CN101329700A - A method for simulating fluid flow - Google Patents

Abstract

The invention discloses a method for simulating fluid flow, the region of fluid flow includes obstacles represented by irregular boundaries; it is characterized in that it includes: creating a structured grid of initial physical space, by processing irregular The boundary evolves the initial physical space structured grid into a composite structured grid, and each irregular boundary is also embedded as a zero isosurface, which is called a composite implicit structured grid (CISgrid); the CISgrid unit vertices are used as Calculate the nodes, and use the finite difference method to simulate the fluid flow according to the node connectivity rules of CISgrid. The post-processing process of fluid flow numerical simulation is carried out according to the internal validity rules of CISgrid. It solves the problem that irregular boundaries cannot be effectively dealt with when directly using structured grids and finite difference method for fluid flow simulation, and avoids the complex grid generation caused by unstructured grids and the unstructured grid-based Complex numerical calculation problems effectively improve the efficiency of fluid simulation.

Description

A method for simulating fluid flow

technical field

The invention relates to a method for simulating fluid flow.

Background technique

Frequently encountered in life, such as the diffusion of oil leaked on the sea surface, the leakage of gas in buildings, the change and development of waves, and the formation and growth of crystals in the production process, the escape and rupture of bubbles in liquids , casting and injection molding processes, etc. are all about fluid flow motion interface issues. In order to formulate an effective rescue plan or to ensure the quality of the product, it is important to carry out accurate and effective simulation of the above-mentioned process. Simulating this process involves modeling the fluid flow behavior and the boundary surfaces within the flow region. Prior art methods have used computational fluid dynamics, finite element analysis, finite difference methods to model the behavior described above.

The finite difference method is an effective technique for numerically solving the behavior of fluid flow. It divides the solution area into rectangular or orthogonal curve grids, and at the intersection points of the grid lines, that is, nodes, the governing equations describing the fluid flow behavior will be described. Each differential in is replaced by a difference quotient, so that the differential equation of the continuous function is discretized into a difference equation defined on the grid node. Each equation contains the value of the function to be found on this node and some nearby nodes. Through Solving these algebraic equations yields the desired numerical solution.

When there is a complex boundary shape in the fluid flow region, because the conventional structured grid cannot describe the complex boundary shape, the finite difference method cannot be applied to the numerical solution of the governing equations of the corresponding fluid flow behavior, or cannot be solved near the irregular boundary. give a satisfactory numerical solution. For complex boundary shapes, the usual solution for fluid flow simulation is to divide the flow region into unstructured grids, and then use the finite element method or finite volume method for numerical solution. However, since the subdivision of regions under complex boundary shapes is a complex computational geometry problem, the finite element and finite volume methods are more complex than the finite difference method, which increases the difficulty and complexity of fluid flow simulation.

Contents of the invention

The technical problem to be solved by the present invention is to provide a method for simulating fluid flow when the region of fluid flow contains obstacles represented by irregular boundaries, so that fluid simulation can be realized more accurately and efficiently.

The technical solution adopted by the present invention to solve the technical problem is: a method for simulating fluid flow, the fluid flow region includes obstacles represented by irregular boundaries, and is characterized in that it includes:

Create an initial physical space structured grid covering the fluid flow area;

The initial physical space grid of the fluid flow area is converted into a compound structured grid embedded with irregular boundaries. The above-mentioned compound structured grid embedded with irregular boundaries is called a compound implicit structural grid (Compound Implicit Structural Grid) ), denoted as CISgrid;

Numerical simulation of fluid flow according to the node connectivity rules of CISgrid;

The post-processing process of fluid flow numerical simulation is carried out according to the internal validity rules of CISgrid.

