Breeding netting structure simulation method based on immersion boundary correction method

Abstract

The invention provides a culture netting structure simulation method based on a correction immersion boundary method, and belongs to the field of mariculture. The method comprises the following steps: selecting a grid unit penetrated by a culture net interface as an immersion boundary unit, calculating a continuous forced source item of the immersion boundary unit by adopting an improved Darcy-Forchheimer equation, and applying the continuous forced source item to a momentum equation in the immersion boundary unit by adopting a semi-implicit processing method, and finally, solving and updating field quantities such as speed and pressure in a computational domain by applying a computational fluid mechanics method, so as to realize simulation calculation of the culture netting structure. According to the method, the submerged boundary method is adopted to simulate the culture net structure, the generation difficulty of computational grids is reduced, the Darcy-Forchheimer equation for calculating the continuous forced source item is improved, the semi-implicit processing method of the continuous forced source item is adopted, the simulation capacity for the culture net cage with the complex shape is improved, the calculation efficiency is remarkably improved, and the method is suitable for large-scale popularization and application. And the hydrodynamic characteristics of a culture netting structure and the distribution characteristics of a surrounding flow field can be accurately simulated.

Description

Technical Field

[0001] This invention belongs to the field of marine aquaculture technology and relates to a method for simulating aquaculture netting structures based on a modified immersion boundary method. Background Technology

[0002] With the rapid development of marine ranching and deep-sea aquaculture, aquaculture facilities are gradually becoming larger and deeper. As the core load-bearing and enclosure structure, aquaculture netting's hydrodynamic characteristics directly affect the structural safety, operational stability, and environmental quality of the aquaculture system. Therefore, in-depth research into the hydrodynamic mechanism of aquaculture netting and accurately describing its impact on flow fields and stress characteristics is of significant engineering importance for improving the safety of aquaculture systems and enhancing the aquaculture aquatic environment.

[0003] Currently, compared to aquaculture netting model experiments, numerical simulation methods have been widely developed and applied due to their advantages of low cost and ease of implementation. Computational fluid dynamics methods based on porous media models can effectively simulate the hydrodynamic properties of netting and the surrounding flow field distribution. However, this computational method has drawbacks such as a relatively complex computational domain meshing process, insufficient ability to handle complex shapes, and low computational efficiency. Summary of the Invention

[0004] In view of this, the present invention develops a simulation method for aquaculture netting structures based on the modified submerged boundary method. This method uses the continuous forced submerged boundary method to simulate aquaculture netting, which can realize rapid simulation of aquaculture netting structures, accurately calculate the hydrodynamic characteristics and wake characteristics of the netting structure under the action of water flow, and analyze the influence of the netting structure on the surrounding flow field distribution.

[0005] The technical solution adopted in this invention is:

[0006] A simulation method for aquaculture netting structures based on the modified submerged boundary method includes:

[0007] S1: Establish a numerical simulation model of aquaculture netting based on actual parameters of the netting.

[0008] S2: Select immersion boundary elements based on the aforementioned mesh numerical simulation model;

[0009] S3: Based on the improved Darcy-Forchheimer equations and the latest computational domain velocity field, the continuous forcing source terms of the submerged boundary element are calculated.

[0010] S4: Discretize the control equations of the computational domain of the netting numerical simulation model to obtain the discretized momentum equations and discretized pressure Poisson equations in each grid cell of the computational domain;

[0011] S5: Apply a continuously forced source term to the discretized momentum equation within the submerged boundary element, and perform semi-implicit processing on the source term to obtain the continuously forced discretized momentum equation.

[0012] S6: Solve the discretized momentum equation and discretized pressure Poisson equation in all grid cells, including the submerged boundary cell, to obtain the computational domain velocity field and pressure field at the current time step;

[0013] S7: Repeat steps S3 to S6 until the velocity and pressure fields of all time steps in the computational domain are calculated, and the final stress and flow field distribution of the netting is obtained.

[0014] Furthermore, in step S1, establishing a numerical simulation model of the aquaculture net based on its actual parameters includes:

[0015] Create a corresponding geometric model file based on the actual shape and size of the aquaculture netting;

[0016] In the OpenFOAM environment, the global coordinate system and the corresponding mesh computation domain are determined, and the mesh near the aquaculture net is densified according to the computation requirements;

[0017] According to the simulation requirements, boundary conditions are set for the numerical simulation model, and initial conditions are set for the velocity and pressure fields in the computational domain.

[0018] Furthermore, in step S2, the selection of immersion boundary elements based on the netting numerical simulation model includes:

[0019] Based on the geometric model file of the aquaculture net and the existing computational domain mesh, the mesh cells through which the aquaculture net interface passes are selected as submerged boundary cells within the computational domain.

