CN112528530A - Splicing algorithm based on arbitrary-shape three-dimensional non-corresponding grid surface - Google Patents

Abstract

The invention relates to a splicing algorithm based on an arbitrary-shape three-dimensional non-corresponding grid surface, which comprises the following steps: identifying two sides τ of non-corresponding interface_AAnd τ_B(ii) a Defining a list L for storing intersecting facets_c(ii) a For all tau_AA certain face K on_AThe following operations are performed: for all tau_BA certain face K on_BThe following operation is performed to determine the median plane τ_CCalculate outSurface normal n of the intermediate plane_CJudging K with a filter_AAnd K_BWhether or not intersections are possible; if K is_AAnd K_BIf there is a possibility of intersection, the next step is carried out: using projection to project K_AAnd K_BProjection onto the median plane tau_CUpper and intersecting; if K is_AAnd K_BIntersecting surface K_CIf so, the next step is carried out: calculating K_CCalculated area, face center and face normal, let K_CIs added to L_c(ii) a Establishing a mapping χ_CA(K_C)＝K_A，χ_CB(K_C)＝K_B，K_CIs composed of K_AAnd K_BObtaining the result of intersection; and checking the area of the intersecting facets. The invention has the advantage of greatly reducing the use limit of the grid in computational fluid mechanics engineering application.

Description

A Mosaic Algorithm Based on 3D Non-corresponding Mesh Surfaces of Arbitrary Shape

technical field

The invention belongs to the technical field of numerical calculation and simulation industrial software, and in particular relates to a splicing algorithm based on three-dimensional non-corresponding grid surfaces of arbitrary shapes.

Background technique

Now CFD (Computational Fluid Dynamics) is developing rapidly and is widely used in engineering problems. As a key part of CFD calculation, grid directly affects calculation time and memory consumption. When dealing with complex geometries, engineering often divides them into simple sub-regions and meshes them separately. The meshes generated separately in this way generally do not correspond one-to-one at the interface, so it is called a non-corresponding interface. A typical example is the coupled heat transfer calculation of the fluid-solid region in the wing design, where the meshes of the two regions are generally generated by different engineers. Therefore, the CFD software should provide a non-corresponding interface processing module at the engineering level that is convenient for users to use.

Judging from the existing relevant literature, the currently known mesh splicing technology has a very limited application range and is limited to simple shapes, such as planes, cylinders, and spheres. These simple shapes are completely unable to meet the existing industrial needs, such as aircraft engine blades, there are many condensate film holes on the solid area, and the two areas form a complex interface. The present invention solves this problem and provides a grid splicing technology that can be applied to any surface.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the above-mentioned problems, and to provide a splicing algorithm based on three-dimensional non-corresponding mesh surfaces of arbitrary shapes in a multi-region numerical simulation calculation, which greatly reduces the restriction on the use of meshes in the application of computational fluid dynamics engineering.

To achieve the above object, the present invention provides the following technical solutions:

A splicing algorithm based on three-dimensional non-corresponding grid surfaces of any shape, comprising the following steps:

S1: Confirm the two sides τ _A and τ _B of the non-corresponding interface;

S2: define a list L _c for storing intersecting facets;

S3: Perform the following operations on _a certain face KA on all τ _A ;

1) Perform the following operations on a certain face _KB on all τ _B ;

1.1 Determine the middle plane τ _C ;

1.2 Calculate the surface normal n _C of the middle surface;

1.3 Use a filter to determine whether K _A and K _B may intersect;

1.4 If K _A and K _B may intersect, proceed to the next step;

1.4.1 Use projection to project _{KA and KB onto the midplane τ C and intersect} ;

1.4.2 If the intersection surface K _C of K _A and K _B exists, proceed to the next step;

1.4.2.1 Calculate the area, face center and face normal direction calculated by K _C ;

1.4.2.2 adding K _C to L _c ;

1.4.2.3 Establish the mapping χ _CA (K _C )=K _A , χ _CB (K _C )= _{KB , indicating that K C is obtained} by the intersection of KA and _KB ;

S4: Check the area of the intersecting facets.

