CN104331584A - Automatic boundary layer calculation-orientated two-dimensional hybrid grid generating method - Google Patents
Automatic boundary layer calculation-orientated two-dimensional hybrid grid generating method Download PDFInfo
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Abstract
The invention discloses an automatic boundary layer calculation-orientated two-dimensional hybrid grid generating method, which comprises the following steps: embedding an input closed curve into triangular meshes by means of a restriction Delaunary triangularization method to obtain topological approximation edges approximating these curves and triangular meshes inside the curves, outwards propelling a topological approximation edge set as a boundary curve, automatically capturing a topological structure of the propelled new boundary and filling a quadrangular mesh of a propelling region to finally obtain a quadrangular/triangular hybrid mesh meeting the condition and the quality requirement. The automatic boundary layer calculation-orientated two-dimensional hybrid grid generating method is simple and easy to realize, good in reliability, and capable of automatically treating the boundary topological change and collision problem in an propelling process, has no special requirement for an initial two-dimensional closed curve, adapts to the requirement of dense computational grids required by large velocity gradient change in a flow field around a boundary layer, can generate an unstructured triangular mesh with flexible scale change in a place far away from the boundary layer, and can provide the high-quality mesh for correlation calculation of computational fluid mechanics.
Description
Technical field
The present invention relates to the field such as computational geometry and computational fluid dynamics, its objective is according to boundary-layer and the around geometrical property in flow field and the needs of Fluid Mechanics Computation, design a kind of automatic hybrid grid generation method being applicable to the two-dimentional closed curve of arbitrary shape, the Fluid Mechanics Computation being applied to boundary-layer calculates, thus improves precision and the efficiency of Flow Field Calculation.Be specifically related to curve discretization, limit the problems such as the topological automatic capturing of mesh generation and curved boundary.
Background technology
When boundary-layer refers to that water, air or other low viscous liquid move in a fluid along solid surface flowing or solid, in high reynolds number situation, invest a layer fluid of solid surface.Be subject to the impact of viscous effect, in the place being close to body surface, the flow velocity of boundary-layer is started from scratch along object normal direction and is increased gradually, increases to the identical speed of air in very short distance.Therefore in order to meet the fast characteristic of boundary-layer change in flow, when carrying out viscosity flow and calculating, need the structured grid generating tiny level closely at boundary-layer, not only internal memory can be saved, very strong direction viscous stress can also be caught, need the part beyond boundary-layer to generate unstructured grid simultaneously and describe complicated geometric shape.
Hybrid grid is between structuring and unstructured grid one and trades off, and it combines the orthogonality of structured grid and directivity, the dirigibility of unstructured grid and ease for use.Current hybrid grid has become a kind of novel, effective grid generation technique processing complex geometry profile.When running into typical high reynolds number in the application of computational fluid dynamics, be very important in the impact of the boundary layer viscosity near surface, can be represented by quadrilateral in these regions, adopt triangular mesh at its complementary space.Its advantage is, because the boundary-layer region near object boundary have employed structuring quadrilateral mesh, intensive grid can be arranged along surface normal direction, improve the accuracy that boundary-layer subfield value calculates, the region comparatively slow in outside fluid properties change uses triangle gridding, can utilize triangle gridding dimensional variation flexibly characteristic number of grid is greatly reduced, thus current computer resource can be effectively utilized, the method for this hybrid grid makes unstrctured grid successfully can be applied to VISCOUS FLOW.Therefore quadrilateral/triangle hybrid grid more meets the actual needs of current Fluid Mechanics Computation.
The algorithm of current generation triangular mesh mainly contains four/Octree method, Delaunay trigonometric ratio method and advancing front technique, wherein Delaunay Triangulation Algorithm is with its complete mathematical theory foundation, becomes current application and research the most full-automatic triangular mesh generation method.But the calculating of application triangular mesh technology is at present calculate without sticky mostly, and VISCOUS FLOW analysis requires that the grid of object plane is more intensive.And the length of normal degree ratio a lot of order of magnitude less of length of tangent degree ratio, therefore needs the grid cell that draw ratio is very large in boundary layer.Common Delaunay trigonometric ratio method needs to adopt anisotropy technology to realize when the large draw ratio unit in generation boundary layer, and the triangular mesh element quality after stretching is difficult to ensure, impact for counting yield also needs to carry out careful assessment, and quadrilateral mesh have can the feature of high elongation, may be used for the grid generating adhesive region.
