Meshless numerical method and device for analyzing the effect of fluid on porous media marine structures

Abstract

This invention provides a meshless numerical method and apparatus for analyzing the effects of fluids on porous marine structures. It establishes a model simulating the effects of fluids on porous marine structures, arranging fluid particles and porous marine structure particles. The continuity and momentum equations of the large eddy simulation smooth particle fluid dynamics model are integrated to obtain the position, velocity, pressure, and density of all fluid particles. Based on the volume fraction, position, velocity, pressure, and density, the energy dissipation power of the diffusion term, the energy dissipation power of the viscous term, the energy change power caused by fluid compression in the porous marine structure, and the energy dissipation power due to drag in the porous marine structure are calculated in the energy conservation equation. These are then integrated, and the mechanical energy and internal energy of all fluid particles are obtained using the expressions for mechanical energy and internal energy in the energy conservation equation. This invention can accurately analyze the energy dissipation mechanism of fluid effects on porous marine structures.

Description

Technical Field

[0001] This invention belongs to the technical field, specifically relating to a meshless numerical method and apparatus for analyzing the effects of fluids on porous marine structures. Background Technology

[0002] To develop and utilize marine space resources and protect coastlines, humans have constructed numerous marine structures in nearshore areas, including revetments, seawalls, and breakwaters. The hydrodynamic characteristics of these structures under wave action have always been a crucial concern for engineers. In recent years, with the continuous maturation of computational fluid dynamics numerical simulation technology, numerical simulation has gradually become an effective means of analyzing the interaction between waves and marine structures.

[0003] Smoothed Particle Hydrodynamics (SPH) is an emerging Lagrangian-form meshless particle method initially used to solve astrophysical problems in three-dimensional open spaces, but it has now been applied to marine engineering problems. Compared to traditional mesh-based numerical algorithms, the SPH method, due to its Lagrangian nature, ensures energy conservation within the system, allowing direct calculation of wave energy dissipation by marine structures. Rockfill porous media breakwaters / revetments are common marine engineering structures; due to their porosity, these structures effectively dissipate wave energy. Simulating and analyzing the interaction between waves and rockfill porous media breakwaters / revetments hinges on a reasonable assessment of wave energy dissipation in porous structures. Currently, the energy dissipation coefficient of rockfill breakwaters / revetments is mainly calculated using transmission and reflection coefficients; however, this generalized approach fails to clearly define the energy dissipation mechanism of rockfill structures. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a meshless numerical method and apparatus for analyzing the effects of fluids on porous marine structures. It applies mixing theory to the Large Eddy Simulation (SPH) model and establishes the energy conservation equation for the model to calculate the mechanical energy and internal energy of fluid particles.

[0005] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0006] A meshless numerical method for analyzing the effects of fluids on porous marine structures is as follows:

[0007] A model simulating the effect of fluid on porous media marine structures was established, and fluid particles and porous media marine structure particles were arranged.

[0008] The continuity equation and momentum equation of the large eddy simulation (SPH) model are integrated to obtain the position, velocity, pressure and density of all fluid particles;

[0009] Based on the volume fraction, position, velocity, pressure, and density of all fluid particles, the energy dissipation power of the diffusion term, the energy dissipation power of the viscous term, the energy change power caused by the compression of fluid in porous media marine structures, and the energy dissipation power of the drag in porous media marine structures in the energy conservation equation of the large eddy simulation SPH model are calculated and integrated.

[0010] Using the expressions for mechanical energy and internal energy in the energy conservation equation, the mechanical energy and internal energy of all fluid particles are obtained; the energy conservation equation is:

[0011]

[0012] Where: ε M ε represents the mechanical energy of a fluid particle. C P represents the internal energy of a fluid particle. δ P represents the energy dissipated by the diffusion term. υ This represents the energy dissipated by the viscous term. P represents the power of the energy change caused by the compression of fluid in a porous marine structure. R This represents the energy dissipation power due to drag in porous media marine structures, and:

[0013]

[0014]

[0015]

[0016]