The initial physical space structured grid of the fluid flow area is a quadrilateral grid in a two-dimensional case, and a hexahedral grid in a three-dimensional case; for a two-dimensional case, the irregular boundaries representing obstacles in the flow area can be is a finite set of polyline segments and curve segments described in any mathematical form; for three-dimensional cases, the irregular boundary can be a finite set of plane and surface patches described in any mathematical form; and for any given irregular boundary element , it can always logically divide the space in two, into left and right, or inside and outside.

The CISgrid grid is obtained by expanding the structured grid at irregular boundaries.

The CISgrid has the following characteristics:

The CISgrid is evolved and formed on the basis of the initial physical space grid of the fluid flow area, and the CISgrid is completely coincident with the initial physical space grid of the fluid flow area in space;

The grid unit form of CISgrid is the same as the unit form of the initial physical space grid of the fluid flow region, that is, a quadrilateral grid in a two-dimensional case, and a hexahedral grid in a three-dimensional case;

The number of CISgrid grid units at the spatial position of the initial physical grid unit in any fluid flow area is not less than 1.

The conversion of the initial physical space grid of the fluid flow region to the CISgrid grid is realized by processing the irregular boundaries one by one, and the processing method for a given irregular boundary Γ is:

Split the CISgrid grid unit that crosses the irregular boundary Γ and is topologically compatible with the points on Γ into two CISgrid grid units G ₁ and G ₂ at the same spatial position, and attach "located on the boundary Γ The topological information nodes on the left side of the boundary Γ and on the right side of the boundary Γ;

Check the vertices of unit G _i , i=1, 2, if the actual left and right orientation of a certain vertex P relative to the boundary Γ is inconsistent with the above-mentioned topological information description about the boundary Γ recorded on G _i , then perform vertex replacement—if the common vertex Among all the CISgrid grid units at position P, there is a unit G′ that is different from G _i and the topological information about the boundary Γ recorded on it is consistent with that of G _i , then use the vertex P’ at position P of G’ Replace the vertex P of G _i ; otherwise, create a new vertex P′ to replace the vertex P, and the new vertex P′ has the same spatial position as the replaced vertex P.

Topological compatibility between the above-mentioned spatial position point P and the CISgrid grid unit G containing this point means:

The topological information description table attached to G does not conflict with the actual topological orientation of point P;

If there is a topology information node in the topological information description table attached to G that declares that G is on the left side of the boundary Γ', but point P is actually located on the right side of the boundary Γ', then P and G topologically conflict;

In particular, if the topology information description table attached to G is empty, then G is always topologically compatible with P;

And, for any spatial position point P, only one CISgrid grid unit among all CISgrid grid units containing this point is topologically compatible with P.

The process of processing each irregular boundary Γ mentioned above to construct the CISgrid grid includes the operation of embedding Γ into the CISgrid grid in the form of zero isosurface to form an implicit expression: marked as "located on the left side of the boundary Γ" or The directional distance information from the vertex position to the boundary Γ is always recorded on the vertex of the CISgrid grid unit "located on the right side of the boundary Γ". If the vertex position is located on the left side of Γ, it has the first symbol; has the opposite sign.

The numerical simulation of fluid flow based on the CISgrid includes using the finite difference method, and the calculation nodes are vertices of the CISgrid grid units.

The node connection rule is: two computing nodes are adjacent if and only if the two nodes are vertices of the same CISgrid grid unit, and the line connecting the two vertices is an edge of the CISgrid unit.

The internal validity rule of the unit is: the point P in the CISgrid grid unit G is located in the valid area of G, if and only if the position point P and the CISgrid grid unit G have topology compatibility.

Compared with the prior art, the present invention has the advantages that it solves the problem that irregular boundaries cannot be effectively dealt with when directly using structured grids and finite difference methods for fluid flow simulation, and avoids the problems caused by the use of unstructured grids. The complex grid generation and complex numerical calculation problems based on unstructured grids have effectively improved the efficiency of fluid simulation.

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments, but it is not intended to limit the present invention. Other objects and features of the present invention can be more clearly understood and the present invention can be fully understood by the following description and claims taken in conjunction with the accompanying drawings.