For there being sticky calculating, existing quadrilateral/triangle hybrid grid is all based on traditional promoting layer method and is improved it and grow up, for can't effectively solving of curve interface fusion and long and narrow clearance issues, and cannot guarantee can both automatically process any complex appearance, quality simultaneously for grid cell also cannot provide theoretic guarantee, and in adhesive region, when surface mesh is forwards advanced, when target area be recessed geometrical construction or be made up of many geometric areas time, the situation of grid node or unit conflict and disappearance can be produced when pushing ahead, also there is no effective disposal route automatically at present.
In verge advance process, key issue is the process to moving interface.Disposal route at present about moving interface is mainly divided into two classes, and a class is Euler's type method, and another kind of is Lagrangian type method.In Euler's type method, the foundation of grid is based on volume coordinate, arrange that some particles carry out marked fluid within a grid, by solving to particle in governing equation the position and shape that catch interface, the locus of grid in whole analytic process is constant, therefore in the process of whole numerical simulation, the precision of numerical evaluation is constant, but the method can not accurately locate multimedium interface, be not suitable for the exigent numerical simulation of interface location.Lagrange rule directly sets up coordinate in research object, interface defines some gauge points, the motion of modeling interface is carried out by the track of tracking point, the method can follow the trail of the evolution of interface accurately, but be difficult to the change (as interface fusion and division) processing interface topological structure, and when being extended to higher-dimension situation, algorithm is very complicated.The Level Set method of the improvement mainly containing grid class methods, VOF method and Level Set method in Euler's type method and propose for various problem.T-Snake model, the interface-tracking method of Glimm and the Particle Level Set method based on particle is mainly contained in Lagrange type method.
What be most widely used in capture moving interfaces problem at present is Level Set method in Euler's type method, its basic thought is using zero contour surface of moving interface as more higher-dimension scalar field, impel the change of scalar field by solving relevant partial differential governing equation, thus drive the moving interface as zero contour surface to develop.The method has a lot of advantages, but find when process advances border to catch, because it needs the calculating of more higher-dimension, therefore solution procedure is complicated, calculated amount is large, simultaneously due to the reason such as numerical dissipation and numerical error, the triangular element quality obtained is unstable, and the method has topological independence, not contact between border before and after advancing, when carrying out quadrangular mesh partition like this between to propelling boundary layer, processing procedure can more complicated.
In sum, the hybrid grid generation method calculated based on boundary-layer at present has a variety of, but often exist and calculate the problems such as loaded down with trivial details, range of application is narrow, robotization is poor, therefore, the algorithm existed cannot be applied to the hybrid grid calculated towards boundary-layer and automatically generate.
Summary of the invention
The technology of the present invention is dealt with problems: overcome the deficiencies in the prior art, provides a kind of two-dimentional hybrid grid generation method calculated towards boundary-layer,
Be intended to solve the robotization Generating Problems towards the quadrilateral/triangulation network hybrid grid during calculating of boundary-layer in Fluid Mechanics Computation, by at boundary-layer area filling hybrid grid, adapt to the attribute acute variation of boundary-layer place fluid under viscous fluid effect, thus the high-precision analog meeting boundary-layer place calculates.Initial conditions of the present invention is any one or more of closed curve on two dimensional surface, after the sequence of operations to curve, the present invention can realize the automatic generation to boundary-layer and surrounding hybrid grid thereof, and to the optimization that the yardstick of grid cell and quality carry out to a certain degree, method is easy to realize, simple and reliable.
