A coupling algorithm for studying the effects of microplastics on fish based on unstructured grids

Abstract

The application discloses a coupling algorithm for studying the influence of microplastics on fish based on an unstructured grid, and aims to deeply understand the influence of microplastics on the ecology of fish in the ocean. The method combines a Lagrangian advection model and a diffusion equation to simulate the transmission and diffusion process of microplastic particles, calculates the spatial position of each particle and tracks the trajectory of each particle by introducing real ocean current data. The GMRES method is used to solve the large-scale sparse linear system generated in the simulation process to ensure the efficiency and stability of the calculation. The Crank-Nicolson method is also used for time stepping to improve the numerical stability. The Lagrangian advection and diffusion processes are coupled by staggered time steps to truly reflect the spatial distribution of microplastics. Considering the specific behavior of the fish population, the density change rate is determined by the inherent motion, diffusion and microplastic concentration gradient, so as to evaluate the potential influence of microplastics on the marine fish ecology.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of environmental science and computational fluid dynamics, and particularly relates to a simulation method for the transport and diffusion of microplastics in water environments. BACKGROUND

[0002] Microplastics, as a type of marine pollutant with a particle size of less than 5 millimeters, have attracted widespread attention worldwide. The long-term presence of these plastic particles in marine environments poses a serious threat to the health of marine ecosystems. Existing simulation methods for microplastics have many shortcomings. For example, some methods use simple models or structured grids when dealing with complex marine environments, which cannot accurately simulate the transport and diffusion of microplastics under complex ocean current changes. Moreover, existing models do not study the quantitative impact of microplastics on fish populations. Some methods use models that do not consider the concentration differences of microplastics in different cells and the interactive diffusion between cells when simulating the impact of microplastics on fish populations, which cannot truly reflect the impact of microplastic pollution in complex and heterogeneous environments.

[0003] The present application proposes a coupling algorithm based on unstructured grids to more accurately simulate the impact of microplastics on fish. SUMMARY

[0004] The present application addresses the problems of existing technology and provides a coupling algorithm based on unstructured grids to study the impact of microplastics on fish, which solves the limitations of traditional simulation methods in dealing with the transport and diffusion of microplastics in complex marine environments, and lacks quantitative evaluation of the impact of microplastics on marine ecosystems, particularly fish populations. By coupling the Lagrangian advection model and the diffusion equation, combined with ocean current data, the present application improves the accuracy of simulating the movement and diffusion of microplastics in marine environments, providing scientific basis for environmental management and pollution control, and providing new technical means for evaluating the potential impact of microplastics on specific marine ecosystems.

[0005] TECHNICAL SOLUTION: To achieve the above-mentioned purpose of the present application, the present application adopts the following technical solution: a coupling algorithm based on unstructured grids to study the impact of microplastics on fish, comprising the following steps:

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

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

[0008] S3, microplastics and fish population diffusion: after determining the trajectory and spatial position of the microplastic particles in the ocean, the diffusion equation of the microplastic particles is solved by finite difference method and by Crank-Nicolson time stepping scheme in a step time period of [Δt / 4, Δt / 2], so as to obtain the concentration distribution of the microplastic particles in the water body;

[0009] S4, influence of microplastics on fish population: in consideration of the change of cell environmental concentration, cell interaction diffusion effect and dynamic change of microplastic concentration, the influence of microplastic particles on fish population is simulated and evaluated based on the dynamic Lotka-Volterra model in a step time period of [Δt / 2, 3Δt / 4], so as to obtain the distribution data of fish population number;

[0010] S5, in a time period with a step of [3Δt / 4, Δt], the diffusion processing of the fish population number is considered for the fish behavior simulation module, so as to obtain the final influence of microplastics on the number of fish;

[0011] S6, iterative update: the microplastic concentration distribution and fish population number distribution at the end of the current step are taken as the initial values of the next step, and steps S2-S5 are repeated for continuous iterative calculation until a predetermined calculation termination condition is reached, so as to obtain the simulation state of the influence of microplastics on fish.

