Coupling algorithm for researching influence of microplastics on fishes based on unstructured grids

Abstract

The invention discloses a coupling algorithm for studying the influence of micro-plastics on fishes based on unstructured grids, and aims to deeply understand the influence of the micro-plastics on fish ecology in the ocean. According to the method, a Lagrange advection model and a diffusion equation are combined to simulate the transmission and diffusion process of the micro-plastic particles, and the spatial position of each particle is calculated and the trajectory of the particle is tracked by introducing real ocean current data. A large-scale sparse linear system generated in the simulation process is solved by adopting a GMRES method, so that the calculation efficiency and stability are ensured. And a Crank-Nicolson method is also utilized to carry out time stepping, so that the numerical stability is improved. The spatial distribution of the micro-plastics is truly reflected by interlacing the time step length and coupling the Lagrange advection and diffusion process. In consideration of specific behaviors of fish schools, the density change rate of the fish schools is jointly determined by inherent movement, diffusion and micro-plastic concentration gradient, so that the potential influence of micro-plastic on marine fish ecology is evaluated.

Description

Technical Field

[0001] The invention belongs to the fields of environmental science and computational fluid dynamics, and in particular relates to a method for simulating the transmission and diffusion of microplastics in an aquatic environment. Background Art

[0002] Microplastics, as a marine pollutant with a particle size of less than 5 mm, have attracted widespread attention worldwide. The long-term presence of these plastic particles in the marine environment poses a serious threat to the health of the marine ecosystem. Some existing microplastic simulation methods have many shortcomings. For example, some methods use simple models or simple structured grids when dealing with complex marine environments, which cannot accurately simulate the transmission and diffusion of microplastics under complex ocean current changes, and the existing models do not study the quantitative impact of microplastics on the population of fish. In addition, when simulating the impact of microplastics on the number of fish, the models used by some methods do not take into account the differences in microplastic concentrations in different cells and the interactive diffusion between cells, and cannot truly reflect the impact of microplastic pollution in complex and heterogeneous environments.

[0003] To address these issues, the present invention proposes a coupling algorithm based on unstructured grids, which can more accurately simulate the impact of microplastics on fish. Summary of the invention

[0004] Purpose of the invention: In view of the problems existing in the prior art, the present invention provides a coupling algorithm based on unstructured grids to study the impact of microplastics on fish, which is used to solve the limitations of traditional simulation methods in dealing with the transmission and diffusion of microplastics in complex marine environments, as well as the lack of quantitative assessment of the impact of microplastics on marine ecosystems, especially fish populations. The present invention improves the accuracy of simulating the movement and diffusion of microplastics in the marine environment by coupling the Lagrangian advection model and the diffusion equation, combined with ocean current data, providing a scientific basis for environmental management and pollution control, and providing a new technical means for evaluating the potential impact of microplastics on specific marine ecosystems.

[0005] Technical solution: To achieve the above invention purpose, the present invention adopts the following technical solution: a coupling algorithm based on unstructured grid to study the impact of microplastics on fish, comprising the following steps:

[0006] S1, initialization variables: divide the target area into unstructured grids, initialize the concentration of microplastics and the number of fish in each grid, and obtain the zero time;

[0007] S2, advection of microplastics: The advection motion of microplastic particles is simulated based on the Lagrangian advection model within a step time period of [0, Δt / 4], thereby simulating the motion trajectory of microplastic particles in the ocean;

[0008] S3, Microplastics and fish diffusion: After determining the movement trajectory and spatial position of microplastic particles in the ocean, the diffusion equation of microplastic particles is solved by the finite difference method and the Crank-Nicolson time stepping scheme within the step time period of [Δt / 4, Δt / 2] to obtain the concentration distribution of microplastic particles in the water body; S4, The impact of microplastics on the number of fish: Considering the changes in cell environmental concentration, cell interactive diffusion and the dynamic changes in microplastic concentration, the dynamic Lotka-Volterra model is used to simulate and evaluate the impact of microplastic particles on fish schools within the step time period of [Δt / 2, 3Δt / 4] to obtain the distribution data of the number of fish schools;

[0009] S5, within the time period of [3Δt / 4,Δt], the diffusion processing of the fish behavior simulation module is carried out for the fish population, and the final impact of microplastics on the number of fish is obtained;

[0010] S6, iterative update: take the microplastic concentration distribution and fish population distribution at the end of the current step as the initial value of the next step, repeat steps S2-S5, and continue iterative calculation until the predetermined calculation termination condition is reached to achieve the simulation state of the impact of microplastics on fish.