Further, in the step S7, the specific method of using _a filter to judge the intersection of KA and _KB is: If _KA and _KB may intersect, the following two formulas should be satisfied:

where r _A is the radius of the smallest sphere that can contain _KA ;

_rB is

n_C是中间面的面法向。d _AB represents the vector from the face center of K _A to the face center of K _B , namely

n _C is the face normal of the midplane.

Further, the spatial convex polygon intersection algorithm is:

₁ ) Identify a pair of potentially intersecting faces KA and _KB , and their midplane;

2) Projecting KA to the mid-plane to obtain _{a space convex polygon P A ;}

3) Perform the following operations on all edges of _KB ;

3.1 Create a cutting surface α _clip through the edge;

3.2 Use α _clip to cut P _A into two parts and get the reserved part;

3.3 Replace P _A with the reserved part obtained in this step;

4 ₎ If PA exists, proceed to the next step;

4.1 Store P _A as a facet, denoted as K _C , attached to K _A and K _B ;

4.2 Calculate the face center, area and face normal of K _C ;

4.3 Return K _C as the result.

The surface normal is calculated by the following formula,

Further, the space three-dimensional convex polygon cutting algorithm is:

1) Given a convex polygon P and its cutting surface α _clip (n _clip , r _clip );

2) Perform the following operations on all the vertices of P;

2.1 Judge and record whether the point is on the inner side of the cutting surface;

3) Create an empty polygon P _new ;

4) Perform the following operations on all the vertices of P;

4.1 If the point (N _i ) is inside the cutting plane, proceed to the next step;

_4.1.1 Add Ni to the vertex list of P _new ;

4.2 If _Ni and its next point Ni ₊₁ are on different sides of α _clip , proceed to the next step;

4.2.1 Calculate the intersection of N _i N _i+1 and α _clip , denoted as N _new ;

4.2.2 Add N _new to the vertex list of P _new ;

5) Return P _new .

Further, the vertex N inside the α _clip needs to satisfy the following formula:

(r _N -r _clip )·n _clip ≥0.

Further, the calculation method of the intersection point is:

r _new =r _i +λ(r _i+1 -r _i )

in,

Further, the facets obtained by the mesh and its intersection should satisfy the following formula:

and

Compared with the prior art, the beneficial effects of the present invention are:

The invention proposes a grid splicing calculation scheme for non-corresponding three-dimensional planes of arbitrary shapes in multi-region numerical simulation calculation, which makes it possible to deal with the non-corresponding region interface of complex geometry, and greatly reduces the grid connection in the application of computational fluid dynamics engineering. The limitation of grid usage can improve the computational efficiency of industrial numerical simulation software and expand its scope of application.

Description of drawings

In order to explain the technical solutions of the embodiments of the present invention more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments. Obviously, the accompanying drawings in the following description are only for explaining the embodiments of the present invention more clearly. Or technical solutions in the prior art, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative effort.

Figure 1 is a schematic diagram of converting a non-corresponding surface into a corresponding intersecting facet;

Fig. 2 is the schematic diagram of the interface with large curvature and rough mesh;

3 is a schematic diagram of a filter for judging whether two sides may intersect;

4 is a schematic diagram of the intersection process of two convex polygons in three-dimensional space;

Figure 5 is a schematic diagram of the fluid-structure coupling flow heat transfer problem in a bellows;

6 is a schematic diagram of the intersecting grid at the interface between the fluid area grid and the solid area grid;

Figure 7 is a schematic diagram of temperature distribution on certain sections in the flow direction in the bellows;

Figure 8. Schematic diagram of temperature distribution at the fluid-solid interface.

Detailed ways

In order to enable those skilled in the art to better understand that the technical solutions of the present invention can be implemented, the present invention will be further described below in conjunction with specific embodiments, but the examples are only used as descriptions of the present invention, not as limitations of the present invention.

As shown in Figure 1-4, a splicing algorithm based on three-dimensional non-corresponding mesh surfaces of any shape, the specific scheme includes:

1. Grid stitching

The core idea of the method of the present invention is to convert non-corresponding faces into smaller intersecting facets.

