CN112163364B - Fluid-solid coupling simulation method for fish school movement in marine environment - Google Patents

Fluid-solid coupling simulation method for fish school movement in marine environment Download PDF

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CN112163364B
CN112163364B CN202011179361.9A CN202011179361A CN112163364B CN 112163364 B CN112163364 B CN 112163364B CN 202011179361 A CN202011179361 A CN 202011179361A CN 112163364 B CN112163364 B CN 112163364B
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刘妹琴
胡双
张森林
郑荣濠
吴争光
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Zhejiang University ZJU
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Abstract

The invention discloses a fluid-solid coupling simulation method for fish school movement in a marine environment, which can be used for solving the influence of movement and convection field of fish schools with small volume and large quantity in a large-scale flow field. The invention adopts finite elements to establish a flow field, takes a small solid in the flow field as a point with the properties of coordinates, speed and acceleration, determines the acting force of the flow field on the solid by a centralized parameter method, and simultaneously feeds back the force to the flow field as an additional force of the finite element where the solid point is positioned, thereby realizing fluid-solid coupling. The invention aims at the condition that the flow field area is far larger than the size of the solid, avoids the solid modeling part in the traditional fluid-solid coupling, simultaneously realizes the dynamic response of the fluid-solid coupling, and greatly saves the calculated amount and the modeling difficulty.

Description

Fluid-solid coupling simulation method for fish school movement in marine environment
Technical Field
The invention belongs to the field of fluid analysis, relates to flow field simulation and centralized parameter method modeling, and particularly relates to a fluid-solid coupling simulation method for fish school movement in a marine environment.
Background
Fluid-solid coupling mechanics is a mechanical branch generated by crossing fluid mechanics and solid mechanics, and is a science for researching the interaction of various behaviors of a deformed solid under the action of a flow field and the influence of solid configuration on the flow field. An important characteristic of fluid-solid coupling mechanics is the interaction between two media, and a deformed solid can deform or move under the action of fluid load. The deformation or movement in turn affects the fluid movement, thereby changing the distribution and magnitude of the fluid load, and it is this interaction that will produce various fluid-solid coupling phenomena under different conditions.
The core of the coupled solution process is to compute the unsteady flow problem with moving boundaries and moving meshes, since the size and shape of the flow field is constantly changing as the structure moves or deforms. Meanwhile, due to the fact that linear and nonlinear problems are mixed in the coupling system, symmetric and asymmetric matrixes exist, the dominant and recessive coupling mechanisms are included, and physical instability conditions occur, so that the coupling problem is very difficult to solve. According to different coupling boundary processing methods, fluid-solid coupling solving methods are mainly divided into two types: the immersion Boundary Method (Immersed Boundary Method) and the Moving Boundary Method (Moving Boundary Method).
Solids in the ocean, such as fish stocks, are unique in that the geometric dimensions are negligible compared to the sea area to be studied, but the large number per se makes it impossible to neglect the influence of the flow field when calculating the flow field.
The traditional moving boundary method regards the objects as porous sparse media, but the method enables a large number of small objects to be equivalent to a solid with a specific shape, so that the relative positions of the solid need to be close and cannot be changed greatly, and the sparsity coefficients at each position cannot be changed, and the actual situation cannot be reflected.
Disclosure of Invention
In order to solve the problems, the invention provides a fluid-solid coupling simulation method for fish school movement in a marine environment. The invention adopts finite elements to establish a flow field, treats a fish school in the flow field as a point with the properties of coordinates, speed and acceleration, determines the acting force of the flow field on the object by a centralized parameter method, and simultaneously feeds back the force to the flow field as additional force of the finite element where the solid point is positioned, thereby realizing fluid-solid coupling. The invention aims at fish schools with flow field areas far larger than the solid size, avoids the solid modeling part in the traditional fluid-solid coupling, simultaneously realizes the dynamic response of the fluid-solid coupling, and greatly saves the calculated amount and the modeling difficulty.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a fluid-solid coupling simulation method for fish school movement in marine environment comprises the following steps:
1) establishing a flow field model and a solid motion model by taking a marine environment as a flow field and a fish school as a solid point, and initializing;
the flow field model comprises Ele ═ { Lnct, Led, EVol, Mstat }, and the vertex attributes forming the finite elements comprise Po ═ { PX, PVol, U, Pre, T }; ele represents an attribute set of finite elements, Lnct is a set of finite element vertex numbers, Led is a set of adjacent finite element numbers sharing a surface with the finite elements, EVol is the volume of the finite elements, and Mstat is a judgment on whether the finite elements are searched when the finite elements where the solid points are located are searched; PX represents the position coordinates of the vertex, PVol represents the volume occupied by the vertex, U represents the velocity of the vertex in three directions, Pre represents the pressure of the vertex, and T represents the temperature of the vertex;
