will be dynamically generated or deleted in the NS-SPH sub-model based on the mass flux.

[0016] Furthermore, the boundary Γ O It is divided into several equally spaced segments, and the height of each segment is set to the particle spacing ∆x. N Any segment S o Its mass flux , where u So and ρ So They represent segments S respectively. o speed, density, n So Indicates from the boundary Γ O The unit normal vector pointing to the NS-SPH computational domain.

[0017] Furthermore, at a time step ∆t N Within, section S o The change in mass flux is expressed as: , where ∆m So S represents the segment within a single time step. o The change in mass.

[0018] Furthermore, when segment S o The cumulative mass flux change Δm So When greater than zero, segment S o The quality will continue to increase, when section S o The cumulative increase in mass flux exceeds the reference mass of a single particle, generating new open boundary particles within the NS-SPH sub-model domain. These new particles are located at a distance Γ from the boundary. O The distance is 0.5∆x N When the cumulative mass flux change Δm So When less than zero, segment S o The quality will continue to decrease when segment S o The absolute value of the cumulative decrease in mass flux is higher than the reference mass of a single particle, so a distance boundary Γ is deleted within the NS-SPH sub-model domain. O Recent open-boundary particles.

[0019] Furthermore, in the B-FD sub-model, the free surface elevation is calculated using the third-order explicit Adams-Bashforth-Moulton scheme:

[0020]

[0021]

[0022]

[0023] Where EZ is an intermediate quantity, the superscript n of the physical quantity indicates the current calculation time step, and the subscript Г B Indicates the boundary Г B At the spatial point location, Г B+1 Indicates the boundary Г B At the position one spatial step forward, ∆x B η represents the spatial step size of the B-FD submodel, h is the water depth, and η is the free surface elevation.

[0024] Furthermore, the governing equations of the B-FD sub-model are:

[0025]

[0026]

[0027] Where η is the free liquid surface elevation, Here, ε is the spatial gradient operator, h is the water depth, and the parameter ε = Parameter μ = h / L L and L represent the characteristic amplitude and wavelength, respectively. Let Λ be the depth-averaged velocity, O represent the order of magnitude of a higher-order small quantity, and Λ be the velocity. 20 Λ 21 Λ 22 Λ 23 Λ 40 Λ 41 All are intermediate values.

[0028] Furthermore, the governing equations of the NS-SPH sub-model are:

[0029]

[0030] Where ρ represents the density of the fluid, Indicates the dynamic viscosity coefficient of a fluid. Here, g is the spatial gradient operator, and g is the gravitational acceleration.

[0031] A multi-scale numerical simulation system for wave evolution and its effects on marine structures includes:

[0032] The B-FD sub-model building module constructs B-FD sub-models based on higher-order Boussinesq equations.

[0033] The NS-SPH sub-model building module constructs NS-SPH sub-models based on the Navier-Stokes equations.

[0034] The coupling module uses a bidirectional open boundary method to couple the B-FD sub-model and the NS-SPH sub-model.

[0035] The beneficial effects of this invention are as follows: This invention proposes a two-way open-boundary method for coupling the B-FD model and the NS-SPH model. The coupling results obtained by this method can be used to analyze the complete evolution process of waves from the open sea to the nearshore, that is, the wave propagation morphology of waves from the open sea to the nearshore and the physical quantities of the interaction between waves and nearshore structures. This coupling method can ensure high efficiency in large-scale wave propagation calculations while also taking into account high-precision nonlinear simulation of local wave breaking processes. Attached Figure Description

[0036] Figure 1 This is a spatial computation region partitioning diagram for coupling the model described in this invention;

[0037] Figure 2 This is a schematic diagram of the open boundary region described in this invention;

[0038] Figure 3 This is a schematic diagram of the calculation process of the coupled SPH model in this invention at one time step;

[0039] Figure 4 This is a schematic diagram of the numerical water tank described in this invention;

[0040] Figure 5(a) shows the pressure distribution at t=0T as described in this invention, as well as a locally enlarged velocity and vorticity distribution diagram;

[0041] Figure 5(b) shows the pressure distribution at t=0.25T as described in this invention, and a locally enlarged velocity and vorticity distribution diagram;

[0042] Figure 5(c) shows the pressure distribution at t=0.5T as described in this invention, as well as a locally enlarged velocity and vorticity distribution diagram;

[0043] Figure 5(d) shows the pressure distribution diagram and the locally enlarged velocity and vorticity distribution diagram at t=0.75T as described in this invention. Detailed Implementation

[0044] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0045] This invention is a multi-scale numerical simulation method for studying the complete wave evolution from the open sea to the nearshore. Its implementation includes three parts: (1) constructing a B-FD sub-model based on the higher-order Boussinesq equation; (2) constructing an NS-SPH sub-model based on the Navier-Stokes equation; and (3) coupling the B-FD sub-model and the NS-SPH sub-model using the bidirectional open boundary method.