[0017] Where: fluid represents fluid, p i ρ represents the pressure exerted by fluid particles. i V represents the density of fluid particles. i The parameter represents the volume of fluid particle i. W(r) is the geometric mean of the magnitudes of the diffusion terms for fluid particles i and j. i -r j ) represents the smoothing kernel function between fluid particle i and fluid particle j, r i r represents the position vector of fluid particle i. j V represents the position vector of fluid particle j. j Let j represent the volume of fluid particle j. This represents the volume fraction of fluid particle i. Represents volume fraction With laminar flow viscosity coefficient υ i The product; for and The geometric mean Represents the volume fraction of fluid particle i Its turbulent kinematic viscosity coefficient The product, Represents the volume fraction of fluid particles j Its turbulent kinematic viscosity coefficient The product of π ij u is the viscous term in the momentum equation. i u represents the velocity of fluid particle i. j This represents the velocity of fluid particle j. Represents the Hamiltonian operator. r represents the fluid volume fraction of particles in porous marine structures. a V represents the position vector of particles in porous media marine structures. a R represents the volume of particles in porous marine structures. i W(r) represents the resistance of the porous medium to fluid particle i. i -r a ) represents the smooth kernel function between fluid particle i and porous media marine structure particle a.

[0018] Furthermore, the continuity equation and momentum equation of the large eddy simulation SPH model are as follows:

[0019]

[0020]

[0021] Where: m j D represents the mass of fluid particle j. ij Let p represent the diffusion term, g represent the gravitational acceleration of the fluid, and p represent the diffusion term. j This represents the pressure of fluid particle j.

[0022] Furthermore, the volume fraction of the fluid particles is calculated using the following formula:

[0023] Furthermore, the volumes of the fluid particles and the porous media marine structure particles were calculated using the initial spacing of the fluid particles and the spacing of the porous media marine structure particles, respectively.

[0024] Furthermore, the viscous term in the momentum equation is:

[0025]

[0026] Where: n is the dimension of the fluid's effect on the porous media marine structure, and h is the smooth length.

[0027] Furthermore, the mechanical energy εM =ε K +ε P ,kinetic energy Potential energy g represents the acceleration due to gravity of the fluid.

[0028] Furthermore, when the fluid is water, the model for simulating the effect of the fluid on porous marine structures is a numerical wave tank.

[0029] A meshless numerical apparatus for analyzing the effects of fluids on porous marine structures, comprising:

[0030] The model building module is used to build models that simulate the effects of fluids on porous marine structures.

[0031] The fluid particle energy change rate calculation module calculates the energy change rate of fluid particles based on the volume fraction, position, velocity, pressure, and density of all fluid particles. This includes the energy dissipation power of the diffusion term, the energy dissipation power of the viscous term, the energy change power caused by the compression of fluid in porous media marine structures, and the energy dissipation power of the drag in porous media marine structures, and then integrates these values.

[0032] The fluid particle energy calculation module integrates the formula for calculating the rate of change of fluid particle energy, and then calculates the mechanical energy and internal energy of the fluid particle.

[0033] An electronic device, comprising a memory and a processor;

[0034] The memory is used to store computer programs;

[0035] The processor is used to execute the computer program and, in executing the computer program, to implement the above-described meshless numerical method for analyzing the effects of fluids on porous marine structures.

[0036] A storage medium storing a computer program that, when executed by a processor, causes the processor to perform the aforementioned meshless numerical method for analyzing the effects of fluids on porous marine structures.

[0037] The beneficial effects of this invention are as follows:

[0038] This invention applies hybridization theory to the Large Eddy Simulation (SPH) model and establishes its energy conservation equation. By integrating the continuity and momentum equations of the SPH model, the position, velocity, pressure, and density of all fluid particles are obtained. Based on these values, the energy dissipation power of the diffusion term, the energy dissipation power of the viscous term, the energy change power caused by fluid compression in porous marine structures, and the energy dissipation power due to drag in porous marine structures are calculated and integrated. Using the expressions for mechanical energy and internal energy in the energy conservation equation, the mechanical energy and internal energy of all fluid particles are obtained. This method accurately analyzes the energy dissipation mechanism of fluid action on porous marine structures. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the numerical wave flume established according to the present invention. Detailed Implementation

[0040] 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.