the attributes of each solid point in the solid motion model comprise Co ═ Loc, CX, Cm, CVol, CU }; wherein Co represents an attribute set of the solid point, Loc is the number of a finite element where the solid point is located, CX is the coordinate of the solid point, Cm is the mass of the solid point, CVol is the volume of the solid point, and CU is the speed of the solid point;
2) updating the serial numbers of the finite elements of the flow field where each solid point is located along with the movement of the fish school; after updating, calculating the influence weight coefficient of the solid point to each vertex in the finite element
Figure BDA0002749709640000021
According to the influence weight coefficient
Figure BDA0002749709640000022
Determining the vertex attribute of a finite element where the solid point is located, and taking the vertex attribute as a flow field parameter where the solid point is located; obtaining the interaction force Fl of the flow field and the solid according to the flow field parameters of the solid point and the self-attribute of the solid pointc；
3) According to the interaction force Fl of the flow field and the solidcUpdating the attribute parameters of the solid points;
4) according to the influence weight coefficient
Figure BDA0002749709640000023
The interaction force Fl of the flow field and the solidcDistributing the vertex of the finite element where the solid point is located to obtain the additional acting force of the vertex; updating the volume of a finite element where the solid point is located and the volume of a vertex forming the finite element according to the additional acting force to finish updating the convection field;
5) repeating the steps 2) to 4) until a preset step length is reached; and outputting the flow field and solid parameters according to a preset time interval to form the dynamic response of fluid-solid coupling of fish swarm movement along with time under the marine environment.
Preferably, the finite element is a triangular mesh, a tetrahedral mesh or a right triangular prism mesh.
Preferably, as the fish school moves, searching and updating the serial numbers of the finite elements of the flow field where each solid point is located by adopting an extensive search algorithm; the method specifically comprises the following steps:
setting up search sequence Ltc ═ { e ═ e1,...,emIn which eiThe number of the ith finite element in the search sequence is m;
initially, m is 1, only one element in a search sequence is a finite element number where a solid point is located at the last moment, and Mstat in the finite element attribute is 1, which indicates that the finite element is added into the search sequence;
searching finite elements in the search sequence one by one along with the movement of the solid point, and if the solid point exists in the searched finite elements, zeroing the Mstat attribute of the finite element where the solid point is located; if the solid point does not exist in the searched finite element, adding the finite element which is adjacent to the finite element and is not searched into a search sequence, and starting to search the next finite element according to the search sequence;
repeating the above process until the finite element where the solid point is located is searched.
Preferably, in the searching process by adopting the breadth searching algorithm, aiming at the finite element to be searched, the coordinates of the solid point are replaced by the n-th vertex coordinates forming the finite element to be searched to form a determinant
Figure BDA0002749709640000031
Each row represents the three-dimensional coordinates of the ith point if
Figure BDA0002749709640000032
The solid point is present in the finite element, otherwise it is not present.
Preferably, the method of step 2) calculates the influence weight coefficient of the solid point on each vertex in the finite element
Figure BDA0002749709640000033
The calculation formula is as follows:
Figure BDA0002749709640000034
in the formula (I), the compound is shown in the specification,
Figure BDA0002749709640000035
representing the tetrahedral volume formed by the solid point and the vertex except the nth vertex in the finite element.
In the present invention, the sum of the influence weight coefficients of the vertices constituting the finite element having the solid point and the solid point is preferably 1.
As a preferable aspect of the present invention, the attribute parameter update of the solid dots is realized by a governing equation expressed as:
Figure BDA0002749709640000036
wherein (cx, cy, cz) is the coordinate of the solid point, (cu, cv, cw) is the velocity of the solid point in three directions, Cm is the mass of the solid point, FlcFl being the interaction force of the flow field with the solidx,c、Fly,c、Flz,cIs FlcComponents in the directions of the x-axis, the y-axis, and the z-axis, respectively; fcIs an interaction force between solids, Fx,c、Fy,c、Fz,cIs FcThe components in the x-axis, y-axis, and z-axis directions, respectively.
Preferably, the step 4) is specifically:
4.1) interaction force Fl of flow field and solidcAnd (3) allocating the vertex of the finite element where the solid point is located to obtain the additional acting force of the vertex:
Figure BDA0002749709640000041
in the formula PQnIs the additional force of the nth vertex, FlcIs the interaction force of the flow field and the solid,
Figure BDA0002749709640000042
is the impact weight coefficient;
4.2) subtracting the volume of the solid point from the volume of the finite element, and updating the volume of the finite element where the solid point is located; and updating the vertex volumes constituting the finite element; the vertex volume calculation formula is as follows:
Figure BDA0002749709640000043
in the formula, sigma EVol represents the sum of finite element volumes of a vertex participating in construction, and N represents the number of finite elements participating in construction of the vertex;
4.3) updating the physical force applied to each vertex of the finite element:
f′pn＝fpn-PQn
in the formula (f)pnIs the physical strength, f ', of the n-th vertex before update'pnIs the physical strength to which the nth vertex is subjected after updating;
and (4) allowing the updated physical power to enter a limit element vertex attribute control equation, completing the updating of the finite element vertex attribute, and completing the updating of the flow field.