[0012] Further, the Lagrangian velocity field V(t; X0) of the microplastic particles in the ocean in step S2 is calculated by the following formula,

[0013] V(t; X0) = v(X(t; X0), t)

[0014] In the formula, V represents the velocity field, which is a function determined by latitude, longitude and time; v represents the ocean velocity field; X0 is the initial position of the particle; X(t; X0) represents the position at time t when the initial position of the particle is X0; the trajectory and spatial position of the particle are obtained by numerical integration of the Lagrangian advection formula as follows:

[0015]

[0016] X(t=0; X0) = X0

[0017] In the formula, the velocity field V is calculated based on the ECCO2 ocean current data of NASA and the Stokes drift velocity data provided by Ifremer; the coastline data in the model is derived from the GSHHG high-resolution geographic data set of NOAA.

[0018] Further, the concentration distribution of the microplastic particles in the water body in step S3 includes the following steps:

[0019] (1) First, the reaction diffusion is expressed by the following semi-linear parabolic partial differential equation,

[0020]

[0021] wherein u represents the diffusion field quantity of the microplastic particle, t represents time, a is a diffusion coefficient, denotes a gradient, and S is a position-dependent input quantity;

[0022] Next, the diffusion process of the microplastic particle in the ocean is simulated by numerically solving the equation; the semi-linear parabolic partial differential equation is extended to two-dimensional space, and the diffusion equation in two-dimensional space is obtained as follows, u t = a (u xx + u yy )

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

[0024] (2) For unstructured grid partitioning, the two-dimensional continuous diffusion equation u t of step (1) is discretized by using the finite difference method, and a linear equation Ax = b is constructed, wherein b and x are expressed as follows:

[0025]

[0026] The value of x obtained by solving the linear equation set is the approximate value of the first and second derivatives u x , u y , u xx , u yy , u xy of u; A represents a coefficient matrix, i.e., the coefficient matrix in Taylor expansion;

[0027] (3) The value of x is obtained by iteratively solving the linear equation set constructed in step (2) by using the GMRES method, and then the Crank-Nicolson method is used to average the time derivative at the middle point of the time step, as follows, to obtain u n+1 ,

[0028]

[0029] wherein u n+1 and u n represent the values of the microplastic particle diffusion field quantity u at the n+1 and n time steps, respectively; Δt represents the time step, i.e., the time interval between adjacent two time steps; a is a diffusion coefficient; u xx and u yyrespectively represent the second-order partial derivatives of the diffusion field quantity u of the microplastic particles with respect to x and y.

[0030] Further, the distribution of the fish population quantity in step S4 is obtained by constructing the following model,

[0031]

[0032] wherein, C Ei respectively represent the derivatives of x1(t), x2(t), C1(t), C2(t); C Ei respectively represent the microplastic concentration distribution in the unit cell in different grids;

[0033] C1(t) and C2(t) respectively represent the changes of the microplastic concentrations in the prey and the predator over time;

[0034] x1(t) and x2(t) respectively represent the population quantities of the prey and the predator at time t;

[0035] r 10 and r 20 respectively are the intrinsic growth rate coefficient of the prey and the mortality rate coefficient of the predator without toxicity;

[0036] r 11 and r 21 respectively represent the response strength of the microplastic particles to the prey and the predator;

[0037] a1 and a2 are respectively used to quantify the effects of the predation behavior on the decrease of the prey quantity and the increase of the predator quantity; a1 x1 x2 is the quantity of the prey being preyed on, and a2 x1 x2 is the quantity of the predator being increased due to the feeding, wherein a1, a2 > 0;

[0038] g1 and g2 respectively represent the microplastic excretion rates of the prey and the predator, g1, g2 ≥ 0;

[0039] S1 and S2 respectively represent the absorption rates of the plastic particles of the prey and the predator, S1, S2 > 0;

[0040] d1, d2 and d3 respectively represent the decrease of the prey's feeding capacity, the adverse effect of the predator's performance, and the loss of the prey being preyed on.