[0020] Record the interface between the aquaculture netting structure and the submerged boundary unit, and calculate the area and unit normal vector of the interface within each submerged boundary unit.

[0021] Furthermore, in step S3, the continuous forcing source terms of the submerged boundary element are calculated based on the improved Darcy-Forchheimer equations and the latest computational domain velocity field, as follows:

[0022] (1)

[0023] (2)

[0024] In the formula, For each submerged boundary element, there is a continuous forced source term; For fluid dynamic viscosity; The fluid velocity vector within each submerged boundary cell; For fluid density; The area of ​​the interface within each submerged boundary cell; and These are the improved Darcy-Forchheimer coefficient matrices for viscosity and inertia, respectively. and These are the improved Darcy-Forchheimer viscosity coefficients in the normal and tangential directions, respectively. and The improved Darcy-Forchheimer inertia coefficients for the normal and tangential directions are respectively; the improved... and The following conversion relationship exists between the Darcy-Forchheimer coefficient matrix and the traditional Darcy-Forchheimer coefficient matrix:

[0025] (3)

[0026] In the formula, and These are the traditional Darcy-Forchheimer viscosity coefficients in the normal and tangential directions, respectively. and These are the traditional Darcy-Forchheimer inertia coefficients in the normal and tangential directions, respectively. This refers to the virtual thickness in traditional porous media models;

[0027] In actual calculations, the unit normal vector of the interface within the submerged boundary element forms an angle with the x-axis of the global coordinate system. Therefore, a coordinate transformation is required for the improved Darcy-Forchheimer coefficient matrix.

[0028] (4)

[0029] (5)

[0030] In the formula, The unit normal vector of the interface within each submerged boundary cell; It is the identity matrix; and These are the improved Darcy-Forchheimer coefficient matrices after coordinate transformation.

[0031] Furthermore, in step S4, the discretized momentum equation and discretized pressure Poisson equation within each grid cell are as follows:

[0032] Based on the finite volume method, the governing equations of the computational domain of the mesh numerical simulation model are discretized to obtain the discretized momentum equation and discretized pressure Poisson equation within each mesh cell:

[0033] (6)

[0034] (7)

[0035] In the formula, and This refers to the influence coefficient of the mesh cell itself. and This represents the influence coefficient of each adjacent cell in the grid. It is a constant vector; It is a constant; This represents the velocity vector within the grid cell at the current time step. This represents the velocity vector within each adjacent cell of the current time step grid cell; This indicates the pressure within the grid cell at the current time step; This represents the pressure within each adjacent cell of the current time step grid cell.

[0036] Furthermore, in step S5, the continuously forced discretized momentum equation is obtained based on the following method:

[0037] Applying a continuous forcing source term to the discretized momentum equation within the submerged boundary element, we obtain:

[0038]

[0039] In the formula, The influence coefficient of the submerged boundary element; The influence coefficients of each adjacent element of the submerged boundary element; It is a constant vector; and These represent the velocity vectors within the submerged boundary cells at the current time step and the previous time step, respectively. This represents the velocity vector within each adjacent cell of the submerged boundary cell at the current time step.

[0040] By semi-implicitly transforming the continuous forcing source term in equation (8), we obtain the discretized momentum equation for continuous forcing:

[0041]

[0042] (9)

[0043] In the formula, and Each is a matrix and The traces.

[0044] Furthermore, in step S6, the solution process for the velocity field and pressure field in the computational domain at the current time step includes:

[0045] Based on turbulence theory, the turbulence equations for turbulence kinetic energy and turbulence dissipation rate are obtained respectively. The finite volume method is used to discretize the turbulence equations, and the discretized turbulence equations in each grid cell of the computational domain are solved iteratively to obtain the updated turbulence kinetic energy field and turbulence dissipation rate field.

[0046] The pressure implicit operator splitting (PISO) algorithm is used to solve the discretized momentum equation and discretized pressure Poisson equation in all grid cells, including the submerged boundary cells. During the solution process, the updated turbulent kinetic energy field and turbulent dissipation rate field are introduced to correct the velocity field for turbulence, so as to obtain the updated velocity field and pressure field at the current time step.