In Figure 1, (a) is the grid on both sides of the interface, and (b) is the generation of the intersecting grid.

Algorithm 1 General non-corresponding interface mesh stitching method for any 3D surface:

S1: Confirm the two sides τ _A and τ _B of the non-corresponding interface;

S2: define a list L _c for storing intersecting facets;

S3: Perform the following operations on _a certain face KA on all τ _A ;

1) Perform the following operations on a certain face _KB on all τ _B ;

1.1 Determine the middle plane τ _C ;

1.2 Calculate the surface normal n _C of the middle surface;

1.3 Use a filter to determine whether K _A and K _B may intersect;

1.4 If K _A and K _B may intersect, proceed to the next step;

1.4.1 Use projection to project _{KA and KB onto the midplane τ C and intersect} ;

1.4.2 If the intersection surface K _C of K _A and K _B exists, proceed to the next step;

1.4.2.1 Calculate the area, face center and face normal direction calculated by K _C ;

1.4.2.2 adding K _C to L _c ;

1.4.2.3 Establish the mapping χ _CA (K _C )=K _A , χ _CB (K _C )= _{KB , indicating that K C is obtained} by the intersection of KA and _KB ;

S4: Check the area of the intersecting facets.

2. Filters

To save computing resources, the present invention uses filters. For a certain face KA on _a certain τ _A , only a few _KBs on τ _B may intersect with it, and these _KBs can be obtained by simple judgment. As shown in Figure 2, (a) the vertical distance between the two sides should not be too large, and (b) the tangential distance between the two sides should not be too large.

As shown in Figure 3(a), the plane τ _C where the intersecting facets are located is determined by a point on the face and the normal direction of the face, as shown in the following equation:

n _C = -ω _A n _A +ω _B n _B (1)

r _C = ω _A r _A + ω _B r _B (2)

The weighting coefficient is expressed as follows,

As shown in Figure 3(b), from the definition of the filter, if K _A and K _B may intersect, the following two equations should be satisfied:

where r _A is the radius of the smallest sphere that can contain _KA ;

_rB is

n_C是中间面的面法向。d _AB represents the vector from the face center of K _A to the face center of K _B , namely

n _C is the face normal of the midplane.

ε ₁ and ε ₂ are filter parameters and default to 0.1 and 1.1.

_The equation ensures that the distance between KA and _KB in the vertical direction is small enough, and the equation ensures that the distance between _KA and _KB in the vertical direction of the surface normal angle is very small. If the two faces do not satisfy either of the formulas, the filter considers them disjoint and filters them out.

3. Space convex polygon intersection algorithm

When two polygonal faces pass the filter check, they are projected onto the midplane and intersected in space. An algorithm for plane intersection in space is disclosed herein. First, the middle plane is determined by equations (1) and (2), and the process of intersection is shown in Figure 4.

The left (a) in Figure 4 represents a polygon intersection graph in three-dimensional space, and the right (b) represents a representation of cutting a polygon in three-dimensional space.

Algorithm 2: Space convex polygon intersection algorithm:

₁ ) Identify a pair of potentially intersecting faces KA and _KB , and their midplane;

2) Projecting KA to the mid-plane to obtain _{a space convex polygon P A ;}

3) Perform the following operations on all edges of _KB ;

3.1 Create a cutting surface α _clip through the edge;

3.2 Use α _clip to cut P _A into two parts and get the reserved part;

3.3 Replace P _A with the reserved part obtained in this step;

4 ₎ If PA exists, proceed to the next step;

4.1 Store P _A as a facet, denoted as K _C , attached to K _A and K _B ;

4.2 Calculate the face center, area and face normal of K _C ;

4.3 Return K _C as the result.

In order to confirm the cutting plane in the above method ④, a known point on the plane and the plane normal of the plane are required. Taking Figure 4 as an example, the point on the cutting surface can be any point on the edge N1N2, such as 0.5(rN1+rN2).

The face normal is calculated by the following formula,

To ensure that the cutting surface is perpendicular to the cut surface. Use the remaining polygons after cutting with this cutting plane, and then use the next edge of _KB to do this cutting. After all the edges are cycled, the remaining polygons are the intersected polygons, as shown in Figure 4(b) . The following Algorithm 3 is an algorithm for cutting a space convex polygon with a cutting plane, and the algorithm returns a residual polygon after cutting, as shown in the center part of Fig. 4(b).