[0041] Further, in step S5, the fish concentration diffusion equation is added while simulating the unique behavior of the fish population, so as to obtain the distribution of the quantity u of the fish, as shown in the following improved formula,

[0042]

[0043] is the inherent velocity vector of the fish population, represents the gradient of the fish population number, D u is the diffusion coefficient of the fish population, represents the Laplacian of the fish population number u, k1 is the reaction coefficient of the fish population to the microplastic concentration gradient, represents the gradient of the microplastic particle concentration, and the above factors are comprehensively considered to simulate the fish behavior.

[0044] Further, in step S6, the microplastic concentration distribution and the fish population number distribution at the end of the current step are taken as the initial values of the next step, and steps S2-S5 are repeated to continuously iterate until the total simulation time t is reached, so as to obtain the simulation state of the influence of microplastics on fish

[0045] Advantages: Compared with the prior art, the present application has the following advantages:

[0046] (1) The microplastic ocean diffusion simulation method based on unstructured grid provided by the present application couples the Lagrangian advection model and the diffusion equation to realize accurate simulation of the transmission and diffusion of microplastic particles in the marine environment, thereby improving the accuracy and reliability of the simulation results.

[0047] (2) Compared with the traditional simulation method, the GMRES method and the Crank-Nicolson time stepping scheme used in the present application effectively handle the large-scale sparse linear system generated during the simulation process, improve the calculation efficiency, reduce the numerical error, and make the distribution and migration prediction of microplastics more stable and accurate.

[0048] (3) The present application also considers the influence of microplastics on the fish population number, and simulates the influence of the microplastic concentration gradient on the fish population density change rate, thereby providing a more comprehensive scientific basis for evaluating the potential threat of microplastics to the marine ecosystem, and providing more effective decision support for environmental management and pollution control. BRIEF DESCRIPTION OF DRAWINGS

[0049] Figure 1 is a logic diagram of the coupling algorithm for studying the influence of microplastics on fish in unstructured grid in the embodiments of the present application;

[0050] Figure 2 is an algorithm flowchart of the coupling algorithm for studying the influence of microplastics on fish in unstructured grid in the embodiments of the present application;

[0051] Figure 3 is an unstructured grid in the coupling algorithm for studying the influence of microplastics on fish in unstructured grid in the embodiments of the present application;

[0052] Figure 4The final simulation results of the coupling algorithm for studying the influence of microplastics on fish in the embodiments of the present application are obtained. DETAILED DESCRIPTION

[0053] The present application will be further illustrated by the following specific examples, which are only used to illustrate the present application and not used to limit the scope of the present application. After reading the present application, those skilled in the art can make various equivalent modifications of the present application, which fall within the scope defined by the appended claims.

[0054] In order to deeply understand the influence of microplastics on fish ecology in the ocean, the present application provides a simulation method based on unstructured grids for studying the influence of microplastics on fish ecology in the ocean. The method couples the Lagrangian advection model and the diffusion equation to simulate the transport 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 Crank-Nicolson method is used for time stepping to improve the 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, the specific behavior of the fish population is considered, and the rate of change of its density is determined by the inherent motion, diffusion and microplastic concentration gradient, so as to evaluate the potential influence of microplastics on marine fish ecology.