[0041] This invention utilizes the hybrid theory Navier-Stokes equations to describe the motion of fluids inside and outside porous marine structures:

[0042]

[0043]

[0044] Among them: ρ, u, p, g, τ, R represents the fluid's density, velocity, pressure, gravitational acceleration, shear stress tensor, fluid volume fraction, and the resistance of the porous medium, respectively. Represents the Hamiltonian operator;

[0045] Based on the large eddy simulation SPH (δ-LES-SPH) model, the continuity equation and momentum equation are obtained by discretizing equations (1) and (2), respectively:

[0046]

[0047]

[0048] Where i and j represent fluid particles, and a represents porous media marine structure particles; ρ i u i p i , r i R iLet m represent the density, velocity, pressure, volume fraction, position vector, and resistance of the porous medium to fluid particle i, respectively; j u j r j V j p j Let p represent the mass, velocity, position vector, volume, and pressure of fluid particle j, respectively; and let p represent the pressure of fluid particle i. i =c 2 (ρ i -ρ0), c represents the speed of sound, and ρ0 represents the initial density of the fluid. In this embodiment, water is selected as the fluid, and its initial density is taken as 1000 kg / m³. 3 , r represents the fluid volume fraction of particles in porous marine structures. a V represents the position vector of particles in porous media marine structures. a This represents the volume of particles in porous marine structures.

[0049] W(r i -r j ) represents the smoothing kernel function between fluid particles i and j, which is calculated by the following formula:

[0050]

[0051] Where: γ is the cutoff radius coefficient, usually γ = 3; h is the smoothing length, for the Gaussian smoothing kernel function h = 1.3dx, dx is the initial spacing between particles;

[0052] W(r i -r a ) represents the smooth kernel function between fluid particle i and porous media marine structure particle a. Its calculation formula is the same as that of equation (5), except that j in equation (5) is replaced with a.

[0053] D ij The diffusion term can be calculated using the following formula:

[0054]

[0055] In the formula It is the regularized density gradient of fluid particle i:

[0056]

[0057]

[0058] L represents the derivative of the regularized smooth kernel function;

[0059] The regularized density gradient of fluid particle j is represented by the same formula as equations (7) and (8), except that i in equations (7) and (8) is replaced with j.

[0060] parameter for and The geometric mean and Let the magnitudes of the diffusion terms for fluid particle i and fluid particle j be respectively:

[0061]

[0062] Where: C δ It is a constant equal to 1.5; l LES The characteristic length of the large eddy simulation filter is equal to γh; the parameter ||D i || is the strain rate tensor D of fluid particle i i The model, fluid particle i strain rate tensor D i The calculation formula is as follows:

[0063]

[0064] π in the momentum equation ij For viscous terms:

[0065]

[0066] Where: n is the dimension of the problem under study (the effect of fluid on porous marine structures);

[0067] Represents volume fraction With laminar flow viscosity coefficient υ i The product, for and The geometric mean Represents the volume fraction of fluid particle i Its turbulent kinematic viscosity coefficient The product, Represents the volume fraction of fluid particles j Its turbulent kinematic viscosity coefficient The product; It can be calculated using the following formula:

[0068]

[0069] Where: C s It is a constant equal to 0.12;

[0070] The calculation formula is the same as that in equation (12), except that i in equation (12) is replaced with j;

[0071] Volume fraction The following can be obtained by interpolation from particles in porous marine structures using a Gaussian smoothing kernel function:

[0072]

[0073] For the large eddy simulation SPH model, the energy conservation equation can be written as:

[0074]

[0075] Where: ε M The mechanical energy of a fluid particle is equal to its kinetic energy ε. K and potential energy ε P The sum of their kinetic energies, ε K and potential energy ε P The calculation formula is as follows:

[0076]

[0077] According to the weak compressibility hypothesis, the internal energy ε of a fluid particle is... C It can be represented as:

[0078]

[0079] P δ P represents the energy dissipated by the diffusion term. υ This represents the energy dissipated by the viscous term. P represents the power of the energy change caused by the compression of fluid in a porous marine structure. R This represents the energy dissipation power due to drag in porous media marine structures, and:

[0080]

[0081]

[0082]

[0083]

[0084] Where: fluid represents fluid, V i This indicates the volume of a fluid particle.

