Wave environment numerical simulation method based on gravity water wave solution

Abstract

The invention provides a wave environment numerical simulation method based on a gravity water wave solution, and the method comprises the steps: constructing a fluctuation generation quantity source item based on the gravity water wave solution, and obtaining a plurality of key parameters of the fluctuation generation quantity source item in combination with a discrete wave spectrum; a basic control equation of a computational domain is established based on Navier-Stokes, a fluctuation quantity generation source item and a wave absorption source item are respectively introduced into equations corresponding to a wave generation area and a wave absorption area, and accurate wave environment numerical simulation can be realized through solving. According to the method, the load range of wave action can be effectively widened, so that the method is suitable for generation of large and steep waves, has high numerical wave generation robustness, and is beneficial to evaluation of load and safety margin of ocean structures.

Description

Technical Field

[0001] The present invention belongs to the technical field of computational fluid dynamics, and in particular relates to a wave environment numerical simulation method based on gravity water wave solution. Background Art

[0002] Currently, the simulation of complex wave environments plays a crucial role in the hydrodynamic performance assessment of marine engineering structures and represents one of the current challenges in this field. Existing wave simulation methods are primarily categorized into boundary wave generation and source term wave generation. The former generates waves by imposing waveform conditions at the computational domain boundary. While this method maintains the theoretical morphology of the incident wave, it is susceptible to numerical reflection interference when simulating high and steep waves, and its simulation accuracy for strong nonlinear phenomena such as breaking waves is limited. The latter method generates waves by introducing artificial source terms into the governing equations. While this can alleviate boundary constraint issues, the source term parameters are highly dependent on engineering experience, leading to phase distortion and abnormal energy accumulation in complex wave conditions. These two methods suffer from significant issues, such as insufficient representation of nonlinear effects and a disconnect between modeling and actual physical mechanisms. Furthermore, the complex parameter adjustment process during execution of these methods leads to low modeling efficiency and limited adaptability. Therefore, providing a wave simulation method that is more compatible with actual physical mechanisms and more accurate and reliable is a pressing technical challenge in this field. Summary of the Invention

[0003] In view of this, and in response to the technical problems existing in this field, the present invention provides a wave environment numerical simulation method based on gravity water wave solution, which specifically includes the following steps:

[0004] Step 1: Set the computational domain, grid cells, boundary conditions, initial conditions, and computational physical time range according to the wave height and wavelength to be generated, and set the wave-generating area, wave-free development area, and wave-breaking area.

[0005] Step 2: Construct a wave momentum source term based on the partial derivatives of the regular wave velocity potential φ of gravity waves at finite depth with respect to space and time, and solve the unknown quantities in the wave momentum source term including amplitude, angular frequency, wave number, wave direction and phase according to the wave spectrum of the wave to be generated;

[0006] Step 3: Add the constructed wave source term to the Navier-Stokes equation in the wave-making zone and solve the equation to obtain the velocity field in the wave-making zone; directly solve the Navier-Stokes equation for the wave free development zone to obtain the corresponding velocity field; add the wave-breaking source term to the Navier-Stokes equation in the wave-breaking zone and solve the equation to obtain the velocity field in the wave-breaking zone;

[0007] Step 4: Capture the wave interface by calculating the fluid volume fraction (VOF), and use the computational domain velocity field obtained in step 3 to solve the fluid volume transport equation to reconstruct the wave interface for the next time step;

[0008] Step 5: Output the wave environment numerical simulation results according to the calculation physical time set in step 1, or return to step 2 and repeat each step.

[0009] Furthermore, the regular wave velocity potential φ of the finite depth gravity wave in the xyz coordinate system used in step 2 is as follows:

[0010]

[0011] Where a is the wave amplitude, ω is the wave angular frequency, k is the wave number, d is the water depth, z is the height coordinate, 2π / k is the wavelength, θ is the angle between the wave propagation direction and the x direction, ε is the wave phase, and t is time;

[0012] For the random waves set, their velocity potential is regarded as the linear superposition of the following regular wave velocity potentials:

[0013]

[0014] Among them, the wave has M frequency components ω and wave number components k, has N different propagation directions θ, and has M×N wave amplitudes a and phases ε;

[0015] Taking the partial derivative of the above velocity potential twice with respect to space and time, we can get the wave-making momentum source term f w as follows:

[0016]

[0017] Where g is the acceleration due to gravity; amplitude a is mn , angular frequency ω m , wave number k m , wave direction θ n and the phase ε mn All are unknown quantities;

[0018] Where, the angular frequency ω m , wave direction θ n and volatility Specifically based on the discrete wave spectrum S(ω m ,θ n ) Get; wave number k m Using dispersion relations: Get; Phase ε mn Take a random number in the range of 0 to 2π.