[0047] Furthermore, in step S7, steps S3 to S6 are executed repeatedly until the velocity and pressure fields for all time steps in the computational domain are calculated, resulting in the final stress and flow field distribution of the mesh, including:

[0048] Based on the updated velocity field obtained at the current time step, the improved Darcy-Forchheimer equation is used to calculate the continuous forcing source terms of the submerged boundary elements in the next time step. Subsequently, the continuous forcing source terms are added to the discretized momentum equation of the corresponding submerged boundary elements, and the continuous forcing source terms are semi-implicitly processed. Finally, the pressure implicit operator splitting (PISO) algorithm is applied to solve the discretized momentum equation and discretized pressure Poisson equation in each grid element in the computational domain, thereby obtaining the velocity field and pressure field in the computational domain at the next time step.

[0049] The beneficial effects of this invention are:

[0050] (1) Based on computational fluid dynamics, this invention takes into account turbulence effects and can accurately analyze flow field changes. At the same time, the submerged boundary method is used to simulate the mesh structure, which significantly reduces the difficulty of generating computational mesh and improves computational efficiency.

[0051] (2) The present invention uses the improved Darcy-Forchheimer equation to calculate the continuous forced source term applied to the submerged boundary element, which eliminates the influence of virtual thickness in the traditional porous media model and performs semi-implicit processing on the source term, which can accurately calculate the hydrodynamic load on the mesh structure in the flow field.

[0052] (3) The present invention has a higher level of geometric shape fitting ability and can be used to simulate aquaculture cages with different complex shapes. Attached Figure Description

[0053] Figure 1 It is a simulation process of aquaculture netting (net cage) structure.

[0054] Figure 2 It is a model of aquaculture cage structure.

[0055] Figure 3 It is a computational grid for aquaculture cage structures.

[0056] Figure 4 This is a schematic diagram of the submerged boundary element selection method.

[0057] Figure 5 This is a flow field distribution diagram around the aquaculture cage structure. Detailed Implementation

[0058] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. The embodiments of the present invention are implemented based on the technical solution of the present invention, and detailed implementation methods and specific operating procedures are given. However, the scope of protection of the present invention is not limited to the following embodiments.

[0059] like Figure 1 As shown, this embodiment of the invention provides a method for simulating aquaculture netting structures based on a modified immersion boundary method, comprising the following steps:

[0060] S1. Taking a cylindrical aquaculture cage structure with a diameter of 16m and a height of 10m as an example, a numerical simulation model of the cage is established. The specific process is as follows:

[0061] S1.1 Based on the cylindrical aquaculture cage, establish as follows: Figure 2 Geometric model of aquaculture cages;

[0062] S1.2. In the OpenFOAM environment, determine the global coordinate system and the corresponding grid computation domain. Then, refine the grid near the aquaculture cages according to computational requirements, such as... Figure 3 As shown,

[0063] S1.3. According to the simulation requirements, set boundary conditions for the net cage numerical simulation model, and set initial conditions for the velocity field and pressure field of the computational domain. The calculation condition is set to a flow velocity of 1.0 m / s.

[0064] S2. Selecting submerged boundary elements based on the geometric model of the aquaculture cage: The specific process is as follows:

[0065] S2.1 Based on the aquaculture cage structure and the created computational grid in S1, according to Figure 4 The method is to select the grid cells through which the aquaculture cage interface passes as submerged boundary cells;

[0066] S2.2 Record the interface between the aquaculture cage structure and the submerged boundary unit, and calculate the area and unit normal vector of the interface within each submerged boundary unit.

[0067] S3. Based on the improved Darcy-Forchheimer equations in this invention, and according to the latest computational domain velocity field, calculate the continuous forcing source terms that need to be applied within each submerged boundary element. The specific process is as follows:

[0068] S3.1 Based on the improved Darcy-Forchheimer equation, the continuous forcing source term within the submerged boundary element is as follows:

[0069] (10)

[0070] (11)

[0071] In the formula, For each submerged boundary element, there is a continuous forced source term; For fluid dynamic viscosity; The fluid velocity vector within each submerged boundary cell; For fluid density; The area of ​​the interface within each submerged boundary cell; and These are the improved Darcy-Forchheimer coefficient matrices for viscosity and inertia, respectively. and These are the improved Darcy-Forchheimer viscosity coefficients in the normal and tangential directions, respectively. and The Darcy-Forchheimer improved inertia coefficients are given for the normal and tangential directions, respectively.

[0072] S3.2 In actual calculations, the unit normal vector of the interface within the submerged boundary element forms an angle with the x-axis of the global coordinate system. Therefore, a coordinate transformation is required for the improved Darcy-Forchheimer coefficient matrix, as follows:

[0073] (12)

[0074] (13)

[0075] In the formula, The unit normal vector of the interface within the submerged boundary element; It is the identity matrix; and These are the improved Darcy-Forchheimer coefficient matrices after coordinate transformation.