[0011] Furthermore, the Lagrangian velocity field V(t; X0) of the microplastic particles in the ocean in step S2 is calculated by the following formula:

[0012] V(t;X0)=v(X(t;X0),t)

[0013] Where V represents the velocity field, a function determined by longitude and latitude and time; v represents the ocean velocity field; X0 is the initial position of the particle; X(t; X0) represents the position of the particle at time t when the initial position is X0; the trajectory and spatial position of the particle are obtained by numerically integrating the Lagrange advection formula, as follows:

[0014]

[0015] X(t=0;X0)=X0

[0016] Wherein, the velocity field V is calculated based on NASA's ECCO2 ocean current data and the Stokes drift velocity data provided by Ifremer; the coastline data in the model comes from NOAA's GSHHG high-resolution geographic dataset.

[0017] Furthermore, the acquisition of the concentration distribution of microplastic particles in the water body in step S3 includes the following steps:

[0018] (1) First, the reaction-diffusion is represented by the following semilinear parabolic partial differential equation,

[0019]

[0020] In the formula, u represents the diffusion field of microplastic particles, t represents time, a is the diffusion coefficient, ▽ represents the gradient, and S is the position-related input;

[0021] Next, the diffusion process of microplastic particles in the ocean is simulated by numerically solving the equation; the above semilinear parabolic partial differential equation is expanded in two-dimensional space to obtain the diffusion equation in two-dimensional space, as shown in the following formula:

[0022] u t =α(u xx +u yy )

[0023] In the formula, u t represents the diffusion field of microplastic particles at time t, a is the diffusion coefficient, the subscript x represents the horizontal coordinate value, and the subscript y represents the vertical coordinate value;

[0024] (2) For unstructured grid division, the finite difference method is used to solve the two-dimensional space continuous diffusion equation u in step (1) t Discretize and construct a linear equation Ax=b, where b and x are expressed as follows:

[0025] Solving the linear equations yields the value of x, which is the first and second derivatives of u. x ,u y ,u xx ,u yy ,u xy The approximate value of ; A represents the coefficient matrix, that is, the coefficient matrix in Taylor expansion;

[0026] (3) The linear equations constructed in step (2) are iteratively solved using the GMRES method to obtain the value of x. The time derivatives are then averaged at the midpoint of the time step using the Crank-Nicolson method, as shown below: n+1 ,

[0027]

[0028] In the formula, u n+1 and u n represents the value of the microplastic particle diffusion field u at the n+1th and nth time steps respectively; Δt represents the time step, that is, the time interval between two adjacent time steps; α is the diffusion coefficient; u xx and u yy They represent the second-order partial derivatives of the microplastic particle diffusion field u with respect to x and y, respectively.

[0029] Furthermore, the distribution of the number of fish in step S4 is obtained by constructing the following model:

[0030]

[0031] In the formula, C Ei They represent the derivatives of x1(t), x2(t), C1(t), and C2(t) respectively; C Ei Respectively represent the distribution of microplastic concentrations within cells in different grids;

[0032] C1(t) and C2(t) represent the temporal changes in the concentrations of microplastics in the prey and predator, respectively;

[0033] x1(t) and x2(t) represent the population size of prey and predator at time t, respectively;

[0034] r 10 and r 20 are the intrinsic growth rate coefficient of the prey and the mortality rate coefficient of the predator when there is no toxicity; r 11 and r 21 represent the intensity of the response of microplastic particles to prey and predator, respectively;

[0035] a1 and a2 are used to quantify the effect of predation on the reduction of prey population and the increase of predator population, respectively; a1x1x2 is the number of preys eaten, and a2x1x2 is the increase in the number of predators due to eating, where a1, a2>0;

[0036] g1 and g2 represent the microplastic excretion rates of prey and predator, respectively, g1 and g2 ≥ 0;

[0037] S1 and S2 represent the absorption rates of plastic particles by the prey and predator, respectively, S1, S2>0;

[0038] d1, d2, and d3 represent the reduction in the prey’s feeding ability, the adverse effects on the predator’s performance, and the amount of loss of the prey due to predation, respectively.