[0019] Furthermore, the Navier-Stokes equations used in step 3 include the continuity equation and the momentum equation, and the specific form is as follows:

[0020]

[0021] Where ρ represents the fluid density, v represents the fluid velocity vector, g is the gravitational acceleration vector, and μ is the dynamic viscosity of the fluid;

[0022] For the wave-generating region, the fluid is considered to be incompressible and the wave-generating momentum source term is added to the momentum equation, so that the Navier-Stokes equations are transformed into the following form:

[0023]

[0024] Where, ρ m is the density of the mixed fluid, μ m is the dynamic viscosity coefficient of the mixed phase, which can be obtained by weighting the volume fractions of the gas and liquid phases:

[0025] ρ m =ρ w α w +ρ a α a

[0026] μ m =μ w μ w +μ a μ a

[0027] u and p are velocity and pressure, respectively, σ is the surface tension coefficient, k is the local curvature of the gas-liquid interface, m is the normal vector of the gas-liquid interface, δ S is the Dirac function of the gas-liquid interface, g is the acceleration due to gravity;

[0028] f is the wave-making momentum source term f w For the free development zone, f = 0; for the wave-breaking zone, based on the consideration of avoiding the influence of the exit reflection wave and ensuring the wave-breaking effect and efficiency, f is set to the following wave-breaking source term f d :

[0029]

[0030] Where x in and x out are the x-coordinate values ​​of the front and tail ends of the clipping band, respectively, and n and C1 are constants;

[0031] A two-step projection method is specifically used to solve the Navier-Stokes equations corresponding to the wave-making region, the free development region and the wave-breaking region.

[0032] Furthermore, in step 4, the following fluid volume fraction transport equation is used to reconstruct the wave interface of the next time step:

[0033]

[0034] Where u is the velocity field, and C is the liquid volume fraction of the grid unit. The finite volume method is used to numerically solve C, and the wave interface is characterized by the isosurface of C.

[0035] Furthermore, in step 5, the processing is performed according to one of the following two situations based on the set calculation physical time:

[0036] Case 1: If the numerical wave generation time is greater than or equal to the calculation physical time set in step 1, the wave environment numerical simulation based on the gravity water wave solution is terminated, and the wave environment numerical simulation results are output.

[0037] Case 2: If the numerical wave generation time is less than the calculation physical time set in step 1, return to step 2.

[0038] After completing steps one to five and outputting the corresponding numerical simulation results of complex wave environments, they can be applied to the generation of larger and steeper waves.

[0039] The wave environment numerical simulation method based on gravity water wave solution provided by the present invention constructs a wave-making momentum source term based on the gravity water wave solution and obtains multiple key parameters of the wave-making momentum source term by combining it with the discrete wave spectrum. The basic control equation of the computational domain is established based on Navier-Stokes, and the wave-making momentum source term and the wave-breaking source term are introduced into the equations corresponding to the wave-making zone and the wave-breaking zone. By solving the equations, a more accurate wave environment numerical simulation can be achieved. The method of the present invention can effectively broaden the load range of wave action, and is therefore suitable for the generation of larger and steeper waves. It also has high numerical wave-making robustness, which is beneficial for the assessment of loads and safety margins of marine structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A flow chart of the method provided by the present invention;

[0041] Figure 2 Schematic diagram of the wave numerical pool calculation domain in an embodiment of the present invention;

[0042] Figure 3 The calculation process of the wave-making momentum source term and its parameters in the method provided by the present invention;

[0043] Figure 4 This is the isosurface result of wave simulation in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0045] The numerical simulation method of wave environment based on gravity water wave solution provided by the present invention is as follows: Figure 1 As shown, the specific steps include:

[0046] Step 1: Set the computational domain, grid cells, boundary conditions, initial conditions, and computational physical time range according to the wave height and wavelength to be generated, and set the wave-generating area, wave-free development area, and wave-breaking area.