[0046] (1) Based on the higher-order Boussinesq equation, construct the B-FD sub-model.

[0047] In computer programming, using the Fortran language, high-order Boussinesq equations are employed as the governing equations for calculating offshore areas.

[0048] (1)

[0049] (2)

[0050] (3)

[0051] (4)

[0052] (5)

[0053] (6)

[0054] (7)

[0055] (8)

[0056] Among them, Λ 20 Λ 21 Λ 22 Λ 23 Λ 40 Λ 41 All are intermediate quantities. η is the elevation of the free liquid surface. The velocity is the depth-averaged velocity, where h is the water depth. For the spatial gradient operator, the subscript t denotes the partial derivative with respect to time, and the parameter ε= μ = h / L L and L are the characteristic amplitude and wavelength, respectively, and the parameters (α1, β1) = (1 / 9, 1 / 945), (α2, β2) = (0.146488, 0.00798359) are given. O represents the order of magnitude of a higher-order small quantity.

[0057] (2) Based on the Navier-Stokes equations, construct the NS-SPH sub-model.

[0058] In computer programming, using the Fortran language, the Navier-Stokes equations in Lagrange form are chosen as the governing equations for calculating nearshore regions.

[0059] (9)

[0060] Among them, ρ, u, p and Let D and Dt represent the fluid density, velocity, pressure, and dynamic viscosity coefficient, respectively; D / Dt represent the time derivative; and g is the acceleration due to gravity.

[0061] The governing equations for the nearshore region can be discretized using the SPH method as follows:

[0062] (10)

[0063] Wherein, subscript i is the particle number, subscript j is the particle number within the support domain of particle i, and r, V, and m represent the position vector, volume, and mass of the fluid particle, respectively. Let c0 be the Hamiltonian operator for particle i, where c0 represents the speed of sound and ρ0 is the reference density (taken as 1000 kg / m³). 3 α takes values ​​in the range [0.01, 0.05], W represents the smoothing kernel function, and l is the kernel radius. The Wendland C2 kernel function is chosen as the smoothing kernel function:

[0064] (11)

[0065] Among them, intermediate quantity , κ=2.0.

[0066] (3) The B-FD sub-model and the NS-SPH sub-model are coupled using the bidirectional open boundary method.

[0067] The model is coupled by partitioning the spatial computational domain as follows: Figure 1 As shown in the diagram, four key interfaces are defined: Г O Γ represents the leftmost boundary of the computational domain of the NS-SPH submodel; I The interface between open-boundary particles and relaxed particles; Γ R Γ represents the interface between the relaxation particle and the computational particle; B This represents the interface between the computational region and the open boundary region in the B-FD sub-model. The open boundaries of the two sub-models are described below.

[0068] The NS-SPH sub-model includes three types of particles: open boundary particles, computational particles, and relaxed particles. The physical quantities of open boundary particles (η, ...) are... The physical quantities (ρ, u, p, r) of the computed particles are obtained by solving the governing equations of the nearshore region, based on the B-FD sub-model. To achieve a smooth transition from open-boundary particles to computed particles, the physical quantity Φ of the relaxed particles is obtained. i (Including velocity vector u, pressure p, and free surface elevation η) The calculation formula is as follows:

[0069] (12)

[0070] Where, Φ i active Φ i inactiveThe values ​​of the corresponding physical quantities are obtained by solving the NS-SPH sub-model and the B-FD sub-model respectively; α i Representing the relaxation function:

[0071] (13)

[0072] in, x i The x-coordinate of the relaxed particle i is represented by x. Г express Figure 1 Middle boundary Г R Horizontal position; L r This represents the length of the transition region, which is equal to the kernel radius of the NS-SPH submodel.

[0073] To ensure mass conservation at the boundary of the NS-SPH sub-model, open boundary particles will be dynamically generated or deleted in the NS-SPH sub-model based on the mass flux.

[0074] A schematic diagram of particle generation is given. Figure 2 In the first process, open boundary Γ O It is divided into several equally spaced segments, and the height of each segment is set to the particle spacing ∆x. N Any segment S o Its mass flux J So It can be represented as:

[0075] (14)

[0076] Among them, u So and ρ So Indicates segment S o Speed ​​and density, n So This represents the unit normal vector pointing from the open boundary to the NS-SPH computational domain.

[0077] Based on mass flux J So At a time step ∆t N Within, section S o The change in mass flux is expressed as:

[0078] (15)

[0079] Where, ∆m So S represents the segment within a single time step. o The change in mass, Δt N This represents the calculation time step.