Compared with the prior art, the invention has the advantages that:
1) aiming at the application of a large number of fish schools in the ocean, the fish schools are simplified into points with certain volumes, flow field parameters of solid points are determined, acting force exerted on solids in the flow field is calculated in solid calculation, so that mutual acting force is obtained, the mutual acting force is regarded as physical force of flow field units, and the influence of the solids on the flow field is realized. The method reduces the requirement on grid division, avoids the increased calculation amount of dynamic grid calculation, and can realize simultaneous calculation of a large number of points in a flow field and only increase a small calculation amount.
2) The invention considers the fluid-solid coupled acting force as a physical force of a fluid finite element, but not the acting force outside the boundary of a dynamic boundary method. Although the traditional immersion boundary method also considers the fluid-solid coupling force as physical force, the traditional immersion boundary method still has definite boundary distinction between solid and fluid, the solid volume or boundary is not negligible relative to a finite element unit, and the solid part is a finite element region without flowing substantially in calculation, but is not the concentrated parameter modeling adopted by the invention.
3) The invention selects the volume to calculate the weight coefficient, and does not calculate the weight coefficient by the connecting line length of the solid point and other vertexes, so the advantage that the flow field force acting on the solid point and the solid acting force acting on each point can not generate mutation when the finite element of the solid point is changed by using the volume as the weight coefficient.
Drawings
FIG. 1 is a flow chart of the fluid-solid coupling method of the present invention.
Fig. 2 is a schematic diagram of the solution region Ω and its boundary Γ.
Fig. 3 is a schematic two-dimensional partial view.
Fig. 4 is a flowchart of a search algorithm in the present embodiment.
FIG. 5 is a schematic diagram of solid point and finite element coupling.
Detailed Description
The invention is further explained below with reference to the drawings.
The fluid-solid coupling method provided by the invention is implemented by embedded calculation of a finite element method and a centralized parameter method, and the main idea of the special case that the solid geometric dimension is far smaller than the flow field grid size comprises the following contents:
establishing a flow field model and a solid motion model, and initializing;
establishing a fluid-solid coupling frame, determining the serial number of the flow field finite element where each solid point is located when the time step begins, and then determining the mutual influence weight coefficient of each vertex formed by the solid to the finite element in the finite element where the solid point is located
Figure BDA0002749709640000052
By influencing the weight coefficient
Figure BDA0002749709640000053
Determining the flow velocity, flow field acceleration and pressure of a flow field where the solid point is located, and determining the interaction force of the flow field and the solid according to the flow field parameters where the solid is located and the dynamic parameters of the solid such as volume, velocity and acceleration.
At this time, the state of the solid point C can be updated by the following method: the interaction between the solids is determined according to the motion relation between the solid points, for example, the fish in the fish swarm can exert a force on water in addition in order to keep relative rest, the relation is converted to the acceleration of the solids, and finally the requirements on the speed and the position of the solids are realized.
And then performing flow field updating iteration, wherein the method comprises the following steps: firstly, updating a finite element where a solid point is located, and enabling interaction force to pass through an influence weight coefficient
Figure BDA0002749709640000051
Additional forces assigned to the finite elements forming the vertices, and then updating or subtracting the volume of the solid point for the finite element volumeAnd then updating the volume of the vertex formed by the finite element, and then performing traditional flow field calculation.
The method is characterized in that a marine environment is used as a flow field, a fish school is used as a solid, a finite element method and a lumped parameter method are adopted for embedding and calculating fluid-solid coupling, the following embodiment aims at modeling of a 3-dimensional space, a grid is a tetrahedral grid, and a fish school model is selected for the solid. The 2-dimensional approach is similar to the 3-dimensional approach, only reducing the dimensions of the parameters.
For the fluid equations referred to below, the finite element principle will be briefly described by taking a second-order elliptic linear partial differential equation as an example. As shown in FIG. 2, let Ω be a bounded area on a plane, whose boundary
Figure BDA0002749709640000061
Is sufficiently smooth. Consider the following second order variable coefficient elliptic equation:
Figure BDA0002749709640000062
wherein alpha (x, y)>0, beta (x, y) ≧ 0, and f (x, y) is defined as
Figure BDA0002749709640000063
A substantially smooth function of (a). This equation describes many time-varying natural phenomena such as elastic membrane equilibrium, thermal or molecular diffusion, electrostatic or static fields, and incompressible, swirl-free fluids, among others, and many of the equations below can be considered as deformations.