[0047] Step 2: Construct a wave momentum source term based on the partial derivatives of the regular wave velocity potential φ of gravity waves at finite depth with respect to space and time, and solve the unknown quantities in the wave momentum source term including amplitude, angular frequency, wave number, wave direction and phase according to the wave spectrum of the wave to be generated;

[0048] Step 3: Add the constructed wave source term to the Navier-Stokes equation in the wave-making zone and solve the equation to obtain the velocity field in the wave-making zone; directly solve the Navier-Stokes equation for the wave free development zone to obtain the corresponding velocity field; add the wave-breaking source term to the Navier-Stokes equation in the wave-breaking zone and solve the equation to obtain the velocity field in the wave-breaking zone;

[0049] Step 4: Capture the wave interface by calculating the fluid volume fraction (VOF), and use the computational domain velocity field obtained in step 3 to solve the fluid volume transport equation to reconstruct the wave interface for the next time step;

[0050] Step 5: Output the wave environment numerical simulation results according to the calculation physical time set in step 1, or return to step 2 and repeat each step.

[0051] In a preferred embodiment of the present invention, a wave spectrum with a significant wave height of 4 m and a wavelength of about λ corresponding to the peak frequency of the wave spectrum is generated. p =50m unidirectional random wave, set the calculation domain as Figure 2 As shown, the total length of the computational domain is 3λ p =150m, height is 0.4λ p =20m, width 0.02λ p =1m; set the left and right end faces as solid walls, set the other four faces as free slip boundaries, specify the pressure at the free surface to be 101325Pa, and specify the initial water depth to be d=0.22λ p=11m, set the total calculation time to 50s, set the time step to 0.02s; set the calculation domain flow field and span grid scale Δx = Δy = 1 meter according to the wave wavelength and wave height, and set the vertical grid scale Δz = 0.1333m. In addition, the gravity is 9.8m / s 2 , the density of water is 1000kg / m 3 , the density of air is 1.25kg / m 3 The wave-making area L is divided along the length of the computational domain. g =50m, free development area L e =50m, wave-breaking zone range L d =50m.

[0052] In this embodiment, after constructing the wave momentum source term using the regular wave velocity potential of gravity waves with finite depth in step 2, the JONSWAP wave spectrum S0 is specifically used to calculate the unknown parameters, considering a single propagation direction, i.e., θ n ≡0, based on the equal energy method, the wave spectrum is discretized into M = 200 frequency ranges, each frequency range satisfies like Figure 3 As shown, it is ensured that the amplitude corresponding to each frequency range is the same, and the frequency ω m (m = 1 ~ 200) Take the midpoint of each frequency range and calculate the wave number k corresponding to each frequency component through the dispersion relation and water depth d m , ε m (m=1~200) Generate pseudo-random numbers in 0~2π, and set θ n 、ω m 、k m and ε m Substitute into the wave-making source term expression to calculate the complete wave-making momentum source term f w .

[0053] The process of solving the Navier-Stokes equations using the finite difference method and the two-step projection method in step 3 includes:

[0054] First, the Navier-Stokes equations without the pressure term are solved by difference. The difference schemes for the time term, convection term, and diffusion term are first-order backward difference, second-order upwind difference, and second-order central difference, respectively. Surface tension is solved based on the continuous force surface tension model to obtain an estimated velocity. Secondly, the pressure at the next time step is solved based on the pressure Poisson equation. The obtained pressure is substituted into the Navier-Stokes equations with the pressure term to obtain the velocity field at the next time step. Following the same process distribution as above, the velocity field results for the wave-generating, free-development, and wave-breaking zones are obtained.

[0055] In step 4, the velocity field information obtained in step 3 is specifically used. Based on the fluid volume fraction transport equation, the finite volume method is used for discretization. Considering the volume fraction change within the hexahedral unit and the volume fraction transport balance on the six faces, an algebraic expression is established to solve the volume fraction field of the next time step.

[0056] In step 5, the calculation physical time of the wave simulation is handled in one of the following two ways:

[0057] Case 1: If the numerical wave generation time t w If the calculation time is greater than or equal to the physical calculation time set in step 1, 50s, the wave environment numerical simulation based on the gravity water wave solution is terminated, and the wave environment numerical simulation results are output.

[0058] Case 2: If the numerical wave generation time t w If it is less than the physical calculation time of 50s set in step 1, return to step 2.

[0059] For the generated liquid volume fraction field results, Tecplot is used for post-processing, and the liquid volume fraction isosurface C = 0.5 is taken, as shown in Figure 4 In specific implementation, a solver can be written in Fortran language to implement the entire solution process.

[0060] After completing steps one to five and outputting the corresponding numerical simulation results of complex wave environments, they can be applied to the generation of larger and steeper waves, effectively broadening the simulation range of wave loads, facilitating the load and safety margin assessment of marine structures, and improving design reliability.

[0061] It should be understood that the size of the serial numbers of the steps in the embodiment of the present invention does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention.