[0055] As shown in Figure 1 and 2 , the coupling algorithm of the present application is implemented by the following steps, including the following steps: first, initialize the variable module based on the unstructured grid as Figure 3 , and set the initial state of microplastics and fish population in the actual environmental data and ecological survey data; then, the Lagrangian advection module calculates the advection motion of microplastic particles using the ECCO2 ocean current data of NASA and the Stokes drift velocity data provided by Ifremer; then, the diffusion equation module simulates the diffusion process of microplastic particles using the finite difference method and the Crank-Nicolson time stepping scheme; the microplastic and fish population interaction module evaluates the influence of microplastics on the number of fish population by the improved dynamic Lotka-Volterra model;

[0056] The numerical solution module is responsible for solving the diffusion equation, and the GMRES iterative solution module handles the linear system generated in the simulation; finally, the fish population behavior simulation module considers the response of the fish population 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, as shown in Figure 4 .

[0057] S1, initialize variables

[0058] Initialize the microplastic concentration and fish population in the area to be calculated, where the microplastic concentration is set according to actual environmental data, and the fish population is set according to ecological survey data; and mark the latitude and longitude of the specific location, where a predetermined number of microplastic particles are discharged, and the number and characteristics of the particles are determined according to experimental design or field sampling data.

[0059] S2, advection of microplastics

[0060] The advection of microplastic particles is simulated using the Lagrangian advection formula, which describes the state of the particles as a function of time. For a particle with initial position X0, the formula for the Lagrangian velocity V(t, X0) is: V(t; X0) = v(X(t; X0), t). Where V represents the velocity field, which is a function determined by latitude, longitude and time. The trajectory of the particle can be obtained by numerical integration of the Lagrangian advection formula:

[0061]

[0062] X(0; X0) = X0

[0063] The velocity field V is calculated based on the ECCO2 ocean current data from NASA and the Stokes drift velocity data provided by Ifremer. The ECCO2 data has a time 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 the GSHHG high-resolution geographic data set from NOAA. Through these data, the trajectory of the microplastic particles in the ocean can be accurately simulated, and the spatial position of the particles is updated at each time point.

[0064] S3, diffusion of microplastics and fish population

[0065] After determining the spatial position of each particle, a diffusion equation is introduced to describe the transport, diffusion and interaction of microplastic particles in the water body, and a finite difference method is used to simulate the transport and diffusion process of the particles. Unstructured grids are used to improve the flexibility and adaptability of the simulation, with the following steps:

[0066] Step (1): Use semi-linear parabolic partial differential equations to describe the reaction-diffusion system. They can be expressed in general form as:

[0067]

[0068] Where t represents time, u represents the diffusion field, and a is the diffusion coefficient, is the gradient, S is the position-dependent input quantity. By numerically solving the equation, the diffusion process of the substance in the marine environment can be simulated.

[0069] In two-dimensional space, assuming the horizontal direction is the x-axis and the vertical direction is the y-axis, the equation is extended to two-dimensional space, and the diffusion equation becomes: u t = α (u xx + u yy );

[0070] Step (2): Discretize the continuous equation using the finite difference method. By expanding the Taylor series of u on an unstructured grid, we can obtain approximate expressions for the first and second derivatives. For example, for a point u0 = u(x0, y0) and its point u1 = u(x1, y1) in two-dimensional space, the Taylor expansion can be approximated as:

[0071]

[0072] where Δx = x1 - x0, Δy = y1 - y0;

[0073] Through the above approximation, we can construct a linear equation system Ax = b, where

[0074]

[0075] The coefficient matrix A is composed of the coefficients in the Taylor expansion, which relates the derivatives of u to the difference between neighboring points. To solve the derivatives, we use the least squares method to find the best fit, i.e., solve the linear equation system Ax = b, so that the sum of the squares of the errors is minimized;

[0076] Step (3): To improve numerical stability, the Crank-Nicolson method is used for time stepping. This method averages the time derivative at the midpoint of the time step to obtain an implicit formula:

[0077]

[0078] where u n+1 and u n represent the field quantity at time steps n + 1 and n, respectively;

[0079] Step (4): For the large-scale sparse linear system generated in the unstructured grid simulation, the GMRES method is used for iterative solution, ensuring the efficiency and stability of the calculation. The Generalized Minimum Residual (GMRES) method is an iterative algorithm for solving nonsymmetric linear systems. The core idea is to find an approximate solution in the Krylov subspace that minimizes the norm of the residual vector. The GMRES method does not require the matrix to be symmetric positive definite, so it has 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.