Let the boundary Γ of Ω be divided into two mutually disjoint parts Γ 1 and Γ 2, on which two types of boundary conditions are given respectively:
Figure BDA0002749709640000064
Figure BDA0002749709640000065
wherein
Figure BDA0002749709640000066
Psi, gamma are known functions on the boundary and gamma ≧ 0, n is the outer normal direction on the boundary. That is, a first type of boundary condition is given on Γ 1, and a third type of boundary condition is given on Γ 2 (a second type of boundary condition when γ ═ 0).
For the above problem solution, the Galerkin method is used. The Galerkin method is derived from the virtual work principle, and means that when any displacement satisfying the condition (actually, no displacement exists, called virtual displacement) is given in the equilibrium state, the work of the external force of the object is equal to the work of the inertial force applied to the object. Namely, it is
Sigma (external force-inertial force, virtual displacement) is 0
Defining the allowable function class as:
Figure BDA0002749709640000067
C1representing that the functions are first order derivable, then each function in M is a "possible displacement".
Let u e M and u second order can be a solution to the edge value problem (1) - (3). Taking v ∈ M, multiplying v by the two ends of equation (1), and then integrating over Ω:
Figure BDA0002749709640000068
using Green formula, obtaining from boundary conditions (2) - (3)
Figure BDA0002749709640000071
Substituting the above formula into (7) to obtain
Figure BDA0002749709640000072
For ease of discussion, we define a bilinear functional:
Figure BDA0002749709640000073
and a linear functional:
Figure BDA0002749709640000074
substituting the formulas (10) and (11) into the formula (9) to obtain:
α(u,v)＝F(v) (12)
i.e. the solution u of the edge value problem satisfies equation (12).
Conversely, if there is u e M that satisfies (12) for any v e M, then when u is second order conductive, it must be the solution of the edge value problem (1) - (3).
We call equation (12) the "weak" form of the equivalent integral of equation (1) because the derivative contained in equation (12) is reduced in order. In fact, the requirement for u continuity is reduced in equation (12) at the expense of improving v continuity, but it is not difficult to properly improve the continuity requirement because they are known functions that can be chosen, and we choose to have v and u in the same function space M in the Galerkin method.
To approximate the problem in an infinite dimensional space to that of a finite dimensional space, the equation is discretized, assuming that M is divisible, i.e., there is a dense subset of the counties in M. Taking a finite dimension subspace S in MNIt is composed of N linearly independent vectors
Figure BDA0002749709640000075
What is meant is that:
Figure BDA0002749709640000076
then solving equation (12) becomes at SNSolving an approximate variational equation: find uN∈SNSo that:
Figure BDA0002749709640000081
solving for u by Galerkin methodNOnly by solving a linear algebraic system of equations. In fact, due to uN,wN∈SNTherefore, it can be set as follows:
Figure BDA0002749709640000082
substituting into formula (14) to obtain:
Figure BDA0002749709640000083
from diAn arbitrary property of (i ═ 1.. N), can be obtained
Figure BDA0002749709640000084
That is, an approximate solution to the variational problem is obtained by solving a system of linear algebraic equations (17).
For convenience of representation, the system of equations (17) is written in matrix form and is written as:
c＝[c1,c2,...cn]T
Figure BDA0002749709640000085
M＝[mij]wherein
Figure BDA0002749709640000086
K＝[kij]Wherein
Figure BDA0002749709640000087
Figure BDA0002749709640000088
It can be deduced that:
Figure BDA0002749709640000089
it is worth noting that the "weak" form formally has reduced continuity requirements for the function u, but often more closely approximates a true solution to practical physical problems than the original differential equation, which often places undue "smoothing" requirements on the solution.
We are not actually aware of SNThe specific expression of the basis for which the requirement is only linearly independent, the weighting factors appearing hereinafter being M-1And a certain subentry of the product term of the corresponding node in the final result of the K matrix. The requirement for the weight coefficients is actually due to the partial derivatives, which require mathematical expressions that can have first order partial derivatives. In fluid-solid coupling, solid nodes can be regarded as an added group of bases, so the continuity requirement of the weight coefficients in fluid-solid coupling is consistent with the continuity requirement of the weight coefficients of fluid nodes, so that an expression similar to that of the fluid nodes is adopted.
The above proof is to partly explain the theoretical basis of modeling of fluid-solid coupling part in the invention, and the weight selection in practical modeling can also realize convergence of the flow field and solid motion state.
As shown in fig. 1, the concrete implementation process of the fluid-solid coupling simulation method for fish school movement in marine environment of the present invention is as follows:
the method comprises the following steps: the flow field is modeled.
Finite elements are divided into flow fields, the finite elements of the flow fields are numbered {1, 2.., Nele }, Nele is the number of the finite elements, vertexes forming the finite elements are numbered {1, 2.., Np }, and Np is the number of the vertexes.