[0080] like Figure 2 In the second process, when segment S o The cumulative mass Δm So When greater than zero, segment So The quality will continue to increase. For example... Figure 2 In the third process, once segment S o When the cumulative increase in mass exceeds the reference mass m0 of a single particle, a new open-boundary particle will be generated within the NS-SPH sub-model domain, with the new particle located at a distance Γ from the open boundary. O The distance is 0.5∆x N Similarly, when the cumulative mass Δm So When less than zero, segment S o The quality will continue to decrease when segment S o If the absolute value of the cumulative decrease in mass exceeds the reference mass m0 of a single particle, a distance Γ will be deleted within the NS-SPH submodel domain. O Recent open-boundary particles.

[0081] In the B-FD sub-model, the open boundary Γ B The depth-averaged velocity ū at the location was obtained from the NS-SPH submodel, and the free surface elevation η was calculated using the third-order explicit Adams-Bashforth-Moulton scheme.

[0082] (16)

[0083] in:

[0084] (17)

[0085] (18)

[0086] In equations (15) to (18), EZ is an intermediate quantity, the superscripts n and n+1 of the physical quantity represent the current calculation time step and the next calculation time step, respectively, and the subscript Г B and Г B+1 They represent Figure 1 China's open border Г B Spatial point location, Г B At the position one spatial step forward, ∆t B and ∆x B Represent the time step and spatial step of the B-FD sub-model, respectively, and the spatial point Γ. B and Г B+1 The depth-average flow velocity ū and the free surface elevation η at that location were calculated using the NS-SPH sub-model.

[0087] In terms of time, the computation time step ∆t of the B-FD sub-model B Much larger than the time step ∆t of the NS-SPH model NTo ensure computational efficiency, the model coupling employs a multi-time-step algorithm: the NS-SPH sub-model computes multiple time steps within one time step of the B-FD sub-model until the two are synchronized in time. Figure 3 The process of the multi-time-step algorithm for model coupling is demonstrated: First, the depth-averaged velocity ū and free surface height η calculated by the NS-SPH sub-model are provided as boundary conditions to the B-FD sub-model; Second, t in the governing equations of the B-FD sub-model is set to a time step ∆t. B Calculate up to t n+1 The third step involves the B-FD sub-model providing the open boundary particles of the NS-SPH sub-model with information such as the free surface elevation η, velocity vector u, and pressure field p. The fourth step involves the NS-SPH sub-model's governing equations calculating multiple time steps ∆t. N Until t is reached n+1 time.

[0088] This invention selects a typical case of regular waves acting on a trapezoidal submerged breakwater to test the model coupling. The numerical flume is as follows: Figure 4 As shown, the initial water depth h0 = 0.71 m, and the open boundary of the model coupling is located 0.5 m to the left of the slope toe. Figures 5(a), (b), (c), and (d) show the pressure distribution and locally magnified velocity and vorticity distributions during model coupling within one wave period T. It can be seen from the figures that the pressure field in the overall computational domain remains stable without numerical oscillations; in the local area above the submerged breakwater, the wave undergoes significant deformation and breaking, accompanied by an increase in velocity vector and a significant increase in vorticity.

[0089] This application also provides a multi-scale numerical simulation system for wave evolution and its effects on marine structures, including:

[0090] The B-FD sub-model building module constructs B-FD sub-models based on higher-order Boussinesq equations.

[0091] The NS-SPH sub-model building module constructs NS-SPH sub-models based on the Navier-Stokes equations.

[0092] The coupling module uses a bidirectional open boundary method to couple the B-FD sub-model and the NS-SPH sub-model.

[0093] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be performed by instructions, or by instructions controlling related hardware. These instructions can be stored in a computer-readable storage medium and loaded and executed by a processor.

[0094] To this end, embodiments of this application also provide a storage medium storing multiple instructions that can be loaded by a processor to execute the steps in the multi-scale numerical simulation method for wave evolution provided in embodiments of this application. The storage medium may include: read-only memory (ROM), random access memory (RAM), a disk, or an optical disk, etc.