[0039] Furthermore, in step S5, the fish concentration diffusion equation is added while simulating the unique behavior of the fish school, so as to obtain the distribution of the number u of fish, as shown in the following improved formula:

[0040]

[0041] is the intrinsic velocity vector of the school of fish, represents the gradient of the number of fish, D u is the diffusion coefficient of the fish school, represents the Laplace quantity of the fish population u, k1 is the reaction coefficient of the fish population to the microplastic concentration gradient, The gradient representing the concentration of microplastic particles is used to simulate the behavior of fish schools by taking the above factors into consideration.

[0042] Furthermore, in step S6, the microplastic concentration distribution and fish population distribution at the end of the current step are used as the initial values ​​of the next step, and steps S2-S5 are repeated, and the iterative calculation is continued until the total simulation time t is reached, so as to achieve the simulation state of the impact of microplastics on fish.

[0043] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0044] (1) The unstructured grid-based microplastic ocean diffusion simulation method provided by the present invention achieves accurate simulation of the transmission and diffusion of microplastic particles in the marine environment by coupling the Lagrangian advection model and the diffusion equation, thereby improving the accuracy and reliability of the simulation results;

[0045] (2) Compared with traditional simulation methods, the GMRES method and Crank-Nicolson time-stepping scheme adopted in the present invention effectively handle the large-scale sparse linear system generated during the simulation process, improve the computational efficiency, reduce the numerical error, and make the distribution and migration prediction of microplastics more stable and accurate;

[0046] (3) The present invention also takes into account the impact of microplastics on the number of fish populations. By simulating the effect of microplastic concentration gradients on the rate of change of fish density, it provides a more comprehensive scientific basis for assessing the potential threat of microplastics to marine ecosystems, thereby providing more effective decision-making support for environmental management and pollution control. DETAILED DESCRIPTION

[0047] Figure 1 It is a logical schematic diagram of a coupling algorithm for studying the impact of microplastics on fish using an unstructured grid in an embodiment of the present invention;

[0048] Figure 2 It is an algorithm flow chart of a coupling algorithm for studying the effects of microplastics on fish using unstructured grids in an embodiment of the present invention;

[0049] Figure 3 It is an unstructured grid in a coupling algorithm for studying the effects of microplastics on fish using unstructured grids in an embodiment of the present invention;

[0050] Figure 4 This is the final simulation result obtained by the coupling algorithm of the unstructured grid in the embodiment of the present invention to study the impact of microplastics on fish.

[0051] Specific implementation methods The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0052] In order to deeply understand the impact of microplastics on fish ecology in the ocean, the present invention provides a simulation method based on unstructured grids to study the impact of microplastics on fish ecology in the ocean. The method couples the Lagrangian advection model and the diffusion equation to simulate the transmission and diffusion process of microplastic particles. By introducing real ocean current data, the spatial position of each particle is calculated to obtain the trajectory of the particle. At the same time, the GMRES method is used to solve the large-scale sparse linear system generated in the simulation to ensure the efficiency and stability of the calculation. In addition, the present invention also uses the Crank-Nicolson method for time stepping to improve numerical stability. The Lagrangian advection and diffusion processes are coupled by staggered time steps to truly reflect the spatial distribution of microplastics. At the same time, considering the specific behavior of fish schools, their density change rate is determined by inherent motion, diffusion and microplastic concentration gradient, so as to evaluate the potential impact of microplastics on marine fish ecology.