Defining attributes Ele ═ { Lnct, Led, EVol, Mstat } of the finite elements; ele represents an attribute set of finite elements, Lnct is a set of finite element vertex numbers, Led is a set of adjacent finite element numbers sharing a surface with the finite element, EVol is the volume of the finite element, and Mstat is a judgment for judging whether the finite element is searched when the finite element where the solid is located is searched. In this embodiment, the finite element uses a tetrahedral mesh, and there are four vertices, so the finite element vertex number set is represented as Lnct ═ { p1, p2, p3, p4 }; each finite element has four faces, i.e. there are four adjacent finite elements having a common face, and the set of adjacent finite element numbers having a common face with the finite element is denoted as Led ═ e1, e2, e3, e4 }.
Defining the property Po of the vertices constituting the finite element, { PX, PVol, U, Pre, T }, where PX represents the position coordinates of the vertex, PVol represents the volume occupied by the vertex, U represents the velocity of the vertex in three directions, Pre represents the pressure of the vertex, and T represents the temperature of the vertex. In the present embodiment, the position coordinates of the vertex are expressed as PX ═ xp,yp,zpAnd expressing the velocities of the vertices in the three directions as U ═ U, v, w.
The volume EVol of the finite element is determined from the determinant consisting of 4 point coordinates, with the formula:
Figure BDA0002749709640000091
in the formula (x)pi,ypi,zpi) Is the position coordinate of the ith point in the finite element. The arrangement sequence of the 4 vertexes forming the finite element needs to meet the following requirements:
any vertex is taken, and the plane formed by the other three vertexes is overlooked from the vertex, so that the three vertexes are arranged in a counterclockwise sequence. If the requirement is not met, the volume EVol of the finite element is changed to be negative, and the numbers of two vertexes are adjusted, so that the result is positive. For example, (x) can bep3,yp3,zp3)、(xp4,yp4,zp4) The stored numbers are exchanged, and the requirements can be met.
Since 1 finite element is bisected by 4 points, the volume calculation for each vertex is:
Figure BDA0002749709640000101
in the formula, since a vertex may participate in the construction of a plurality of finite elements, Σ EVol represents the sum of the finite element volumes that a vertex participates in the construction, and N represents the number of finite elements that the vertex participates in the construction.
The property changes for the above finite element vertices are governed by Navier-Stokes and Euler equations and are expressed as a uniform form of conservation as follows:
Figure BDA0002749709640000102
Figure BDA0002749709640000103
Figure BDA0002749709640000104
Figure BDA0002749709640000105
Figure BDA0002749709640000106
Figure BDA0002749709640000107
wherein phi and F, G, Q represent vectors forming a mass, momentum and energy conservation equation set, the 1 st term of each vector in the formula forms a mass conservation equation, the 2 nd to 4 th terms form a momentum conservation equation, and the 5 th term forms an energy conservation equation. ρ is the vertex density, (u, v, w) is the velocity of the vertex in three directions, E is the internal energy per unit mass, H is the enthalpy, μ is the viscosity coefficient, pre is the pressure of the vertex, - τxx、-τyx、-τzxAre respectively on three sidesThe parameters of the upward direction are the parameters,
Figure BDA0002749709640000111
and
Figure BDA0002749709640000112
the partial derivatives of the parameters of the vertex are respectively shown, T is temperature, and k is the thermal conductivity. DeltaxyAnd is equal to 1 only when x is equal to y, and is equal to 0 otherwise. (f)x,fy,fz) Representing physical strength in three directions, qHIndicating an internal heat source.
Energy equations can be selected and not considered in flow field calculation, the important point of the method is not to model the flow field, so that the details of programming implementation are not described too much, and only the details related to coupling are expanded.
As can be seen from the above equation, the parameter derivation is required when updating the attributes of the vertices. Since the partial derivatives of the parameters of the vertices cannot be directly obtained, the partial derivatives in the finite elements are obtained first, and the volume weighting coefficients are used
Figure BDA0002749709640000117
To the respective vertices constituting the finite element.
Taking the finite element to calculate the partial derivative formula of the speed U as an example:
Figure BDA0002749709640000113
given the derivation in the two-dimensional case of the above equation, taking the partial derivative of the variable U to x in the triangle unit as an example:
in the triangular finite element, three vertexes are labeled 1,2 and 3 respectively and are arranged in a counterclockwise sequence, a line segment passing through the point 1 is parallel to the x direction and is intersected with a line segment 23 at a point 4, and the length of the line segment is dx, as shown in fig. 3.
Then there are:
Figure BDA0002749709640000114
Figure BDA0002749709640000115
wherein S is the area of a triangle.