Description of drawings

Figure 1 simulates the problem of parallel outward diffusion of linear pollution sources on a rectangular grid;

Fig. 2 Simulating the problem of parallel outward diffusion of linear pollution sources on a rectangular grid cannot give a satisfactory simulation effect near the irregular boundary;

Figure 3 Unstructured grids can represent irregular boundaries;

Fig. 4 is a kind of flow chart that adopts CISgrid grid to carry out fluid flow simulation;

In the two-dimensional case of Fig. 5A, there is a T-shaped intersecting curved boundary;

FIG. 5B finds the CISgrid grid unit that the irregular boundary 500 passes through and is topologically compatible with;

FIG. 5C identifies the CISgrid grid cell to the left of boundary 500;

FIG. 5D identifies the CISgrid grid cell to the right of boundary 500;

FIG. 5E finds the CISgrid grid unit that the irregular boundary 510 passes through and that is topologically compatible with it;

FIG. 5F identifies the CISgrid grid cell to the left of boundary 510;

FIG. 5G identifies the CISgrid grid cell to the right of boundary 510;

Figure 5H identifies the effective area of the CISgrid grid unit at position 580 on the left side of boundary 500;

Fig. 5I marks the effective area of the CISgrid grid unit at the right side of the boundary 500 and the 580 position on the left side of the boundary 510;

Fig. 5J marks the effective area of the CISgrid grid unit at position 580 on the right side of the boundary 500 and the right side of the boundary 510;

Figure 6 has a T-shaped intersecting curved surface boundary in the three-dimensional situation;

Figures 7 to 8 respectively show the problem of radial diffusion of point pollution sources and the simulation results displayed in gradient colors when there are obstacles in the propagation domain in the two-dimensional case;

Figures 9 to 12 respectively show the problem of radial diffusion of point pollution sources when there are obstacles in the propagation domain in the three-dimensional situation and the simulation effect displayed in a gradient color mode.

Detailed ways

Frequently encountered in life, such as the diffusion of oil leaked on the sea surface, the leakage of gas in buildings, the change and development of waves, and the formation and growth of crystals in the production process, the escape and rupture of bubbles in liquids , casting and injection molding processes, etc. are all about fluid flow motion interface issues. In order to formulate an effective rescue plan or ensure the quality of the product, it is important to carry out accurate and effective simulation of the above process, the above simulation is by solving the partial differential control equation - Eikonal equation: $|\▿u\left(x\right)|=\frac{1}{v\left(x\right)},$ x∈R ⁿ (where the boundary condition is u(x)=φ(x), $x\∈\mathrm{\Γ}\⋐R^{\mathrm{no}},$ , v(x) is the flow velocity) to achieve. The Eikonal equation is exemplary and other equations describing fluid flow behavior may be used without changing the scope of the claimed invention.

Figure 1 shows the problem of simulating the parallel outward diffusion of linear pollution sources on a rectangular grid. The black dots represent the sampling points on the linear pollution sources. There are irregular boundary lines in the diffusion area. The governing equation of fluid flow is the Eikonal equation, Among them, the velocity v(x) is always 1, and the diffusion time at the location of the pollution source is the reference time 0. It is necessary to investigate the time for the pollution source to diffuse to other locations in the area. Since the rectangular grid cannot describe the irregular boundary, and the finite difference is only calculated at the grid node, this makes the finite difference method unable to give a satisfactory numerical solution near the irregular boundary, as shown in Figure 2. The location indicates the same arrival time of pollutants.

In the case of irregular boundaries, the usual solution is to divide the problem domain to be solved into an unstructured grid, as shown in Figure 3, and then use the finite element method or finite volume method for numerical solution. The resulting problem is that the subdivision of the region under the condition of irregular boundaries is a complex computational geometry problem, especially in the three-dimensional case to generate tetrahedral subdivision of the region that satisfies the limitation of complex surfaces; followed by finite element, finite The volume method is more complex than the finite difference method, which increases the difficulty and complexity of fluid flow simulation.