[0053] like Figure 1 and 2 As shown, the coupling algorithm of the present invention is implemented by the following steps, including the following steps: First, the variable module is initialized based on Figure 3 The unstructured grid is constructed and the initial states of microplastics and fish schools are set based on actual environmental data and ecological survey data. Then, the Lagrangian advection module uses NASA's ECCO2 ocean current data and Stokes drift velocity data provided by Ifremer to calculate the advection motion of microplastic particles. Next, the diffusion equation module uses the finite difference method and Crank-Nicolson time stepping scheme to simulate the diffusion process of microplastic particles. The microplastic and fish school interaction module evaluates the impact of microplastics on the number of fish schools through the improved dynamic Lotka-Volterra model.

[0054] The numerical solution module is responsible for solving the diffusion equation, while the GMRES iterative solution module handles the linear system generated in the simulation;

[0055] Finally, the fish behavior simulation module considers the response of fish schools to the microplastic concentration gradient, the data coupling module couples the above steps with staggered time steps, and the result output module provides the final simulation results, such as Figure 4 shown.

[0056] S1, initialize variables

[0057] The microplastic concentration and fish population in the area to be calculated are initialized, where the microplastic concentration is set according to the actual environmental data and the fish population is set according to the ecological survey data; and the longitude and latitude of a specific location are marked, at which a predetermined number of microplastic particles are discharged, and the number and characteristics of the particles are determined according to the experimental design or field sampling data.

[0058] S2, advection of microplastics

[0059] The Lagrangian advection formula is used to simulate the advection motion of microplastic particles. This formula describes the state of the particle as a function of time. For a particle with an initial position of X0, the formula for its Lagrangian velocity V(t,X0) is: V(t;X0) = v(X(t;X0),t). Among them, V represents the velocity field, which is a function determined by longitude and latitude and time. The trajectory of the particle can be obtained by numerically integrating the Lagrangian advection formula:

[0060]

[0061] The velocity field V is calculated based on NASA's ECCO2 ocean current data and Stokes drift velocity data provided by Ifremer. The ECCO2 data has a temporal resolution of 3 days and a spatial resolution of 0.2 degrees, while the Stokes drift data is updated every 3 simulation hours with a velocity field resolution of 0.5°. The coastline data in the model comes from NOAA's GSHHG high-resolution geographic dataset. With these data, the movement trajectory of microplastic particles in the ocean can be accurately simulated and the spatial position of the particles can be updated at each time point.

[0062] S3, Microplastics and the spread of fish populations

[0063] After the spatial location of each particle is determined, the diffusion equation is introduced to describe the transmission, diffusion and interaction of microplastic particles in the water body. The finite difference method is combined with the diffusion equation to simulate the transmission and diffusion process of particles. The flexibility and adaptability of the simulation are improved through unstructured grids. The steps are as follows:

[0064] Step (1): The reaction-diffusion system adopts the form of semilinear parabolic partial differential equations. They can be expressed in general form as:

[0065]

[0066] Where t represents time, u represents the diffusion field, α is the diffusion coefficient, is the gradient, and S is the position-dependent input quantity. By numerically solving the equation, the diffusion process of substances in the marine environment can be simulated.

[0067] In two-dimensional space, assuming that the horizontal direction is the x-axis and the vertical direction is the y-axis, this equation is extended to two-dimensional space, and the diffusion equation becomes: t =α(u xx +u yy );

[0068] Step (2): Discretize the continuous equation using the finite difference method. By performing a Taylor series expansion on u on an unstructured grid, we can obtain approximate expressions for the first-order and second-order derivatives. For example, for a point u0 = u(x0, y0) and a point u1 = u(x1, y1) in two-dimensional space, the Taylor expansion can be approximated as:

[0069]

[0070] Among them, Δx=x1-x0, Δy=y1-y0;

[0071] Through the above approximation, we can construct a linear equation system Ax = b, where

[0072]

[0073] The coefficient matrix A consists of the coefficients in the Taylor expansion, which relates the relationship between the derivative of u and the difference between neighboring points. To solve the derivative, we use the least squares method to find the best fit, that is, to solve the linear equation system Ax = b so that the sum of the squares of the errors is minimized;

[0074] Step (3): To improve numerical stability, the Crank-Nicolson method is used for time stepping. This method averages the time derivatives at the midpoint of the time step to obtain an implicit formula:

[0075]