U at point 4 can be obtained by two-point weighting of 2,3, then:
Figure BDA0002749709640000116
the partial derivatives of the triangular finite elements can be considered as:
Figure BDA0002749709640000121
three points are alternately symmetrical, if 2 points are selected to make straight lines to intersect with 13 lines, the same conclusion can still be obtained, but the intersection point is on the extension line of 13.
Expanding to three dimensions, namely the above formula, proves that the method is similar, and only the area becomes the volume, and the intersection line becomes the intersection plane.
Weighting coefficient
Figure BDA0002749709640000122
Figure BDA0002749709640000123
Where EVol denotes the volume of the finite element to be solved, PVol denotes the volume of the vertices constituting the finite element,
Figure BDA0002749709640000124
are the weighting coefficients of the vertices and finite elements.
Then, knowing the partial derivatives of each finite element, the partial derivatives of each point are the sum of the partial derivatives of the finite elements of which the point participates in the construction multiplied by the coefficients:
Figure BDA0002749709640000125
step two: modeling the solid module.
The solid spots are numbered {1, 2.., Nc } which is the number of solid spots.
Defining the attribute Co of the solid point, wherein the Loc is the number of a finite element where the solid point is located, the CX is the coordinate of the solid point, the Cm is the mass of the solid point, the CVol is the volume of the solid point, and the CU is the velocity of the solid point in three directions.
The property change for the solid dots is governed by the following equation:
Figure BDA0002749709640000126
Flc＝f(Co,Po) (28)
Fc＝f(Coc,Co1,...,CoNc-1) (29)
wherein, FlcThe interaction force of the flow field and the solid is influenced by the property of the solid point and the property of the flow field where the solid point is located; fcThe interaction force between solids is influenced by the properties of the solid point and the properties of other solid points; coiAnd (3) representing the attribute of the ith solid point, wherein a specific expression is related to the targeted solid object. Flx,c、Fly,c、Flz,cIs FlcComponents in the directions of the x-axis, y-axis and z-axis, respectively, FcIs an interaction force between solids, Fx,c、Fy,c、Fz,cIs FcThe components in the x-axis, y-axis, and z-axis directions, respectively.
Step three: and updating the flow-fixed association parameters.
The finite element Loc and the weight coefficient will be described with reference to FIG. 4
Figure BDA0002749709640000131
And (4) updating.
Firstly, updating the number Loc of the finite element where the solid point c is located, realizing by traversing each finite element during initialization, and then updating by adopting a wide area search algorithm, wherein the specific method comprises the following steps:
setting up search sequence Ltc ═ { e ═ e1,...,emIn which eiThe number m is the number of elements in the search sequence. Initially, m is 1, only one element in the search sequence is the finite element number where the solid point c is located at the last moment, and Mstat in the finite element attribute is 1, which indicates that the finite element has been added into the search sequence.
As the solid point moves, it may no longer belong to the finite element. Therefore, finite elements in the search sequence need to be searched one by one, and if the solid point exists in the searched finite elements, the Mstat attribute of the finite element where the solid point is located is set to zero; if the solid point does not exist in the searched finite element, the finite element with Mstat being 0 in the adjacent finite element stored in the Led set of the finite element attribute is taken into the search sequence, the next finite element is searched according to the search sequence, the process is repeated until the finite element with the solid point is searched, and the weight coefficient is updated
Figure BDA0002749709640000132
Method for judging whether solid point c exists in finite element e or not, and updating
Figure BDA0002749709640000133
The method comprises the following steps:
calculating a determinant by replacing one of the four vertices constituting the finite element by the coordinates of the solid point c
Figure BDA0002749709640000134
To be provided with
Figure BDA0002749709640000135
For example, the following steps are carried out:
Figure BDA0002749709640000136
wherein (cx)c,cyc,czc) Indicates the position of the solid point c, (x)pi,ypi,zpi) Is the position coordinate of the ith vertex in the finite element. If it is not
Figure BDA0002749709640000141
The solid c is present in the finite element e,
Figure BDA0002749709640000142
is the tetrahedral volume formed by the solid c and three points except the nth point, and the weight coefficient is further calculated as shown in FIG. 5
Figure BDA0002749709640000143
Namely:
Figure BDA0002749709640000144
the reason why the invention selects the volume to calculate the weight coefficient, rather than the length of the connecting line of the solid point c and other vertexes, is that: the volume is used as a weight coefficient, so that the flow field force Fl acting on the solid point c when the finite element where the solid point c is positioned is changed can be realizedcAnd the solid acting force applied to each point can not generate mutation.
Step four: and updating the parameters of the solid flow field.
The flow field force Fl acting on the solid point c can be obtained from the formula (9)cIf the parameters of the flow field at the solid point c need to be obtained, the parameters of the four top points in the finite element e where the solid point c is located can be multiplied by the corresponding weight coefficients
Figure BDA0002749709640000145
The sum is obtained as the flow field velocity U at the solid point ccFor example, the following steps are carried out:
Figure BDA0002749709640000146
Unis the velocity of the nth vertex in the finite element.