[0085] This invention discloses a meshless numerical method for analyzing the effects of fluids on porous marine structures. In this embodiment, water is used as an example of the fluid, and the method specifically includes the following steps:

[0086] Step (1), establish as follows Figure 1The numerical wave tank shown is equipped with porous media marine structures. The wave generated by the wave source has a period of T = 1.2s and a wave height of H = 0.06m. Water particles are arranged in the fluid region of the numerical wave tank with an initial spacing of dx, and porous media marine structure particles are arranged in the porous media region with a spacing of dx. Based on the initial spacing of the water particles and the spacing of the porous media marine structure particles, the volumes of the water particles and the porous media marine structure particles are calculated.

[0087] Step (2): Use formula (13) to obtain the volume fraction of each water particle;

[0088] Step (3) uses the fourth-order Runge-Kutta method to integrate the continuity equation and momentum equation (corresponding to formulas (3) and (4)) of the large eddy simulation SPH model to obtain the position, velocity, pressure and density of all water particles in the numerical wave tank; the time step Δt of the fourth-order Runge-Kutta method is calculated by the following formula:

[0089]

[0090] Wherein: the sound velocity c takes a value of 30-50 m / s, and the constant CFL is 2.2;

[0091] Step (4): Based on the volume fraction, position, velocity, pressure and density of all water particles, use formulas (17)-(20) to calculate the energy change rate of water particles in the numerical wave tank, including: energy dissipation power of diffusion term, energy dissipation power of viscosity term, energy change power caused by the compression of fluid in porous media marine structures and energy dissipation power of resistance in porous media marine structures.

[0092] Step (5) is to use the fourth-order Runge-Kutta method to integrate the formula in step (4), and at the same time use formulas (15) and (16) to obtain the mechanical energy and internal energy of all water particles in the numerical wave tank.

[0093] Step (6): Determine whether the time termination condition t>tend is met. If it is met, end the calculation; if the time termination condition is not met, t = t + Δt, and return to step (2).

[0094] A meshless numerical apparatus for analyzing the effects of waves on porous marine structures includes:

[0095] The model building module is used to build models that simulate the effects of fluids on porous marine structures.

[0096] The fluid particle energy change rate calculation module calculates the energy change rate of fluid particles based on the volume fraction, position, velocity, pressure, and density of all fluid particles.

[0097] The fluid particle energy calculation module integrates the formula for calculating the rate of change of fluid particle energy, and then calculates the mechanical energy and internal energy of the fluid particle.

[0098] Based on the same inventive concept as the meshless numerical method for analyzing the effect of fluids on porous marine structures, this application also provides an electronic device comprising one or more processors and one or more memories. The memories store computer-readable code, which, when executed by the one or more processors, implements the meshless numerical method for analyzing the effect of fluids on porous marine structures. The memories may include a non-volatile storage medium and internal memory; the non-volatile storage medium may store an operating system and the computer-readable code. The computer-readable code includes program instructions that, when executed, cause the processor to execute any meshless numerical method for analyzing the effect of fluids on porous marine structures. The processor provides computational and control capabilities to support the operation of the entire electronic device. The memories provide an environment for the execution of the computer-readable code in the non-volatile storage medium, which, when executed by the processor, causes the processor to execute any meshless numerical method for analyzing the effect of fluids on porous marine structures.

[0099] It should be understood that the processor can be a Central Processing Unit (CPU), but it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. Among these, a general-purpose processor can be a microprocessor or any conventional processor.

[0100] The embodiments of this application also provide a computer-readable storage medium storing computer-readable code, which includes program instructions. The processor executes the program instructions to implement the meshless numerical method of this application for analyzing the effect of fluids on porous marine structures.

[0101] The computer-readable storage medium can be an internal storage unit of the electronic device described in the foregoing embodiments, such as the hard disk or memory of the computer device. The computer-readable storage medium can also be an external storage device of the electronic device, such as a plug-in hard disk, SmartMedia Card (SMC), Secure Digital (SD) card, or Flash Card equipped on the electronic device.