[0095] The embodiments described above are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A multi-scale numerical simulation method of wave evolution and its effect on marine structures, characterized in that: in a computer, based on Fortran language programming, a B-FD sub-model is constructed by solving high-order Boussinesq equations through a finite difference method, and a NS-SPH sub-model is constructed by solving Navier-Stokes equations through a smoothed particle hydrodynamics method; the B-FD sub-model and the NS-SPH sub-model are coupled through a two-way open boundary method to obtain wave propagation patterns from the open sea to the near shore and physical quantities of interaction with near-shore structures, wherein the wave propagation patterns include wave height, wave shape, and free surface movement state, and the physical quantities of interaction between the wave and the near-shore structures include pressure field, velocity field, density, vorticity field, turbulent motion, and turbulent viscosity field; to ensure mass conservation at the boundary of the NS-SPH sub-model, open boundary particles are dynamically generated or deleted in the NS-SPH sub-model according to mass flux. 10.A system for implementing the multi-scale numerical simulation method of wave evolution and its effect on marine structures according to any one of claims 1-9, comprising: a B-FD sub-model construction module for constructing a B-FD sub-model based on high-order Boussinesq equations; a NS-SPH sub-model construction module for constructing a NS-SPH sub-model based on Navier-Stokes equations; and a coupling module for coupling the B-FD sub-model and the NS-SPH sub-model through a two-way open boundary method. ​ In each time step, the specific process of coupling is: the depth-averaged velocity ū and the free surface height calculated by the NS-SPH sub-model are provided as boundary conditions to the B-FD sub-model; in the control equation of the B-FD sub-model, the time t takes a time step ∆t B The calculation is until t n+1 ; the B-FD sub-model provides the free surface elevation, the velocity vector u and the pressure field p to the open boundary particles of the NS-SPH sub-model; the control equation of the NS-SPH sub-model calculates a plurality of time steps ∆t N until t n+1 is reached.

2. The multi-scale numerical simulation method of wave evolution according to claim 1, characterized in that, When coupled, the spatial computational domain is divided by the following interfaces: the leftmost boundary of the NS-SPH submodel computational domain Γ O , the interface between open boundary particles and relaxation particles Γ I , the interface between relaxation particles and computational particles Γ R , the interface between the computational region and the open boundary region in the B-FD submodel Γ B .

3. The multi-scale numerical simulation method of wave evolution and its effects on marine structures according to claim 2, characterized in that, ​ 4. The multi-scale numerical simulation method of wave evolution and its effects on marine structures according to claim 3, characterized in that, boundary Γ O divided into several equidistant sections, each section is set to particle spacing Δx N , any section S o , mass flux , where u So and ρ So respectively represent the velocity, density of section S o , n So represent the unit normal vector from the boundary Γ O pointing to the NS-SPH calculation domain.

5. The multi-scale numerical simulation method of wave evolution and its effects on marine structures according to claim 4, characterized in that, At a time step At N The change in mass flux of a section S o is expressed as: where Δm So represents the change in mass of a section S o at a single time step.

6. The multi-scale numerical simulation method of wave evolution and its effects on marine structures according to claim 5, characterized in that, When the cumulative mass flux change amount Am o of the section S So is greater than zero, the mass of the section S o will continue to increase, and when the cumulative increased mass flux change amount of the section S o is greater than the reference mass of a single particle, a new open boundary particle is generated within the NS-SPH sub-model domain, and the distance of the new particle from the boundary Г O is 0.5∆x N ; when the cumulative mass flux change amount Am So is less than zero, the mass of the section S o will continue to decrease, and when the absolute value of the cumulative decreased mass flux change amount of the section S o is higher than the reference mass of a single particle, an open boundary particle closest to the boundary Г O is deleted within the NS-SPH sub-model domain.

7. The multi-scale numerical simulation method of wave evolution and its impact on marine structures according to claim 2, characterized in that, In the B-FD sub-model, the free surface elevation is calculated using the third-order explicit Adams-Bashforth-Moulton scheme: , , where EZ is the intermediate quantity, the superscript n of the physical quantity denotes the current calculation time step, the subscript Г B denotes the spatial point position at the boundary Г B , and Г B+1 denotes the position one spatial step forward of the boundary Г B , and Δx B denotes the spatial step of the B-FD sub-model, h is the water depth, and η is the free surface elevation.

8. The multi-scale numerical simulation method of wave evolution and its impact on marine structures according to claim 1, characterized in that, The control equation of the B-FD sub-model is: , where η is the free surface elevation, is the spatial gradient operator, h is the water depth, and parameters ε , μ = h / L, and L are the characteristic wave amplitude and wavelength, is the depth-averaged velocity, and O represents the order of magnitude of the higher-order small quantity, Λ 20 , Λ 21 , Λ 22 , Λ 23 , Λ 40 , Λ 41 are intermediate quantities.

9. The multi-scale numerical simulation method of wave evolution and its impact on marine structures according to claim 1, characterized in that, The control equation of the NS-SPH sub-model is: wherein p represents the density of the fluid, represents the dynamic viscosity coefficient of the fluid, is a spatial gradient operator, and g is the acceleration of gravity. ​ ​ ​ ​

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