The invention discloses a method for simulating fluid flow, which is used to realize the simulation of fluid flow by using the finite difference method under irregular boundary conditions, avoiding the complex grid generation caused by the use of unstructured grids and based on unstructured grids. The complex numerical calculation problem of grid effectively improves the efficiency of fluid flow simulation.

In the present invention, the CISgrid grid is based on the initial structured grid covering the fluid flow area, and is evolved by processing the irregular boundaries one by one. obtained by expanding at the boundary. When performing fluid flow simulation, the CISgrid grid node will be used as the calculation node for calculation, and finally the post-processing process of the fluid flow simulation will be performed according to the internal validity rules of the CISgrid unit. Numerical solutions, etc.

Fig. 4 is a kind of flow chart that adopts CISgrid grid to carry out fluid flow simulation, it is characterized in that, comprises step 400, creates the initial physical space grid that covers fluid flow area; Step 410, carries out the relevant preprocessing that generates CISgrid; Step 420 , step 430, by processing the irregular boundaries one by one, the CISgrid grid is continuously evolved and the irregular boundaries are embedded in the CISgrid; step 440 is numerically solved for the fluid governing equations according to the node connectivity rules of the CISgrid; step 450, according to the CISgrid The post-processing of fluid flow simulation, such as visualization, etc., is carried out by the internal validity rules of the element.

Step 400, creating an initial physical space grid covering the fluid flow area. Usually, the step size of the grid unit in the direction of each coordinate axis is determined according to the accuracy required by the problem to be solved, and a regular bounding box covering the fluid flow area is divided into a structural grid with the above step size, generally a rectangular grid in a two-dimensional case , in the 3D case is a cuboid grid.

Step 410, perform related preprocessing for generating CISgrid. The irregular boundaries described in the present invention can be a finite set of broken line segments and curve segments described in any mathematical form for two-dimensional situations; for three-dimensional situations, the irregular boundaries can be plane sheets and curved surfaces described in any mathematical forms A finite set of slices. In the present invention, it is always considered that for any given irregular boundary element, it can always logically divide the space into two, into left and right, or inside and outside, and the left and right are always used uniformly in the present invention right term. The preprocessing of generating the CISgrid mainly includes sorting the irregular boundaries to determine the processing order of the irregular boundaries during the evolution of the CISgrid grid. The rules for sorting irregular boundaries can be customized according to the current fluid flow behavior. The generally applicable sorting rules are: large-scale irregular boundaries are sorted before small-scale irregular boundaries; if the boundary Γ and boundary Γ′ form a T-shaped Intersect, then the boundary Γ ranks before the boundary Γ'. As shown in FIG. 5A , the boundary 500 is arranged before the boundary 510 . As shown in FIG. 6 , border 610 is arranged before border 600 , and border 630 is arranged before border 620 .

The CISgrid grid proposed by the present invention can be considered as the expansion of the structured grid at irregular boundaries. The method for generating the CISgrid grid—step 420 , is described below from the perspective of the CISgrid unit, that is, how the CISgrid grid evolves during the process of processing irregular boundaries one by one.

First, the initial physical space grid is expressed as a collection of CISgrid units, each CISgrid unit contains n vertex pointers (n=4 in two-dimensional cases, n=8 in three-dimensional cases), pointing to the corresponding vertex data objects, this , there is only one vertex data object at each initial physical grid cell vertex position.