[0080] S4, the impact of microplastics on fish population

[0081] To more accurately simulate the impact of microplastics pollution in complex and heterogeneous environments, the dynamic Lotka-Volterra model was improved. Considering that different cells may have different levels of microplastic concentration, we changed the environmental concentration from a single constant CE to a different CEi for each cell. In addition, we also considered the interactive diffusion effect between cells and the dynamic change of microplastic concentration, thereby improving the applicability and accuracy of the model in simulating real-world conditions. These modifications enable us to capture the complex effects of microplastic pollution on the dynamics of predator-prey populations in ecosystems in more detail, resulting in the following model:

[0082] where x1(t), x2(t), C1(t), C2(t), t ≥ 0. This model ignores the effects of intraspecific competition and shows the effects of microplastics through the environmental concentration CEi of each cell. C1(t) and C2(t) represent the changes in microplastic concentrations in the prey and predator over time, respectively. x1 and x2 represent the population sizes of the prey and predator, respectively. r10 x1 and r20 x2 are the intrinsic growth rates of the prey and the death rates of the predator without toxicity, respectively. a1 x1 x2 is the number of prey being preyed upon, and a2 x1 x2 is the increase in the number of predators due to feeding, where a1, a2 > 0. The parameters d1, d2, and d3 represent the decline in the prey's foraging ability, the adverse effects on the predator's performance, and the loss of prey due to predation, respectively. The response strengths of microplastics to the prey and predator are represented by r11 and r21, respectively. The microplastic excretion rates of the prey and predator are g1, g2 ≥ 0. kC1 represents the cumulative toxicity transferred from the prey to the predator. Finally, S1 and S2 ≥ 0 represent the uptake rates of microplastics by the prey and predator, respectively, which are related to the bioavailability of microplastics and may be influenced by the physical properties of microplastics (such as size and density) and the feeding behavior of organisms.

[0083] S5, using the operation splitting method design of S2-S4 above to couple the above steps at staggered time steps, truly reflecting the spatial range of microplastics. First, the advection and diffusion of microplastics are coupled and simulated by S2, S3, which is split into two parts in a step [0, Δt], the particle path of microplastics is tracked in the step time period [0, Δt / 2] (S2), and the spatial position of the particle is diffused in the step time period [Δt / 2, Δt] (S3), and finally the concentration distribution of microplastics is obtained. According to the obtained spatial concentration distribution of microplastics, the improved dynamic Lotka-Volterra model (S4) is used to obtain the fish population under the influence of microplastics in the step time period [0, Δt / 2], and the fish population is diffused in the step time period [Δt / 2, Δt], and the final influence of microplastics on fish is obtained.

[0084] S6, the unique behavior of the fish population is simulated, and the formula is improved based on S3: the change rate of fish density with time is determined by the comprehensive effect of the inherent motion of the fish population, diffusion and the movement of the fish population to the low concentration area due to the concentration gradient of microplastics, and then S5 is repeated again, and the improved formula is as follows, is the inherent velocity vector of the fish population, D u is the diffusion coefficient of the fish population, k1 is the reaction coefficient of the fish population to the concentration gradient of microplastics, and ▽v represents the gradient of the concentration of microplastics:

[0085] The present application provides a coupling simulation method for the influence of marine microplastics on fish based on unstructured grids, which simulates the advection and diffusion of microplastic particles in the marine environment while considering the influence of microplastics on the number of fish population. The method first initializes the concentration of microplastics and the number of fish population, then simulates the advection motion of microplastic particles by using the Lagrangian advection model, wherein the velocity field data is based on the ECCO2 ocean current data of NASA and the Stokes drift velocity data provided by Ifremer. Then, the finite difference method and Crank-Nicolson time stepping scheme are used to simulate the diffusion process of microplastic particles, and the GMRES method is used to process the large-scale sparse linear system generated in the simulation. In addition, the present application also considers the influence of microplastic concentration on the change rate of fish density, and evaluates the potential influence of microplastics on fish population by using the improved dynamic Lotka-Volterra model. Finally, the above steps are coupled at staggered time steps to truly reflect the spatial distribution of microplastics, and the distribution and migration path of microplastics and the influence evaluation result of fish population are output.

[0086] The coupling simulation method provided by the application improves the flexibility and adaptability of simulation by using unstructured grid technology, especially in dealing with complex marine environment, which 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 application improves the accuracy of simulating the movement and diffusion of microplastics in the marine environment. In addition, the application also uses 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 the calculation efficiency, and reduce the numerical error. Compared with existing microplastic simulation methods, this coupling simulation method based on unstructured grid can greatly reduce the dependence on the 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. The above is only part of the embodiments of the application, it should be pointed out that for ordinary skilled in the art, without departing from the principles of the application, a number of improvements and refinements can be made, these improvements and refinements should also be considered as the protection scope of the application.

Claims

1. A coupling algorithm for studying the impact of microplastics on fish based on unstructured mesh characterized in that The method comprises the following steps: S1, initializing variables: performing unstructured grid division on a target area, initializing and setting the microplastic concentration and fish population in each grid to obtain the zero time; S2, advection of microplastics: simulating the advection movement of microplastic particles based on the Lagrangian advection model in a step time period of [0, Δt / 4], so as to simulate the movement trajectory of the microplastic particles in the ocean; S3, diffusion of microplastics and fish population: after determining the movement trajectory and spatial position of the microplastic particles in the ocean, the diffusion equation of the microplastic particles is solved by the finite difference method and by the Crank-Nicolson time stepping scheme in a step time period of [Δt / 4, Δt / 2], so as to obtain the concentration distribution of the microplastic particles in the water body; S4, influence of microplastics on fish population: based on the dynamic Lotka-Volterra model, the influence of the microplastic particles on the fish population is simulated and evaluated in a step time period of [Δt / 2, 3Δt / 4] by considering the cell environmental concentration change, the cell interaction diffusion effect and the dynamic change of the microplastic concentration, so as to obtain the distribution data of the fish population; S5, in a time period with a step of [3Δt / 4, Δt], the diffusion processing of the fish population quantity is performed by considering the fish behavior simulation module, so as to obtain the final influence of the microplastics on the quantity of the fish; S6, iterative updating: the microplastic concentration distribution and the fish population quantity distribution at the end of the current step are taken as the initial values of the next step, and steps S2-S5 are repeated for continuous iterative calculation until a predetermined calculation termination condition is reached, so as to obtain the simulation state of the influence of the microplastics on the fish; The distribution of the fish population quantity is obtained by constructing the following model, wherein C Ei respectively denote the derivative of x1(t), x2(t), C1(t), C2(t); C Ei respectively denote the microplastic concentration distribution within the cells in different grids; C1(t) and C2(t) represent the changes of the microplastic concentrations in the prey and the predator with time, respectively; x1(t) and x2(t) represent the population quantities of the prey and the predator at time t, respectively; r 10 and r 20 are the intrinsic growth rate coefficient of the prey and the mortality coefficient of the predator, respectively, in the absence of toxicity. r 11 and r 21 respectively represent the response strength of the microplastic particles to the prey and the predator. a1 and a2 are used to quantify the influence of the predation behavior on the decrease of the prey quantity and the increase of the predator quantity, respectively; a1 x1 x2 is the quantity of the prey being preyed on, and a2 x1 x2 is the quantity of the predator being increased due to feeding, wherein a1, a2 > 0; g1 and g2 represent the microplastic excretion rates of the prey and the predator, respectively, and g1, g2 ≥ 0; S1 and S2 represent the absorption rates of the plastic particles of the prey and the predator, respectively, and S1, S2 > 0; 2. The coupling algorithm for studying the impact of microplastics on fish based on unstructured grids according to claim 1, characterized in that, d1, d2 and d3 represent the decrease of the prey's feeding capacity, the adverse effect of the predator's performance and the loss of the prey being preyed on, respectively. The Lagrangian velocity field V(t; X0) of the microplastic particles in the ocean in step S2 is calculated by the following formula, V(t; X0) = v(X(t; X0), t) In the formula, V represents the velocity field, which is a function determined by the latitude and longitude and time; v represents the ocean velocity field; X0 is the initial position of the particle; X(t; X0) represents the position at time t when the initial position of the particle is X0; the trajectory and spatial position of the particle are obtained by numerically integrating the Lagrangian advection formula as follows: X(t=0; X0) = X0 In the formula, the velocity field V is calculated based on the ECCO2 ocean current data of NASA and the Stokes drift velocity data provided by Ifremer; The coastline data in the model is derived from the GSHHG high-resolution geographic data set of NOAA.