[0076] S4. Discretize the governing equations of the computational domain of the net cage numerical simulation model to obtain the discretized momentum equation and discretized pressure Poisson equation in each grid cell of the computational domain, as follows:

[0077] (14)

[0078] (15)

[0079] In the formula, and This refers to the influence coefficient of the mesh cell itself. and This represents the influence coefficient of each adjacent cell in the grid. It is a constant vector; It is a constant; This represents the velocity vector within the grid cell at the current time step. This represents the velocity vector within each adjacent cell of the current time step grid cell; This indicates the pressure within the grid cell at the current time step; This represents the pressure within each adjacent cell of the current time step grid cell.

[0080] S5. Apply a continuous forcing source term to the discretized momentum equation within the submerged boundary element, and perform semi-implicit processing on the source term to obtain the continuously forcibly discretized momentum equation. The specific process is as follows:

[0081] S5.1 Based on the finite volume method, the discretized momentum equation within the submerged boundary element is obtained:

[0082]

[0083] In the formula, The influence coefficient of the submerged boundary element; The influence coefficients of each adjacent element of the submerged boundary element; It is a constant vector; and These represent the velocity vectors within the submerged boundary cells at the current time step and the previous time step, respectively. It represents the velocity vector within each adjacent cell of the submerged boundary cell at the current time step.

[0084] S5.2. Perform semi-implicit processing on continuous forced source terms, as follows:

[0085]

[0086] (17)

[0087] In the formula, and Each is a matrix and The traces.

[0088] S6. Solve the discretized momentum equation and discretized pressure Poisson equation in all mesh elements, including the submerged boundary element, to obtain the computational domain velocity field and pressure field at the current time step, as follows:

[0089] S6.1 Based on turbulence theory, the turbulence equations for turbulence kinetic energy and turbulence dissipation rate are obtained respectively. The turbulence equations are discretized using the finite volume method, and the discretized turbulence equations in each grid cell of the computational domain are solved iteratively to obtain the updated turbulence kinetic energy field and turbulence dissipation rate field.

[0090] S6.2. The Pressure Implicit Operator Splitting (PISO) algorithm is used to solve the discretized momentum equation and discretized pressure Poisson equation in all grid cells, including the submerged boundary cells. During the solution process, the updated turbulent kinetic energy field and turbulent dissipation rate field are introduced to correct the velocity field for turbulence, so as to obtain the updated velocity field and pressure field at the current time step.

[0091] S7. Repeat steps S3 to S6 until the velocity and pressure fields of all time steps in the computational domain are calculated, and the final force distribution of the aquaculture cage and the surrounding flow field are obtained.

[0092] The flow field results of the cage in this embodiment are as follows: Figure 5 As shown, the flow velocity decreases both inside and downstream of the cage, indicating that the simulation method of the present invention can accurately simulate the flow field state around the cage. The drag coefficient results and calculation speed of the cage in this embodiment are shown in Table 1. It can be seen that the simulation method of the present invention can more accurately calculate the hydrodynamic load on the cage structure, and has a calculation speed improvement of more than 30 times compared with the traditional porous media model.

[0093] Table 1. Cage resistance coefficient and simulation calculation speed

[0094]

[0095] The above description represents a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A simulation method for aquaculture netting structures based on the modified submerged boundary method, characterized in that, include: S1: Establish a numerical simulation model of aquaculture netting based on actual parameters of the netting. S2: Select immersion boundary elements based on the aforementioned mesh numerical simulation model; S3: Based on the improved Darcy-Forchheimer equations and the latest computational domain velocity field, the continuous forcing source terms of the submerged boundary element are calculated. S4: Discretize the control equations of the computational domain of the netting numerical simulation model to obtain the discretized momentum equations and discretized pressure Poisson equations in each grid cell of the computational domain; S5: Apply a continuously forced source term to the discretized momentum equation within the submerged boundary element, and perform semi-implicit processing on the source term to obtain the continuously forced discretized momentum equation. S6: Solve the discretized momentum equation and discretized pressure Poisson equation in all grid cells, including the submerged boundary cell, to obtain the computational domain velocity field and pressure field at the current time step; S7: Repeat steps S3 to S6 until the velocity and pressure fields of all time steps in the computational domain are calculated, and the final stress and flow field distribution of the netting is obtained.

2. The method for simulating aquaculture netting structures based on the modified submersion boundary method according to claim 1, characterized in that, In step S1, establishing a numerical simulation model of the aquaculture net based on its actual parameters includes: Create a corresponding geometric model file based on the actual shape and size of the aquaculture netting; In the OpenFOAM environment, the global coordinate system and the corresponding mesh computation domain are determined, and the mesh near the aquaculture net is densified according to the computation requirements; Set boundary conditions for the numerical simulation model and initial conditions for the velocity and pressure fields in the computational domain.