In the present invention, the processing logic for each irregular boundary Γ in the process of constructing the CISgrid grid is: each CISgrid grid unit G passing through the irregular boundary Γ and having topological compatibility with the points on Γ (It can also include its adjacent units) split into two CISgrid grid units at the same spatial position. Here, the two units obtained by duplicating the CISgrid grid unit G are denoted as G ₁ and G ₂ respectively, and are respectively appended Topological information nodes "located on the left side of the boundary Γ" and "located on the right side of the boundary Γ". Check the vertices of the unit G _i (i=1, 2), if the actual left and right orientation of a certain vertex P relative to the boundary Γ is inconsistent with the above-mentioned topological information description about the boundary Γ recorded on G _i , then perform vertex replacement—if the same In all the CISgrid grid units at the position of vertex P, there is a unit G′ that is different from G _i and the topological information about the boundary Γ recorded on it is consistent with that of G _i , then the vertex P at position P of G’ is used 'Replace the vertex P of G _i ; otherwise, create a new vertex P' to replace the vertex P, and the new vertex P' has the same spatial position as the replaced vertex P.

For a given irregular boundary Γ, to find the CISgrid grid unit that the irregular boundary Γ passes through and has topological compatibility with the points on Γ, can be searched in the following linear manner:

a) Randomly select a point P on the irregular boundary Γ, locate the initial physical grid unit where P is located according to the parameters of the initial structured grid (grid reference point, step size information in each direction), and then determine this The only CISgrid grid unit G that is topologically compatible with point P on the initial physical grid unit. Add G to stack S.

b) while (stack S is not empty)

{

Pop an element from the top of the stack S, which is denoted as CISgrid grid unit G'.

if (the vertices of G' are not all on one side of the boundary Γ)

{ Put the unprocessed CISgrid unit adjacent to G' into the stack S;

G' is added to the linked list C

}

}

When the stack S is empty, the CISgrid units in the linked list C are all CISgrid grid units that cross the boundary Γ and have topology compatibility with the points on it.

The above-mentioned CISgrid unit G" adjacent to G' refers to the vertex object that G' and G" have a common point to; the spatial position point P is topologically compatible with the CISgrid grid unit G containing this point means: the topological information description table attached to G does not conflict with the actual topological orientation of point P, especially, if the topological information description table attached to G is empty, then G is always compatible with the topology of P.

See Figure 5B, boundary 500 is the first irregular boundary to be processed:

(1) There is only one CISgrid unit on the initial physical grid unit where the point P is located, so it is always compatible with the P topology. Starting from this CISgrid unit, using the above linear search, finally the CISgrid unit in the linked list C is all the CISgrid grid units that cross the boundary 500 and are topologically compatible with the points on it, see the shaded unit in Figure 5B.

(2) According to the processing logic, it is necessary to duplicate all the CISgrid units in the above linked list C, and respectively identify them as topological information "located on the left side of the boundary Γ" and "located on the right side of the boundary Γ", and each CISgrid unit thus generated The vertices of the cell are checked. The shaded unit in Fig. 5C represents the CISgrid unit identified as the left side of the boundary 500 after double copying, and the position shown by the small dot in the figure is located on the right side of the boundary 500, so new vertex data objects need to be generated at these positions, and the above-mentioned The corresponding vertex pointer in the CISgrid cell points to the newly created vertex data object. Similar to this, the shaded cells in Figure 5D represent the CISgrid cells identified as the right side of the boundary 500 after the double copy, and the positions indicated by the small dots in the figure are located on the left side of the boundary 500, so new vertex data need to be generated at these positions object, and let the corresponding vertex pointer in the above CISgrid unit point to the newly created vertex data object.

In Figure 5E, boundary 510 is an irregular boundary processed after boundary 500:

(1) Assuming that the position of point P located on the boundary 510 is arbitrarily determined as shown in the figure, there is only one CISgrid unit on the initial physical grid unit where point P is located, so it is always compatible with P topology. Starting from this CISgrid unit, adopt the above linear search, and finally the CISgrid unit in the linked list C is all the CISgrid grid units that cross the boundary 510 and are topologically compatible with the points on it, see the filled shaded unit in Figure 5E . It should be noted that there are two CISgrid grid units at the unit position 580 identified in the figure: one is marked as the left side of the boundary 500, and the other is marked as the right side of the boundary 500, because the linear search is performed through the adjacent relationship of the CISgrid unit Therefore, the filled shaded cell at cell position 580 should be the CISgrid grid cell "identified as the right side of boundary 500".