Algorithm 3: The spatial three-dimensional convex polygon cutting algorithm is:

1) Given a convex polygon P and its cutting surface α _clip (n _clip , r _clip );

2) Perform the following operations on all the vertices of P;

2.1 Judge and record whether the point is on the inner side of the cutting surface;

3) Create an empty polygon P _new ;

4) Perform the following operations on all the vertices of P;

4.1 If the point (N _i ) is inside the cutting plane, proceed to the next step;

_4.1.1 Add Ni to the vertex list of P _new ;

4.2 If _Ni and its next point Ni ₊₁ are on different sides of α _clip , proceed to the next step;

4.2.1 Calculate the intersection of N _i N _i+1 and α _clip , denoted as N _new ;

4.2.2 Add N _new to the vertex list of P _new ;

5) Return P _new .

In ③ of Algorithm 3, the vertex N inside α _clip needs to satisfy the following formula:

(r _N -r _clip )·n _clip ≥0.

中，交点的计算方法为：In order to reflect the closure of polygons, when looping vertices (Lines 6 to 14 of Algorithm 3), after looping all points, the next vertex of the last point is the first vertex of the loop, thus forming a closed loop. in step

, the calculation method of the intersection point is:

r _new =r _i +λ(r _i+1 -r _i )

in,

4. Grid quality check

The grid quality check can be used to determine whether the grid quality is up to standard for the invention. As mentioned earlier, using a coarse mesh at large curvatures will result in too large a vertical distance between two mesh faces that should intersect, and the filter may filter them out as two faces that are unlikely to intersect. As shown in Figure 2(a). In this case, the sum of the area of the generated facets will be significantly different from the area of the original face, because some of the facets that should exist are not generated. Ultimately, the conservation requirement of the finite volume method cannot be satisfied.

Numerically, the mesh quality is judged by comparing the sum of the area of the intersected facets with the area of the original face. The meshes that meet the requirements and their intersecting facets should satisfy the following formula,

and

Among them, ε3 is the allowable area error, which is generally set to 0.01. Meshes with substandard quality can be optimized by refining the mesh, especially where the curvature is large.

Example:

A coupled heat transfer problem solved using the present invention is presented here. As shown in Figure 5, the computational domains are the fluid region (Ω _A ) and the solid region (Ω _B ). The internal pipe diameter is 8mm-14mm. The fluid region is a high temperature inlet (100°C) with a fixed flow rate (0.1m/s). The outer walls of the solid region are at a fixed temperature (0°C).

The fluid density is 1000kg/m ³ , the dynamic viscosity coefficient is , the specific heat capacity is , and the thermal conductivity is . The thermal conductivity of the solid region is . This problem solves the steady-state fluid-structure coupled heat transfer.

The fluid and solid regions are discretized with hexahedrons and tetrahedrons, respectively. Figure 6 shows the interface obtained by this method.

Figures 7-8 show the temperature distribution of different sections in the bellows and the temperature distribution of the solid-liquid interface. Typical bellows flow heat transfer characteristics can be seen in the results. Under the cooling effect of the outlet boundary, the temperature tends to decrease in the flow direction. In the solid region, the high temperature is concentrated in the trough region because the central axis of the tube is closer in these regions. The temperature distribution maintains continuity at the interface. This example demonstrates the applicability of the present invention to coupled heat transfer problems.

The invention proposes a grid splicing scheme for non-corresponding three-dimensional planes of any shape, which makes it possible to deal with the non-corresponding area interface of complex geometry, greatly reduces the use restriction of grids in computational fluid dynamics engineering applications, and can improve industrial numerical value The computational efficiency of the simulation software and its scope of application are expanded.

Contents that are not described in detail in the present invention are all in the prior art.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of the present invention. within the scope of protection.