[0102] 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 meshless numerical method for analyzing the effects of fluids on porous marine structures, characterized in that: A model simulating the effect of fluid on porous media marine structures was established, and fluid particles and porous media marine structure particles were arranged. The continuity equation and momentum equation of the large eddy simulation (SPH) model are integrated to obtain the position, velocity, pressure and density of all fluid particles; Based on the volume fraction, position, velocity, pressure, and density of all fluid particles, the energy dissipation power of the diffusion term, the energy dissipation power of the viscous term, the energy change power caused by the compression of fluid in porous media marine structures, and the energy dissipation power of the drag in porous media marine structures in the energy conservation equation of the large eddy simulation SPH model are calculated and integrated. Using the expressions for mechanical energy and internal energy in the energy conservation equation, the mechanical energy and internal energy of all fluid particles are obtained; The continuity equation and momentum equation of the large eddy simulation (SPH) model are as follows: Where: m j D represents the mass of fluid particle j. ij Let p represent the diffusion term, g represent the gravitational acceleration of the fluid, and p represent the diffusion term. j This represents the pressure of fluid particle j; The energy conservation equation is as follows: Where: ε M ε represents the mechanical energy of a fluid particle. C P represents the internal energy of a fluid particle. δ P represents the energy dissipated by the diffusion term. υ P represents the energy dissipated by the viscous term. φ P represents the power of the energy change caused by the compression of fluid in a porous marine structure. R This represents the energy dissipation power due to the drag of porous media marine structures, and: Where: fluid represents fluid, p i ρ represents the pressure exerted by fluid particles. i V represents the density of fluid particles. i The volume of fluid particle i is represented by the parameter υδij, which is the geometric mean of the order of magnitude of the diffusion terms of fluid particles i and j. i -r j ) represents the smoothing kernel function between fluid particle i and fluid particle j, r i r represents the position vector of fluid particle i. j V represents the position vector of fluid particle j. j φ represents the volume of fluid particle j. i υφi represents the volume fraction of fluid particle i, and υφi represents the volume fraction φ. i With laminar flow viscosity coefficient υ i The product of υTφij and υTφj is the geometric mean of υTφi and υTφj, where υTφi represents the volume fraction φi of fluid particle i. i The product of its turbulent kinematic viscosity coefficient υT i, υTφ j represents the volume fraction φ of fluid particle j. j Its product with its turbulent kinematic viscosity coefficient υTj; π ij u is the viscous term in the momentum equation. i u represents the velocity of fluid particle i. j Let φ represent the velocity of fluid particle j, ▽ represent the Hamiltonian operator, and φ represent the velocity of fluid particle j. a r represents the fluid volume fraction of particles in porous marine structures. a V represents the position vector of particles in porous media marine structures. a R represents the volume of particles in porous marine structures. i W(r) represents the resistance of the porous medium to fluid particle i. i -r a ) represents the smooth kernel function between fluid particle i and porous media marine structure particle a.

2. The meshless numerical method according to claim 1, characterized in that, The volume fraction of the fluid particles is calculated using the following formula: .

3. The meshless numerical method according to claim 1, characterized in that, The volumes of fluid particles and porous media marine structure particles were calculated using the initial spacing of fluid particles and the spacing of porous media marine structure particles, respectively.

4. The meshless numerical method according to claim 1, characterized in that, The viscous term in the momentum equation is: Where: n is the dimension of the fluid's effect on the porous media marine structure, and h is the smooth length.

5. The meshless numerical method according to claim 1, characterized in that, The mechanical energy ε M =ε K +ε P ,kinetic energy Potential energy , where g represents the gravitational acceleration of the fluid.

6. The meshless numerical method according to claim 1, characterized in that, When the fluid is water, the model for simulating the effect of the fluid on porous marine structures is a numerical wave tank.

7. An apparatus for implementing the meshless numerical method according to any one of claims 1-6, characterized in that, include: The model building module is used to build models that simulate the effects of fluids on porous marine structures. The fluid particle energy change rate calculation module calculates the energy change rate of fluid particles based on the volume fraction, position, velocity, pressure, and density of all fluid particles. This includes the energy dissipation power of the diffusion term, the energy dissipation power of the viscous term, the energy change power caused by the compression of fluid in porous media marine structures, and the energy dissipation power of the drag in porous media marine structures, and then integrates these values. The fluid particle energy calculation module integrates the formula for calculating the rate of change of fluid particle energy, and then calculates the mechanical energy and internal energy of the fluid particle.

8. An electronic device, characterized in that, Including memory and processor; The memory is used to store computer programs; The processor is configured to execute the computer program and, in executing the computer program, implement the meshless numerical method as described in any one of claims 1-6.

9. A storage medium, characterized in that, The storage medium stores a computer program that, when executed by a processor, causes the processor to perform the meshless numerical method as described in any one of claims 1-6.

Images