[0076] Among them, u n+1 and u n Respectively represent the field quantities at time steps n+1 and n;

[0077] Step (4): For the large-scale sparse linear system generated in the unstructured grid simulation, the GMRES method is used for iterative solution to ensure the efficiency and stability of the calculation. The generalized minimum residual (GMRES) method is an iterative algorithm for solving asymmetric linear systems. The core idea is to find an approximate solution in the Krylov subspace so that the norm of the residual vector is minimized. The GMRES method does not require the matrix to be symmetric and positive definite, so it has a wider applicability than methods such as the conjugate gradient method. This method has the characteristics of fast convergence and is widely used in scientific and engineering calculations.

[0078] S4. Impact of microplastics on fish populations

[0079] In order to more accurately simulate the impact of microplastic pollution in complex and heterogeneous environments, the dynamic Lotka-Volterra model was improved. Considering that different cells may have different microplastic concentration levels, we changed the environmental concentration from a single constant CE to a CEi that varies from cell to cell. In addition, the cross-diffusion between cells and the dynamic changes in microplastic concentrations are taken into account, thereby improving the applicability and accuracy of the model in simulating real-world conditions. These modifications allow us to more carefully capture the complex effects of microplastic pollution on the predator-prey population dynamics in the ecosystem, and obtain the model:

[0080]

[0081] Where x1(t), x2(t), C1(t), C2(t), t≥0. The model ignores the impact of intraspecific competition and shows the effect of microplastics through the environmental concentration CEi of each cell. C1(t) and C2(t) represent the changes in the concentration of microplastics in the prey and predator over time. x1 and x2 represent the population size of the prey and predator, respectively. r10 x1 and r20x2 are the intrinsic growth rate of the prey and the mortality rate of the predator in the absence of toxicity, respectively. a1 x1 x2 is the number of prey preyed, and a2 x1 x2 is the number of predators increased due to feeding, where a1 and a2>0. The parameters d1, d2 and d3 represent the decline in the feeding ability of the prey, the adverse effects on the performance of the predator, and the loss of the prey due to predation, respectively. The response intensity of MP particles to the prey and predator is represented by r11 and r21, respectively. The microplastic excretion rates of prey and predator g1 and g2≥0. kC1 represents the cumulative toxicity transferred from prey to predator. Finally, S1 and S2 ≥ 0 represent the ingestion rate of microplastics by prey and predator, respectively, which is related to the bioavailability of microplastics and may be affected by the physical properties of microplastics (such as size and density) and the feeding behavior of organisms.

[0082] S5, the above S2-S4 is designed to couple the above steps with staggered time steps using the operation splitting method to truly reflect the spatial range of microplastics. First, the advection and diffusion of microplastics are coupled and simulated through S2 and S3, and split into two parts in a step [0, Δt]. The path of microplastic particles is tracked in the step time period of [0, Δt / 2] (S2), and the spatial position of the particles is diffused in the step time period of [Δt / 2, Δt] (S3), and finally the concentration distribution of microplastics is obtained. According to the obtained spatial concentration distribution of microplastics, the number of fish under the influence of microplastics is obtained in the step time period [0, Δt / 2] through the improved dynamic Lotka-Volterra model (S4), and the number of fish populations is diffused in the step time period of [Δt / 2, Δt] to obtain the final impact of microplastics on fish.

[0083] S6 simulates the unique behavior of fish schools and improves the formula based on S3: the rate of change of fish school density over time is determined by the combined effect of the inherent movement of fish schools, diffusion, and the movement of fish schools to low-concentration areas due to the microplastic concentration gradient. S5 is then repeated again, and the improved formula is as follows: is the intrinsic velocity vector of the school of fish, D u is the diffusion coefficient of the fish school, k1 is the reaction coefficient of the fish school to the microplastic concentration gradient, Gradient representing the concentration of microplastics:

[0084] The present invention proposes a coupled simulation method for the impact of marine microplastics on fish based on unstructured grids, which simulates the advection and diffusion of microplastic particles in the marine environment and considers the impact of microplastics on the number of fish. The method first initializes the microplastic concentration and the number of fish, and then uses the Lagrangian advection model to simulate the advection motion of microplastic particles, where the velocity field data is based on NASA's ECCO2 ocean current data and the Stokes drift velocity data provided by Ifremer. Then, the diffusion process of microplastic particles is simulated by the finite difference method and the Crank-Nicolson time stepping scheme, and the large-scale sparse linear system generated in the simulation is processed by the GMRES method. In addition, the present invention also considers the impact of microplastic concentration on the rate of change of fish density, and evaluates the potential impact of microplastics on fish populations through an improved dynamic Lotka-Volterra model. Finally, the above steps are coupled with staggered time steps to truly reflect the spatial distribution of microplastics, and output the distribution and migration path of microplastics, as well as the impact assessment results on fish populations.

[0085] The coupled simulation method provided by the present invention utilizes unstructured grid technology to improve the flexibility and adaptability of simulation, especially when dealing with complex marine environments, and can more effectively capture the dynamic behavior of microplastics. By coupling the Lagrangian advection model and the diffusion equation, combined with ocean current data, the present invention improves the accuracy of simulating the movement and diffusion of microplastics in the marine environment. In addition, the present invention also adopts the GMRES method and the Crank-Nicolson time stepping scheme to effectively handle the large-scale sparse linear system generated during the simulation process, improve computational efficiency, and reduce numerical errors. Compared with existing microplastic simulation methods, this coupled simulation method based on unstructured grids can greatly reduce the reliance on simplification of the marine environment, more accurately predict the distribution and migration of microplastics, and provide more effective decision support for environmental management and pollution control.

[0086] The above descriptions are only some embodiments of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A coupling algorithm based on unstructured grids to study the impact of microplastics on fish, characterized by The following steps are involved: S1, initialization variables: divide the target area into unstructured grids, initialize the concentration of microplastics and the number of fish in each grid, and obtain the zero time; S2, advection of microplastics: The advection motion of microplastic particles is simulated based on the Lagrangian advection model within a step time period of [0, Δt / 4], thereby simulating the motion trajectory of microplastic particles in the ocean; S3, Microplastics and fish diffusion: After determining the movement trajectory and spatial position of microplastic particles in the ocean, the diffusion equation of microplastic particles is solved by the finite difference method and the Crank-Nicolson time stepping scheme within a step time period of [Δt / 4, Δt / 2] to obtain the concentration distribution of microplastic particles in the water body; S4, the impact of microplastics on the number of fish: considering the changes in cell environmental concentration, cell-cell cross-diffusion and the dynamic changes in microplastic concentration, the impact of microplastic particles on fish was simulated and evaluated based on the dynamic Lotka-Volterra model within a step time period of [Δt / 2,3Δt / 4] to obtain the distribution data of fish population; S5, within the time period of step length [3Δt / 4,Δt], the diffusion processing of the fish school behavior simulation module is carried out for the number of fish populations to obtain the final impact of microplastics on the number of fish; S6, iterative update: take the microplastic concentration distribution and fish population distribution at the end of the current step as the initial value of the next step, repeat steps S2-S5, and continue iterative calculation until the predetermined calculation termination condition is reached to achieve the simulation state of the impact of microplastics on fish.

2. According to claim 1, the coupling algorithm for studying the impact of microplastics on fish based on unstructured grids is characterized in that: The Lagrangian velocity field V(t; X0) of microplastic particles in the ocean in step S2 is calculated by the following formula: V(t;X0)=v(X(t;X0),t) Where V represents the velocity field, a function determined by longitude and latitude and time; v represents the ocean velocity field; X0 is the initial position of the particle; X(t; X0) represents the position of the particle at time t when the initial position is X0; the trajectory and spatial position of the particle are obtained by numerically integrating the Lagrange advection formula, as follows: X(t=0;X0)=X0 Wherein, the velocity field V is calculated based on NASA's ECCO2 ocean current data and the Stokes drift velocity data provided by Ifremer; The coastline data in the model comes from NOAA's GSHHG high-resolution geographic dataset.