The technical scheme that technical solution problem of the present invention adopts is: provide a kind of two-dimentional hybrid grid automatic generating method calculated towards boundary-layer, in order to the characteristic of the VISCOUS FLOW according to boundary-layer, very fine and closely woven structuring quadrilateral mesh is generated to improve the precision of Viscous Flow numerical evaluation in Fluid Mechanics Computation near boundary-layer, adapt to the large computing grid of flow field velocity graded around boundary-layer and require close requirement, and generating the larger destructuring triangular mesh of yardstick away from boundary-layer place, to reduce integral grid quantity, improve the efficiency of numerical evaluation.Its feature comprises the following steps:
Steps A: input one or more of closed two-dimensional curve;
Step B: generate the Delaunay triangulation network lattice under the restriction of above-mentioned two-dimensional curve, two-dimensional curve is embedded in triangle gridding, and is the triangle gridding unit that boundary marker closes two-dimensional curve inside with two-dimensional curve;
Step C: the triangle gridding unit of the two-dimensional curve be embedded in triangle gridding together with inside is advanced along direction of propulsion, to generate after advancing on curve new Delaunay triangulation network lattice a little, and ball detection of attribute is closed to obtain the topological structure advancing rear curve by topology, finally identify in new triangle gridding and drop on the rear curvilinear inner of propelling and outside triangle;
Step D: fill hybrid grid between curve at two-dimensional curve with after advancing, if also need outside propelling, is then set to two-dimensional curve by curve after propelling and returns step C, otherwise, complete boundary-layer structured grid and generate, perform step e;
Step e: the triangle gridding of curved exterior after advancing in extraction step C, the generation of the overall hybrid grid that finished surface calculates to boundary-layer.
Described hybrid grid comprises triangle and quadrilateral mesh; Boundary-layer is the closed curve of input, after this curve discrete is become line segment aggregate, curve method vows that outside generates the structuring quadrilateral mesh of specifying the number of plies, be especially triangle gridding unit at outermost one deck network of quadrilaterals, wherein outermost quadrilateral mesh and triangle gridding topological coherence, namely the outer side edges of outermost quadrilateral mesh is the limit of triangle gridding unit.
Described steps A comprises further, and the two-dimensional curve inputted can be the closed curve of one or more mutually disjoint arbitrary shape; The form of two-dimensional curve can be arbitrary, and both can be connected with line segment the broken line formed by point, also can be the smooth two-dimentional closed curve compacted; The expression-form of two-dimensional curve also can be arbitrary, as long as correctly can describe two-dimensional curve.
Described step B comprises further, first the quadrilateral bounding box of input two-dimensional curve is generated, using two triangles after this bounding box diagonally subdivision as initial Delaunay triangulation network lattice, whether meet topology by the antithesis Voronoi limit of detecting Delaunay triangulation network lattice and the intersection point of input two-dimensional curve to close ball attribute and constantly in Delaunay triangulation network lattice, add new summit according to rule, until its satisfied topology closes ball attribute.In final grid, the two-dimentional closed curve of every bar input is all embedded in Delaunay triangulation network lattice, namely represented by the broken line that this curve can be formed with the triangle edges of its topological homeomorphism by a group, these triangle edges are defined as topology and approach limit, can not there is the triangular element striding across input curve both sides.And identify in triangle gridding the triangle that surrounds by two-dimentional closed curve as inside triangle.
Described step C comprises further, and the topology of the two-dimensional curve be embedded in triangle gridding is approached limit as initial propelling limit, the inside triangle be communicated with associated by this limit advances to direction of propulsion together; Direction of propulsion is advance the method for the point on limit on curve to vow or direction defined by the user, and advance distance is user's appointment; If the triangular element of all curvilinear inner its leg-of-mutton three summits after propelling occur in sequence reversion change, from inside triangle set, reject this triangle; The new Delaunay triangulation network lattice on summit, all propelling limits are generated after advancing, and make the antithesis Voronoi limit in this triangle gridding meet topology relative to the region that all inner triangular grids are formed to close ball attribute by adding point operation, topology in final triangle gridding approach set that limit forms be curve advance after the topological structure of curve after new propelling, finally identify in new Delaunay triangulation network lattice drop on advance after curvilinear inner and outside triangle.
Described step D comprises further, if initial propulsion limit still exists after propelling in new Delaunay triangulation network lattice in step C, then characterizes this region topology and does not change, and directly connects these two and advances the corresponding point on limit to form quadrilateral mesh unit.If do not exist, illustrate that this region there occurs change in topology, form change in topology band after advancing limit to collect these, fill suitable quadrilateral mesh or triangular mesh wherein; If advance number of times do not meet user setting number of times, then arranging the curve after propelling is that original two-dimensional curve returns previous step, otherwise complete boundary-layer structured grid generate carry out next step.