And (3) updating the parameters of the solid point c after the parameters of the flow field at the solid point c are obtained, wherein the speed and the coordinate of the solid point c need to be updated, and the updating method is introduced in the modeling of the second step.
In the process of updating the flow field, Fl acting force exists on the solid point c due to the flow fieldcThere will be a reaction force-FlcActing on the fluid finite element e, namely updating the physical force f on each vertex of the finite element, wherein the updating method comprises the following steps:
Figure BDA0002749709640000147
this formulation represents the parameter update procedure, fpnIs the physical force experienced by the nth vertex in the finite element, the left side of the equal sign represents the physical force when the solid point is present in the finite element, i.e. the updated physical force, and the right side of the equal sign represents the physical force when the solid point is not present in the finite element-the reaction force distributed to each point. Wherein, physical strength f has three directions, which are expressed as:
Figure BDA0002749709640000148
at the same time, the volume of the finite element e where the solid point c is located will decrease, i.e. the updated volume should be the original volume minus the volume of the solid point c:
EVole＝EVole-CVolc (34)
the formula represents the finite element volume updating process, the left side of the equal sign represents the finite element volume when the solid point exists in the finite element, namely the updated finite element volume, and the right side of the equal sign represents the finite element volume when the solid point does not exist in the finite element-the volume of the solid point. Due to EVoleChange of (2), volume PVol of each vertex constituting e and influence weight coefficient
Figure BDA0002749709640000151
Updating is also carried out, the flow field is also updated later, and the updating method is used in the flow field modeling of the step oneAlready described.
And repeating the third step and the fourth step to obtain the change of the flow field and the solid along with the time, so that the dynamic update on the time can be realized.
It should be noted that the finite element mesh used is triangular in two dimensions and tetrahedral or right triangular prism in three dimensions, and the purpose is to determine whether a solid point is in a finite element and calculate a weight coefficient
Figure BDA0002749709640000152
Then, there can be a geometric figure consisting of the solid point c and the remaining construction points p' corresponding to the constituent finite element points p. In two dimensions, the volume is replaced by an area.
The invention has guiding function for fish culture. Taking feeding as an example, the traditional evaluation model can not take the interaction between the fish school movement and the flow field into consideration, so that the feed is mostly considered to be naturally settled in water, but the influence of the fish school on the flow field in the feeding process actually greatly enhances the diffusion effect of the water area, and the feed is reflected on the feed, namely the suspension time of the feed in water is prolonged, and the horizontal diffusion rate and the radius are increased. The problem is that the protein conversion rate of the feed is higher in a feeding mode of multiple set points and less feeding than in a centralized feeding mode in a theoretical model, but in practice, the feed is only fed in the center of a breeding area to prevent excessive feed from flowing out of the outer net.
The foregoing lists merely illustrate specific embodiments of the invention. It is obvious that the invention is not limited to the above embodiments, but that many variations are possible. All modifications which can be derived or suggested by a person skilled in the art from the disclosure of the present invention are to be considered within the scope of the invention.

Claims (8)

1. A fluid-solid coupling simulation method for fish school movement in marine environment is characterized by comprising the following steps:
1) establishing a flow field model and a solid motion model by taking a marine environment as a flow field and a fish school as a solid point, and initializing;
the flow field model comprises Ele ═ { Lnct, Led, EVol, Mstat }, and the vertex attributes forming the finite elements comprise Po ═ { PX, PVol, U, Pre, T }; ele represents an attribute set of finite elements, Lnct is a set of finite element vertex numbers, Led is a set of adjacent finite element numbers sharing a surface with the finite elements, EVol is the volume of the finite elements, and Mstat is a judgment on whether the finite elements are searched when the finite elements where the solid points are located are searched; PX represents the position coordinates of the vertex, PVol represents the volume occupied by the vertex, U represents the velocity of the vertex in three directions, Pre represents the pressure of the vertex, and T represents the temperature of the vertex;
the attributes of each solid point in the solid motion model comprise Co ═ Loc, CX, Cm, CVol, CU }; wherein Co represents an attribute set of the solid point, Loc is the number of a finite element where the solid point is located, CX is the coordinate of the solid point, Cm is the mass of the solid point, CVol is the volume of the solid point, and CU is the speed of the solid point;
2) updating the serial numbers of the finite elements of the flow field where each solid point is located along with the movement of the fish school; after updating, calculating the influence weight coefficient of the solid point to each vertex in the finite element
Figure FDA0002749709630000011
According to the influence weight coefficient
Figure FDA0002749709630000012
Determining the vertex attribute of a finite element where the solid point is located, and taking the vertex attribute as a flow field parameter where the solid point is located; obtaining the interaction force Fl of the flow field and the solid according to the flow field parameters of the solid point and the self-attribute of the solid pointc；
3) According to the interaction force Fl of the flow field and the solidcUpdating the attribute parameters of the solid points;
4) according to the influence weight coefficient
Figure FDA0002749709630000013
The interaction force Fl of the flow field and the solidcDistributing the vertex of the finite element where the solid point is located to obtain the additional acting force of the vertex; renewing solids according to additional forceThe volume of the finite element where the point is located and the volume of the vertex forming the finite element are updated, so that the updating of the flow field is completed;
5) repeating the steps 2) to 4) until a preset step length is reached; and outputting the flow field and solid parameters according to a preset time interval to form the dynamic response of fluid-solid coupling of fish swarm movement along with time under the marine environment.