Claims (8)

1. a splicing algorithm based on the three-dimensional non-corresponding grid surface of any shape, is characterized in that, comprises the following steps: S1: Confirm the two sides τ _A and τ _B of the non-corresponding interface; S2: define a list L _c for storing intersecting facets; S3: Perform the following operations on _a certain face KA on all τ _A ; 1) Perform the following operations on a certain face _KB on all τ _B ; 1.1 Determine the middle plane τ _C ; 1.2 Calculate the surface normal n _C of the middle surface; 1.3 Use a filter to determine whether K _A and K _B may intersect; 1.4 If K _A and K _B may intersect, proceed to the next step; 1.4.1 Use projection to project _{KA and KB onto the midplane τ C and intersect} ; 1.4.2 If the intersection surface K _C of K _A and K _B exists, proceed to the next step; 1.4.2.1 Calculate the area, face center and face normal direction calculated by K _C ; 1.4.2.2 adding K _C to L _c ; 1.4.2.3 Establish the mapping χ _CA (K _C )=K _A , χ _CB (K _C )= _{KB , indicating that K C is obtained} by the intersection of KA and _KB ; S4: Check the area of the intersecting facets. 2. a kind of splicing algorithm based on three-dimensional non-corresponding grid surface of arbitrary shape according to claim 1, is characterized in that, adopts filter in described step S7 to judge the concrete mode that K _A and K _B intersect as: K _A If it is possible to intersect with K _B , the following two formulas should be satisfied:

where r _A is the radius of the smallest sphere that can contain _KA ;

_rB is

d _AB represents the vector from the face center of K _A to the face center of K _B , namely

n _C is the face normal of the midplane. 3. a kind of splicing algorithm based on arbitrary shape three-dimensional non-corresponding mesh surface according to claim 1, is characterized in that, space convex polygon intersection algorithm is: ₁ ) Identify a pair of potentially intersecting faces KA and _KB , and their midplane; 2) Projecting KA to the mid-plane to obtain _{a space convex polygon P A ;} 3) Perform the following operations on all edges of _KB ; 3.1 Create a cutting surface α _clip through the edge; 3.2 Use α _clip to cut P _A into two parts and get the reserved part; 3.3 Replace P _A with the reserved part obtained in this step; 4 ₎ If PA exists, proceed to the next step; 4.1 Store P _A as a facet, denoted as K _C , attached to K _A and K _B ; 4.2 Calculate the face center, area and face normal of K _C ; 4.3 Return K _C as the result. 4. a kind of splicing algorithm based on arbitrary shape three-dimensional non-corresponding mesh surface according to claim 1 and 2, is characterized in that, described surface normal is calculated by following formula,

5. a kind of splicing algorithm based on arbitrary shape three-dimensional non-corresponding mesh surface according to claim 1, is characterized in that, described space three-dimensional convex polygon cutting algorithm is: 1) Given a convex polygon P and its cutting surface α _clip (n _clip , r _clip ); 2) Perform the following operations on all the vertices of P; 2.1 Judge and record whether the point is on the inner side of the cutting surface; 3) Create an empty polygon P _new ; 4) Perform the following operations on all the vertices of P; 4.1 If the point (N _i ) is inside the cutting plane, proceed to the next step; _4.1.1 Add Ni to the vertex list of P _new ; 4.2 If _Ni and its next point Ni ₊₁ are on different sides of α _clip , proceed to the next step; 4.2.1 Calculate the intersection of N _i N _i+1 and α _clip , denoted as N _new ; 4.2.2 Add N _new to the vertex list of P _new ; 5) Return P _new . 6. a kind of splicing algorithm based on arbitrary shape three-dimensional non-corresponding mesh surface according to claim 5, is characterized in that, the vertex N in the inside of α _clip needs to satisfy following formula: (r _N -r _clip )·n _clip ≥0. 7. a kind of splicing algorithm based on arbitrary shape three-dimensional non-corresponding grid surface according to claim 5, is characterized in that, the calculation method of intersection is: r _new =r _i +λ(r _i+1 -r _i ) in,

8. a kind of splicing algorithm based on arbitrary shape three-dimensional non-corresponding grid surface according to claim 1, is characterized in that, the facet that grid and its intersection obtain should satisfy following formula:

and

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