Described step e comprises further, after advancing in step C, curve is the last curved boundary advanced, extract the external triangular set in the Delaunay triangulation network lattice of last curved boundary, these triangular elements with advances border to meet topological coherence for the last time, then the hybrid grid unit of generation each in all external triangular unit, step D be together form the two-dimentional hybrid grid that entirety is used for boundary-layer calculating.
Method of the present invention may be summarized to be: be first embedded in Delaunay triangle meshes by input closed curve by limiting Delaunay Triangulation Algorithm, and the topology obtaining approaching these curves approaches limit and inner triangular grid, topology approached limit set and outwards advance as boundary curve, by the automatic capturing of the topological structure to border new after propelling, and to advancing the quadrilateral mesh in region to fill, be finally met the quadrilateral/triangle hybrid grid of condition and quality requirements.
The present invention's advantage is compared with prior art: the requirement of the present invention to initial conditions is general, and namely arbitrary shape, the arbitrarily two-dimentional closed curve of expression-form all meet requirement of the present invention; Mess generation process of the present invention is automatic, and the process of the existing hybrid grid generation method towards boundary-layer calculating is all very loaded down with trivial details, and the position that topology changes in verge advance process can not well catch new border.And formation efficiency of the present invention is very high, and in verge advance process, inside triangle is driven to advance together, and catch the border after propelling by diabolo inside, outside sign, border catches more accurate, and the border changed for topology also can automatic capturing, thus generates the compact fine and closely woven structured grid of level at boundary-layer, therefore more tally with the actual situation, high-quality grid can be provided for Fluid Mechanics Computation.
Accompanying drawing explanation
Fig. 1 two dimension quadrilateral/triangle hybrid grid schematic diagram;
Fig. 2 convex curve is vowed to advance along method and is generated hybrid grid schematic diagram;
Fig. 3 inner concave shape curve conflicts with the topology in many curves progradation schematic diagram;
The two-dimentional hybrid grid that Fig. 4 calculates towards boundary-layer generates method flow diagram;
Fig. 5 antithesis Voronoi schemes the final crossing situation schematic diagram with closed curve;
The final grid chart of Fig. 6 closed curve after being embedded into Delaunay triangulation network lattice;
Inside triangle before and after Fig. 7 advances and topology approach limit;
The quadrilateral mesh unit formed in Fig. 8 filling process and the schematic diagram of polygonal element band;
The input of Fig. 9 first instance model closes concave curve;
The restriction Delaunay triangulation network lattice of Figure 10 first instance model;
The first time of Figure 11 first instance model advances result to the 4th time;
The border of Figure 12 first instance model advances for the 5th time the rear border occurred to intersect situation;
The topological diagram of the outer boundary that Figure 13 first instance model catches after intersecting after advancing for the 5th time;
The polygonal element of the boundary topology region of variation formation of Figure 14 first instance model;
The filling situation of hybrid grid in the change in topology region of Figure 15 first instance model;
The final hybrid grid of Figure 16 first instance model;
Delanay triangle gridding under the original input closed curve of Figure 17 second instance model and curve constraint;
First three verge advance result figure of Figure 18 second instance model;
Topological conflict situations after 4th propelling of Figure 19 second instance model;
Outer boundary figure after Figure 20 second instance model the 4th time advances after the detail view of topological conflict area and automatic Reconstruction;
The polygonal element of topological conflict area and the hybrid grid of filling thereof after Figure 21 second instance model advances for the 4th time;
The hybrid grid generation result figure that Figure 22 second instance model is final.
Embodiment
In process fluid flow, fluid flowing affecting its character and in wall normal direction, violent change can occur by VISCOUS FLOW on thin layer near object outside wall surface, in order to the physical phenomenon of accurate simulation flowing, set up with regard to needing the precision that very fine and closely woven structured grid ensures Viscous Flow numerical evaluation at wall thin layer place.Meanwhile, in order to avoid the problem of the numerical evaluation efficiency reduction that too much number of grid brings, adopt in the region away from this wall thin layer the efficiency improving numerical evaluation compared with the triangular mesh of large scale.This quadrilateral/triangle hybrid grid has a very wide range of applications in Fluid Mechanics Computation, as shown in Figure 1.