[0062] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A numerical simulation method for wave environment based on gravity water wave solution, characterized by: The specific steps include: Step 1: Set the computational domain, grid cells, boundary conditions, initial conditions, and computational physical time range according to the wave height and wavelength to be generated, and set the wave-generating area, wave-free development area, and wave-breaking area. Step 2: Construct a wave momentum source term based on the partial derivatives of the regular wave velocity potential φ of gravity waves at finite depth with respect to space and time, and solve the unknown quantities of the wave momentum source term including amplitude, angular frequency, wave number, wave direction and phase for the wave spectrum of the wave to be generated; Step 3: Add the constructed wave source term to the Navier-Stokes equation in the wave-making zone and solve the equation to obtain the velocity field in the wave-making zone; directly solve the Navier-Stokes equation for the wave free development zone to obtain the corresponding velocity field; add the wave-breaking source term to the Navier-Stokes equation in the wave-breaking zone and solve the equation to obtain the velocity field in the wave-breaking zone; Step 4: Capture the wave interface by calculating the fluid volume fraction, and use the computational domain velocity field obtained in step 3 to solve the fluid volume transport equation to reconstruct the wave interface for the next time step; Step 5: Output the wave environment numerical simulation results according to the calculation physical time set in step 1, or return to step 2 and repeat each step.

2. The method according to claim 1, wherein: The regular wave velocity potential φ of the finite depth gravity wave in the xyz coordinate system used in step 2 is as follows: Where a is the wave amplitude, ω is the wave angular frequency, k is the wave number, d is the water depth, z is the height coordinate, 2π / k is the wavelength, θ is the angle between the wave propagation direction and the x direction, ε is the wave phase, and t is time; For the random waves set, their velocity potential is regarded as the linear superposition of the following regular wave velocity potentials: Among them, the wave has M frequency components ω and wave number components k, has N different propagation directions θ, and has M×N wave amplitudes a and phases ε; Taking the partial derivative of the above velocity potential twice with respect to space and time, we can get the wave-making momentum source term f w as follows: Where g is the acceleration due to gravity; amplitude a is mn , angular frequency ω m , wave number k m , wave direction θ n and the phase ε mn All are unknown quantities; Where, the angular frequency ω m , wave direction θ n and volatility Specifically based on the discrete wave spectrum S(ω m ,θ n ) Get; wave number k m Using dispersion relations: Get; Phase ε mn Take a random number in the range of 0 to 2π.

3. The method according to claim 1, wherein: The Navier-Stokes equations used in step 3 include the continuity equation and the momentum equation, and the specific form is as follows: Where ρ represents the fluid density, v represents the fluid velocity vector, g is the gravity acceleration vector, μ is the dynamic viscosity of the fluid, represents the gradient; For the wave-generating region, the fluid is considered to be incompressible and the wave-generating momentum source term is added to the momentum equation, so that the Navier-Stokes equations are transformed into the following form: Where, ρ m is the density of the mixed fluid, μ m is the dynamic viscosity coefficient of the mixed phase, which can be obtained by weighting the volume fractions of the gas and liquid phases: r m =ρ w a w +r a a a m m =μ w m w +m a m a u and p are velocity and pressure, respectively, σ is the surface tension coefficient, k is the local curvature of the gas-liquid interface, m is the normal vector of the gas-liquid interface, δ S is the Dirac function of the gas-liquid interface, g is the acceleration due to gravity; f is the wave-making momentum source term f w For the free development zone, f = 0; for the wave-breaking zone, based on the consideration of avoiding the influence of the exit reflection wave and ensuring the wave-breaking effect and efficiency, f is set to the following wave-breaking source term f d : Where x in and x out are the x-coordinate values ​​of the front and tail ends of the clipping band, respectively, and n and C1 are constants; A two-step projection method is specifically used to solve the Navier-Stokes equations corresponding to the wave-making region, the free development region and the wave-breaking region.

4. The method according to claim 1, wherein: In step 4, the following fluid volume fraction transport equation is used to reconstruct the wave interface of the next time step: Where u is the velocity field, and C is the liquid volume fraction of the grid unit. The finite volume method is used to numerically solve C, and the wave interface is characterized by the isosurface of C.

5. The method according to claim 1, wherein: In step 5, the processing is performed according to one of the following two situations based on the set calculation physical time: Case 1: If the numerical wave generation time is greater than or equal to the calculation physical time set in step 1, the wave environment numerical simulation based on the gravity water wave solution is terminated, and the wave environment numerical simulation results are output. Case 2: If the numerical wave generation time is less than the calculation physical time set in step 1, return to step 2.

Images