3. The coupling algorithm for studying the effects of microplastics on fish based on unstructured grids according to claim 1, characterized in that, The obtaining of the concentration distribution of the microplastic particles in the water body in step S3 includes the following steps: (1) First, the reaction diffusion is represented by the following semi-linear parabolic partial differential equation, In the formula, u represents the diffusion field quantity of the microplastic particles, t represents time, a is a diffusion coefficient, ∇ represents a gradient, and S is a position-dependent input quantity; Then, the diffusion process of the microplastic particles in the ocean is simulated by numerically solving the equation; the semi-linear parabolic partial differential equation is extended to two-dimensional space to obtain a diffusion equation in two-dimensional space, as shown in the following formula, u t = a(u xx + u yy ) In the formula, u t represents the diffusion field of the 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 discretize the two-dimensional space continuous diffusion equation u t of step (1), and a linear equation Ax = b is constructed, where b and x are expressed as follows: Solving the linear equations for the value of x, which is the first and second derivative of u x , u y , u xx , u yy , u xy approximation; A represents the coefficient matrix, that is, the coefficient matrix in Taylor expansion; (3) The value of x is obtained by solving the linear equations constructed in step (2) using the GMRES method, and then the Crank-Nicolson method is used to average the time derivative at the middle point of the time step, as follows, to obtain u n+1 , where u n+1 and u n denote the value of the microplastic particle diffusion field u at the (n+1)th and nth time steps, respectively; At denotes the time step, i.e. the time interval between two adjacent time steps; a is the diffusion coefficient; u xx and u yy denote the second-order partial derivatives of the microplastic particle diffusion field u with respect to x and y, respectively.

4. The coupled algorithm for studying the effects of microplastics on fish based on unstructured grids of claim 1, wherein: In step S5, the fish concentration diffusion equation is added while simulating the specific behavior of the fish school, so as to obtain the distribution of the number u of the fish, as shown in the following improved formula, is the inherent velocity vector of the fish population, ∇u represents the gradient of the fish population number, D u is the diffusion coefficient of the fish population, ∇ 2 u represents the Laplacian of the fish population number u, k1 is the reaction coefficient of the fish population to the gradient of microplastic concentration, ∇v represents the gradient of the microplastic particle concentration, and the above factors are comprehensively considered to simulate the fish behavior.

5. The coupling algorithm for studying the effects of microplastics on fish based on unstructured grids according to claim 1, characterized in that, In step S6, the microplastic concentration distribution and the fish number distribution at the end of the current step are taken as the initial values of the next step, and steps S2-S5 are repeated for continuous iteration calculation until the total simulation time t is reached, so as to obtain the simulation state of the influence of the microplastic on the fish.

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