The generation of hybrid grid is the committed step of the Computational fluid mechanics numerical simulation carrying out high-accuracy high-efficiency rate, designs one and can be applicable to polytype geometrical boundary flexibly and the mess generation method that can efficiently automatically generate is exactly a very important job.
The method generating this kind of grid is a lot, its key is that the structured grid how solving boundary-layer place generates, and for convex curve, the discrete point on curve successively advances along its method arrow by general employing, advancing front technique is finally adopted to generate outside triangular mesh, as shown in Figure 2.But when its subject matter is along wall normal orientation structural texture grid, when wall be inner concave curve or be made up of multiple closed curve time, to direction of normal advance structured grid can clash, as shown in Figure 3.In existing hybrid grid generating algorithm, boundary edge is just pushed ahead by traditional front advancing method, cannot accurately calculate for the change on border when border is intersected, be therefore difficult to automatically capture border intersect after topology.The object of the invention is to overcome above-mentioned deficiency, provide a set of and effectively meet above-mentioned feature, and be easy to the hybrid grid generation method of realization.
The present invention proposes a kind of robotization hybrid grid generation method towards boundary-layer, except can generate meet behavior of boundary layer quadrilateral/triangle hybrid grid except, automatically can also process the topological collision problem in boundary-layer place structured grid generative process.In the present invention, first carry out the division of the restriction Delaunay triangle meshes inputting closed curve, input closed curve is embedded in triangle gridding; The triangle gridding being positioned at closed curve inside is defined as interior zone, in the process of verge advance, makes border drive interior zone triangle to advance together, thus drive inner area extension of a field; Then by the Boundary Extraction advancing rear interior zone, capture the new border that the topology after propelling changes, and carry out quadrilateral mesh filling on new border and original boundaries interlayer, repeat the hybrid grid that said process finally obtains whole region.Fig. 4 gives the two-dimentional hybrid grid product process figure calculated towards boundary-layer of the present invention.Below be described in detail further.
First be step 200, input one or more of closed two-dimensional curve.The curve of input can be the closed curve of arbitrary shape, also can be the curve of any expression-form, as SPL, parametric line or the broken line that is made up of line segment.There is not self intersection in single curve, there is not overlapping relation between many closed curves.
Step 210, the Delaunay triangulation network lattice under using complicated restriction Delaunay Triangulation Algorithm to calculate above-mentioned curve constraint, are embedded into boundary curve in triangle gridding.
First the quadrilateral bounding box of input curve is generated, using two triangles after this bounding box diagonally subdivision as initial Delaunay triangulation network lattice, whether meet topology by the intersection point on the antithesis Voronoi limit and input curve of detecting Delaunay triangulation network lattice to close ball attribute and constantly in Delaunay triangulation network lattice, add new summit according to rule, until its satisfied topology closes ball attribute.The method adding new point in Delaunay triangulation network lattice can adopt classical Delaunay cavity algorithm (Bowyer/Watson algorithm) or partial transformation method.
Specifically, namely calculate the antithesis Voronoi limit of each triangle edges in Delaunay triangulation network lattice and input closed curve intersection of sets point, and take following operation according to the number of intersection point:
If with the number of certain closed curve intersection point more than 1, then the end points of its middle distance triangle edges intersection point is farthest joined in Delaunay triangulation network lattice;
If equal 1 with the number of certain closed curve intersection point, then judge whether that two end points of triangle edges are all on this closed curve, then join in tetrahedral grid by intersection point if not;
If meet at respectively a bit with multiple closed curve, then these intersection points are all joined in Delaunay triangulation network lattice.