3. The method for simulating aquaculture netting structures based on the modified submersion boundary method according to claim 2, characterized in that, In step S2, the selection of immersion boundary elements based on the netting numerical simulation model includes: Based on the geometric model file of the aquaculture net and the existing computational domain mesh, the mesh cells through which the aquaculture net interface passes are selected as submerged boundary cells within the computational domain. Record the interface between the aquaculture netting structure and the submerged boundary unit, and calculate the area and unit normal vector of the interface within each submerged boundary unit.

4. The method for simulating aquaculture netting structures based on the modified submersion boundary method according to claim 3, characterized in that, In steps S2 and S3, the continuous forcing source terms of the submerged boundary elements are calculated, as follows: (1) (2) In the formula, For each submerged boundary element, there is a continuous forced source term; For fluid dynamic viscosity; The fluid velocity vector within each submerged boundary cell; For fluid density; The area of ​​the interface within each submerged boundary cell; and These are the improved Darcy-Forchheimer coefficient matrices for viscosity and inertia, respectively. and These are the improved Darcy-Forchheimer viscosity coefficients in the normal and tangential directions, respectively. and The improved Darcy-Forchheimer inertia coefficients for the normal and tangential directions are respectively; the improved... and The following conversion relationship exists between the Darcy-Forchheimer coefficient matrix and the traditional Darcy-Forchheimer coefficient matrix: (3) In the formula, and These are the traditional Darcy-Forchheimer viscosity coefficients in the normal and tangential directions, respectively. and These are the traditional Darcy-Forchheimer inertia coefficients in the normal and tangential directions, respectively. This refers to the virtual thickness in traditional porous media models; In actual calculations, a coordinate transformation is performed on the improved Darcy-Forchheimer coefficient matrix: (4) (5) In the formula, The unit normal vector of the interface within each submerged boundary cell; It is the identity matrix; and These are the improved Darcy-Forchheimer coefficient matrices after coordinate transformation.

5. The method for simulating aquaculture netting structures based on the modified submersion boundary method according to claim 4, characterized in that, In step S4, the discretized momentum equation and discretized pressure Poisson equation within each grid cell are as follows: Based on the finite volume method, the governing equations of the computational domain of the mesh numerical simulation model are discretized to obtain the discretized momentum equation and discretized pressure Poisson equation within each mesh cell: (6) (7) In the formula, and This refers to the influence coefficient of the mesh cell itself. and This represents the influence coefficient of each adjacent cell in the grid. It is a constant vector; It is a constant; This represents the velocity vector within the grid cell at the current time step. This represents the velocity vector within each adjacent cell of the current time step grid cell; This indicates the pressure within the grid cell at the current time step; This represents the pressure within each adjacent cell of the current time step grid cell.

6. The method for simulating aquaculture netting structures based on the modified submersion boundary method according to claim 5, characterized in that, In step S5, the continuously forced discretized momentum equation is obtained based on the following method: Applying a continuous forcing source term to the discretized momentum equation within the submerged boundary element, we obtain: In the formula, The influence coefficient of the submerged boundary element; The influence coefficients of each adjacent element of the submerged boundary element; It is a constant vector; and These represent the velocity vectors within the submerged boundary cells at the current time step and the previous time step, respectively. This represents the velocity vector within each adjacent cell of the submerged boundary cell at the current time step. By semi-implicitly transforming the continuous forcing source term in equation (8), we obtain the discretized momentum equation for continuous forcing: (9) In the formula, and Each is a matrix and The traces.

7. The method for simulating aquaculture netting structures based on the modified submersion boundary method according to claim 6, characterized in that, In step S6, the solution process for the velocity field and pressure field in the computational domain at the current time step includes: Based on turbulence theory, the turbulence equations for turbulence kinetic energy and turbulence dissipation rate are obtained respectively. The finite volume method is used to discretize the turbulence equations, and the discretized turbulence equations in each grid cell of the computational domain are solved iteratively to obtain the updated turbulence kinetic energy field and turbulence dissipation rate field. The pressure implicit operator splitting algorithm is used to solve the discretized momentum equation and the discretized pressure Poisson equation in all grid cells, including the submerged boundary cells. During the solution process, the updated turbulent kinetic energy field and turbulent dissipation rate field are introduced to correct the velocity field for turbulence, so as to obtain the updated velocity field and pressure field at the current time step.

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