3. According to claim 1, the coupling algorithm for studying the impact of microplastics on fish based on unstructured grids is characterized in that: The acquisition of the concentration distribution of microplastic particles in the water body in step S3 comprises the following steps: (1) First, the reaction-diffusion is represented by the following semilinear parabolic partial differential equation, In the formula, u represents the diffusion field of microplastic particles, t represents time, a is the diffusion coefficient, ▽ represents the gradient, and S is the position-related input; Next, the diffusion process of microplastic particles in the ocean is simulated by numerically solving the equation; the above semilinear parabolic partial differential equation is expanded in two-dimensional space to obtain the diffusion equation in two-dimensional space, as shown in the following formula: in t =α(in xx +in yy ) In the formula, u t represents the diffusion field of microplastic particles at time t, a is the diffusion coefficient, the subscript x represents the horizontal coordinate value, and the subscript y represents the vertical coordinate value; (2) For unstructured grid division, the finite difference method is used to solve the two-dimensional space continuous diffusion equation u in step (1) t Discretize and construct a linear equation Ax=b, where b and x are expressed as follows: Solving the linear equations yields the value of x, which is the first and second derivatives of u. x ,u y ,u xx ,u yy ,u xy The approximate value of ; A represents the coefficient matrix, that is, the coefficient matrix in Taylor expansion; (3) The linear equations constructed in step (2) are iteratively solved using the GMRES method to obtain the value of x. The time derivatives are then averaged at the midpoint of the time step using the Crank-Nicolson method, as shown below: n+1 , In the formula, u n+1 and u n represents the value of the microplastic particle diffusion field u at the n+1th and nth time steps respectively; Δt represents the time step, that is, the time interval between two adjacent time steps; α is the diffusion coefficient; u xx and u yy They represent the second-order partial derivatives of the microplastic particle diffusion field u with respect to x and y, respectively.

4. According to claim 1, the coupling algorithm for studying the impact of microplastics on fish based on unstructured grids is characterized in that: Step S4 The distribution of the number of fish is obtained by constructing the following model: In the formula, C Ei They represent the derivatives of x1(t), x2(t), C1(t), and C2(t) respectively; C Ei Respectively represent the distribution of microplastic concentrations within cells in different grids; C1(t) and C2(t) represent the temporal changes in the concentrations of microplastics in the prey and predator, respectively; x1(t) and x2(t) represent the population size of prey and predator at time t, respectively; r 10 and r 20 are the intrinsic growth rate coefficient of the prey and the mortality rate coefficient of the predator when there is no toxicity; r 11 and r 21 represent the intensity of the response of microplastic particles to prey and predator, respectively; a1 and a2 are used to quantify the effect of predation on the reduction of prey population and the increase of predator population, respectively; a1x1x2 is the number of preys eaten, and a2x1x2 is the increase in the number of predators due to eating, where a1, a2>0; g1 and g2 represent the microplastic excretion rates of prey and predator, respectively, g1 and g2 ≥ 0; S1 and S2 represent the absorption rates of plastic particles by the prey and predator, respectively, S1, S2>0; d1, d2, and d3 represent the reduction in the prey’s feeding ability, the adverse effects on the predator’s performance, and the amount of loss of the prey due to predation, respectively.

5. The method of claim 1 for studying the diffusion of fish schools under the unique behavior based on unstructured grids, characterized in that: In step S5, the fish concentration diffusion equation is added while simulating the unique behavior of the fish school, so as to obtain the distribution of the number u of fish, as shown in the following improved formula: is the intrinsic velocity vector of the school of fish, represents the gradient of the number of fish, D u is the diffusion coefficient of the fish school, represents the Laplace quantity of the fish population u, k1 is the reaction coefficient of the fish population to the microplastic concentration gradient, The gradient representing the concentration of microplastic particles is used to simulate the behavior of fish schools by taking the above factors into consideration.

6. According to claim 1, the coupling algorithm for studying the impact of microplastics on fish based on unstructured grids is characterized in that: In step S6, the microplastic concentration distribution and fish population distribution at the end of the current step are used as the initial values ​​of the next step, and steps S2-S5 are repeated, and the iterative calculation is continued until the total simulation time t is reached to achieve the simulation state of the impact of microplastics on fish.

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