If the arbitrarily selected point P on the boundary 510 is just the point Q as shown in Figure 5E, that is, at the unit position 580, as mentioned above, there are two CISgrid grid units at the unit position 580: One is identified as the left side of the boundary 500, and the other is identified as the right side of the boundary 500, then the CISgrid unit "identified as the right side of the boundary 500" should be topologically compatible with point Q. Starting from this CISgrid unit, using the above linear search, finally the CISgrid unit in the linked list C should be consistent with the result described above, that is, the filled shaded unit in Figure 5E.

(2) According to the processing logic, it is necessary to duplicate all the CISgrid units in the above linked list C, and respectively identify them as topological information "located on the left side of the boundary Γ" and "located on the right side of the boundary Γ", and each CISgrid unit thus generated The vertices of the cell are checked. The filled shaded unit in FIG. 5F represents the CISgrid unit on the left side of the boundary 510 after the double copy, and the position shown by the small dot in the figure is located on the right side of the boundary 510, so new vertex data objects need to be generated at these positions, and Let the corresponding vertex pointer in the above CISgrid unit point to the newly created vertex data object. Similar to this, the shaded cells in FIG. 5G represent the CISgrid cells identified as the right side of the boundary 510 after double copying, and the positions indicated by the small dots in the figure are located on the left side of the boundary 510, so new vertex data need to be generated at these positions object, and let the corresponding vertex pointer in the above CISgrid unit point to the newly created vertex data object.

Step 420 discussed above—the process of processing each irregular boundary Γ to construct a CISgrid grid can easily realize the operation of step 430—the operation of embedding Γ in the form of zero isosurface into the CISgrid grid to form an implicit expression: Record the directional distance information from the vertex position to the boundary Γ on the vertex data objects of those CISgrid grid units related to the boundary Γ (that is, the CISgrid grid units identified as "located on the left side of the boundary Γ" or "located on the right side of the boundary Γ") , vertex positions to the left of Γ have the first sign, and vertex positions to the right of Γ have the opposite sign.

If yes, a CISgrid grid with grid expansion effect at the irregular boundary is constructed. When numerical simulation of fluid flow is performed in step 440, the calculation node corresponds to the vertex data object of the CISgrid grid unit, and the connection rule of the calculation node is: two calculation nodes are adjacent, if and only if the vertex data corresponding to the two nodes Objects are considered to belong to the same CISgrid grid unit, and the line connecting these two vertices is an edge of the CISgrid unit. Therefore, the finite difference method can be used to solve it. The process of numerically simulating fluid flow using the finite difference method can be considered to be well known in the industry when the connectivity relationship between nodes is known.

For any spatial position point P, only one CISgrid grid unit among all CISgrid grid units containing this point is topologically compatible with P. Therefore, in step 450, when it is necessary to calculate the numerical solution of point P near the irregular boundary, it is only necessary to interpolate the numerical solution of the vertices of the CISgrid grid cells that contain point P and are topologically compatible with point P. By interpolating the directional distance to the boundary Γ recorded on the vertex data object of the CISgrid grid unit, the directional distance from the point P inside the unit to the boundary Γ can be determined, and then it can be determined that the point P is on the left or right side of the boundary Γ , if the orientation information of point P relative to the boundary Γ is inconsistent with the topology information description of the relative boundary Γ on the current CISgrid, then point P does not belong to the valid area inside the current CISgrid unit. Figure 5H shows the valid area of the CISgrid grid cell at location 580 identified as "left side of boundary 500". Figure 5I shows the valid area of the CISgrid grid cell at position 580 identified as "right side of boundary 500, left side of boundary 510". Figure 5J shows the valid area of the CISgrid grid cell at position 580 identified as "Right of Boundary 500, Right of Boundary 510".