2. The method as claimed in claim 1, wherein the finite elements are triangular meshes, tetrahedral meshes or right triangular prism meshes.
3. The method for simulating fluid-solid coupling of fish school movement in marine environment according to claim 1, wherein in step 2), as the fish school moves, the serial number of the finite element of the flow field where each solid point is located is searched and updated by using the breadth search algorithm; the method specifically comprises the following steps:
setting up search sequence Ltc ═ { e ═ e1,...,emIn which eiThe number of the ith finite element in the search sequence is m;
initially, m is 1, only one element in a search sequence is a finite element number where a solid point is located at the last moment, and Mstat in the finite element attribute is 1, which indicates that the finite element is added into the search sequence;
searching finite elements in the search sequence one by one along with the movement of the solid point, and if the solid point exists in the searched finite elements, zeroing the Mstat attribute of the finite element where the solid point is located; if the solid point does not exist in the searched finite element, adding the finite element which is adjacent to the finite element and is not searched into a search sequence, and starting to search the next finite element according to the search sequence;
repeating the above process until the finite element where the solid point is located is searched.
4. The method as claimed in claim 3, wherein the simulation method comprises collecting fish in a marine environmentIn the process of searching by using the breadth searching algorithm, aiming at the finite element to be searched, the coordinates of the solid point are replaced by the nth vertex coordinates of the finite element to be searched to form a determinant
Figure FDA0002749709630000021
Each row represents the three-dimensional coordinates of the ith point if
Figure FDA0002749709630000022
The solid point is present in the finite element, otherwise it is not present.
5. The method as claimed in claim 1, wherein the step 2) of calculating the influence weight coefficient of the solid point on each vertex in the finite element is performed by using a fluid-solid coupling method
Figure FDA0002749709630000023
The calculation formula is as follows:
Figure FDA0002749709630000024
in the formula (I), the compound is shown in the specification,
Figure FDA0002749709630000025
representing the tetrahedral volume formed by the solid point and the vertex except the nth vertex in the finite element.
6. The method as claimed in claim 5, wherein the sum of the weight coefficients of the vertices of the finite elements forming the solid point and the influence of the solid point is 1.
7. The method as claimed in claim 1, wherein the updating of the attribute parameters of the solid point is implemented by a control equation expressed as:
Figure FDA0002749709630000026
wherein (cx, cy, cz) is the coordinate of the solid point, (cu, cv, cw) is the velocity of the solid point in three directions, Cm is the mass of the solid point, FlcFl being the interaction force of the flow field with the solidx,c、Fly,c、Flz,cIs FlcComponents in the directions of the x-axis, the y-axis, and the z-axis, respectively; fcIs an interaction force between solids, Fx,c、Fy,c、Fz,cIs FcThe components in the x-axis, y-axis, and z-axis directions, respectively.
8. The method for simulating fluid-solid coupling of fish school movement in marine environment according to claim 1, wherein the step 4) is specifically as follows:
4.1) interaction force Fl of flow field and solidcAnd (3) allocating the vertex of the finite element where the solid point is located to obtain the additional acting force of the vertex:
Figure FDA0002749709630000031
in the formula PQnIs the additional force of the nth vertex, FlcIs the interaction force of the flow field and the solid,
Figure FDA0002749709630000032
is the impact weight coefficient;
4.2) subtracting the volume of the solid point from the volume of the finite element, and updating the volume of the finite element where the solid point is located; and updating the vertex volumes constituting the finite element; the vertex volume calculation formula is as follows:
Figure FDA0002749709630000033
in the formula, sigma EVol represents the sum of finite element volumes of a vertex participating in construction, and N represents the number of finite elements participating in construction of the vertex;
4.3) updating the physical force applied to each vertex of the finite element:
f′pn＝fpn-PQn
in the formula (f)pnIs the physical strength, f ', of the n-th vertex before update'pnIs the physical strength to which the nth vertex is subjected after updating;
and (4) allowing the updated physical power to enter a limit element vertex attribute control equation, completing the updating of the finite element vertex attribute, and completing the updating of the flow field.
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