In summary, the following examples are given. The fluid diffusion simulation is performed under irregular boundary conditions, and the fluid flow governing equation is the Eikonal equation: $|\▿u\left(x\right)|=\frac{1}{v\left(x\right)},$ x∈R ⁿ (where the boundary condition is u(x)=φ(x), $x\∈\mathrm{\Γ}\⋐R^{\mathrm{no}},{}^{}$ v(x) is the flow velocity), the equation shows that the fluid will spread outward along the boundary features, here the radial outward diffusion of point pollution sources is simulated, black dots represent point pollution sources, and there are irregular boundary lines in the diffusion area, this In the embodiment of the invention, v(x)≡1 is taken. The initial condition is that u(p _i )=0 at P _i at the point pollution source, p _i ∈ R ⁿ means that the diffusion time at the pollution source position is the reference time 0, and the time for the pollution source to spread to other positions in the area needs to be considered. Consider the 2D and 3D cases separately. Figures 7 to 8 are two-dimensional situations, and Figures 9 to 12 are three-dimensional situations. The irregular curves and curved surface boundaries in Fig. 7 and Fig. 9 respectively represent obstacles in the propagation domain in two-dimensional and three-dimensional situations, and u(p _i )=0 at a given point shown in the figure. Figure 7 and Figure 9 generate two-dimensional and three-dimensional CISgrid grids respectively and use the finite difference method to solve them. Figure 8 shows the numerical solution in the two-dimensional case in a gradient color display. Figures 10 to 12 show the numerical solutions in the three-dimensional case It is displayed in gradient color on the section, and the positions with the same gray level in the figure indicate that the pollutants arrive at the same time. Here, due to the use of CISgrid grids, the problem that the finite difference method cannot effectively deal with irregular boundaries is solved. The numerical solution of the points near the irregular boundaries will be determined by the numerical value on the vertices of the CISgrid unit that contains this point and is topologically compatible with it. The solution is obtained by interpolation. The embodiment shows that fluid flow simulation based on two-dimensional and three-dimensional CISgrid grids under irregular boundary conditions is simple and efficient, and avoids the complex grid generation and unstructured grid-based The complex numerical calculation problem of grid optimization can effectively improve the efficiency of fluid flow simulation.

Of course, the present invention can also have other multiple embodiments, and those skilled in the art can make various corresponding changes and deformations according to the present invention without departing from the spirit and essence of the present invention, such as other fluid Flow control formula, but these corresponding changes and deformations should fall within the scope of protection of the appended claims of the present invention.

Claims (10)

1, a kind of method that is used for model fluid comprises the barrier of representing with non-regular borders in the zone that this fluid flows, and it is characterized in that, comprising:

Create the initial physical space structure grid of covering fluid flow region;

With the initial physical space lattice in fluid flow region territory be converted into embed non-regular borders the composite structure grid, below the composite structure grid of the non-regular borders of above-mentioned embedding is called compound implicit type structure grid (Compound ImplicitStructural Grid), be designated as CISgrid;

Node connection rule according to CISgrid is carried out Numerical simulation of fluid flow;

Carry out the rearmounted processing procedure of fluid flow numerical simulation according to the unit internal availability rule of CISgrid.

2, a kind of method that is used for model fluid according to claim 1 is characterized in that, the initial physical space structure grid in described fluid flow region territory is a quadrilateral mesh in two-dimensional case, is hexahedral mesh in three-dimensional case; To two-dimensional case, the non-regular borders of barrier can be the broken line of any mathematical form description, the finite set of segment of curve in the described expression flow region; To three-dimensional case, described non-regular borders can be the planar chip of any mathematical form description, the finite set of patch; And to any given non-regular borders element, it always can logically be divided into two the space, is divided into the left side and the right, or inside and outside.

3, a kind of method that is used for model fluid according to claim 1 is characterized in that, described CISgrid grid is that structured grid is expanded at non-regular borders place and obtained.

4, a kind of method that is used for model fluid according to claim 1 is characterized in that described CISgrid has following feature:

CISgrid develops to form on the initial physical space lattice basis in described fluid flow region territory, and CISgrid spatially overlaps fully with the initial physical space lattice in described fluid flow region territory;

The grid cell form of CISgrid is identical with the unit form of the initial physical space lattice in described fluid flow region territory, is quadrilateral mesh in two-dimensional case promptly, is hexahedral mesh in three-dimensional case;

The CISgrid grid cell number at place, the locus of the initial physical grid cell in fluid flow region territory is not less than 1 arbitrarily.

5, a kind of method that is used for model fluid according to claim 1, it is characterized in that, the initial physical space lattice in fluid flow region territory realizes by non-regular borders is handled one by one to the conversion of CISgrid grid, to the disposal route of given non-regular borders Γ is:

That non-regular borders Γ is passed and split into two CISgrid grid cell G of isospace position with the CISgrid grid cell that point on the Γ has a topological compatibility ₁, G ₂, and add the topology information node of " being positioned at the Γ left side, border ", " being positioned at border Γ the right " respectively;

Inspection unit G _i, i=1, if 2 summit is orientation, the actual left and right sides and the G of certain summit P retive boundary Γ _iThe above-mentioned topology information about border Γ of last record is described contradiction, replaces if then carry out the summit---exist in all CISgrid grid cells of common P position, summit to differ from G _iAnd on it the record topology information and G about border Γ _iThe unit G ' of unanimity, then with the summit P ' replacement G that is positioned at P place, position of G ' _iSummit P; Otherwise, creating a new summit P ' replacement summit P, new summit P ' has the locus identical with being replaced summit P.

6, the disposal route to non-regular borders Γ according to claim 5 is characterized in that, described locus point P has topological compatibility with the CISgrid grid cell G that comprises this point and is meant:

The incidental topology information description list of G does not conflict with the practical topology orientation that P is ordered;

If have a topology information node to declare the left side of G at border Γ ' in the incidental topology information description list of G, and the P point is physically located in the right of border Γ ', then P conflicts with the G topology;

Especially, if the incidental topology information description list of G is empty, then G is always compatible with the P topology;

And to locus point P arbitrarily, all comprise, and to have only a CISgrid grid cell and P in the CISgrid grid cell of this point be that topology is compatible.

7, disposal route to non-regular borders Γ according to claim 5, it is characterized in that, each non-regular borders Γ is handled process with structure CISgrid grid have been comprised Γ has been embedded the operation that the CISgrid grid forms implied expression with zero contour surface form: be designated on the summit of CISgrid grid cell of " being positioned at the Γ left side, border " or " being positioned at border Γ the right " and always write down the directed distance information of this vertex position to border Γ, the left side that vertex position is positioned at Γ then has first symbol, and the right side that vertex position is positioned at Γ then has contrary sign.

8, a kind of method that is used for model fluid according to claim 1 is characterized in that, describedly carries out the fluid flow numerical simulation based on CISgrid and comprises the use finite difference method, and computing node is the summit of CISgrid grid cell.

9, a kind of method that is used for model fluid according to claim 1, it is characterized in that, described node is communicated with rule: two computing nodes are adjacent, if and only if these two summits that node is same CISgrid grid cell, and these two summit lines are limits of CISgrid unit.

10, a kind of method that is used for model fluid according to claim 1, it is characterized in that, described unit internal availability rule is: the some P in the CISgrid grid cell G is positioned at the effective coverage of G, and and if only if, and location point P and CISgrid grid cell G have topological compatibility.

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