If the antithesis Voronoi limit of this triangle edges only meets at a bit with a closed curve, then recording this triangle edges is that the topology of this closed curve approaches limit, record the Delaunay ball (centre of sphere is the intersection point of antithesis Voronoi limit and this closed curve, and radius is the distance that the centre of sphere arrives triangle edges end points) corresponding to this limit simultaneously.If it is not crossing with any closed curve, then recording this triangle edges is empty limit.All carried out traveling through when limits all in triangle gridding and it be set or approach limit for the topology of certain closed curve, or be behind empty limit, then should carry out one dimension topology and close ball detection of attribute, namely for each triangular apex in Delaunay triangulation network lattice, judge that in all coupled triangle edges, the topology whether existed more than certain closed curve of 2 approaches limit, if then illustrate that the antithesis Voronoi unit on now this summit and the friendship of closed line do not meet one dimension topology and close ball attribute, this triangular apex of Delaunay centre of sphere middle distance Delaunay centre of sphere point farthest that then these should be approached corresponding to limit joins in grid, until all triangular apex meet the demands, final generation meets the Delaunay tetrahedral grid of closed curve constraint condition.Fig. 5 gives antithesis Voronoi and schemes the final crossing situation schematic diagram with closed curve, and Fig. 6 gives the final grid chart of multiple closed curve after being embedded into Delaunay triangulation network lattice.
In final grid, the closed curve of every bar input is all embedded in Delaunay triangulation network lattice, namely represented by the broken line that this curve can be formed with the triangle edges of its topological homeomorphism by a group, these triangle edges are defined as topology and approach limit, can not there is the triangular element striding across input curve both sides.Utilize these to be embedded into closed curve in triangle gridding, can calculate and identify in triangle gridding the triangle being closed Curves and surrounding, defining these triangles is inside triangle.
Step 220, curve advances and rebuilds the topology advancing rear curve.The topology of above-mentioned curve is approached limit as initial propelling limit, the triangle being communicated with the curvilinear inner associated by this limit advances to direction of propulsion together; Direction of propulsion is advance the method for the point on limit on curve to vow or direction defined by the user, and advance distance is user's appointment.If the triangular element of all curvilinear inner its leg-of-mutton three summits after propelling occur in sequence reversion change (direction of normal that namely an Atria summit obtains according to right-hand rule there occurs change), from inner triangular grid, reject this triangle.
Then generate the Delaunay triangulation network lattice on the summit, propelling limit after all propellings, and make the antithesis Voronoi limit in this triangle gridding meet topology relative to the region that all inner triangular grids are formed to close ball attribute by adding point operation.The detection method of concrete grammar and step 210 is similar, the intersection point in region shared by what its key distinction calculated when being intersection point calculation is antithesis Voronoi limit and inside triangle, an end points namely along this antithesis Voronoi limit passes in and out the frontier point once of region shared by inside triangle in another one end points advance process.
The topology in the inside triangle region in the final triangle gridding that topology is formed after closing ball detection of attribute is approached set that limit forms and is curve and advances topological structure new once.Before Fig. 7 gives and advances, inside triangle (triangle that in figure, left figure is filled) and borderline topology thereof approach the shape on limit, and the topology after advancing the change (middle graph light-colored part is the inside triangle be reversed) of rear inside triangle and final topology to rebuild approaches limit and inside triangle (in figure right figure).
Step 230, catches the new border after advancing, and carries out hybrid grid filling at verge advance interlayer.If advance limit still approach limit as topology in new Delaunay triangulation network lattice and exist after propelling in previous step, then characterizing this region topology does not change, and directly connects these two and advances the corresponding point on limit can form a quadrilateral mesh unit.If do not exist, illustrate that this region there occurs change in topology, form change in topology polygonal band after advancing limit to collect these, fill suitable quadrilateral mesh or triangular mesh according to the delaunay triangle method of classics wherein.Finally judge to advance the number of times whether meeting user's setting, then return step 220 if not, if carry out step 240.Fig. 8 gives the schematic diagram of quadrilateral mesh unit and the polygonal element band formed in filling process.
Step 240, curve advances outside optimization triangle gridding the last time.The propelling border after last propelling is captured in Delaunay triangulation network lattice after advancing the last time, all triangular elements at border outer in mark triangle gridding, these triangular elements meet topological coherence with advancing border, and quality optimization is carried out to these triangle gridding unit, specific practice is outside each triangular element, if its quality index triangle circumradius is greater than given quality threshold with the ratio of most bond length, then calculate the circumcenter of this unit, if this centre point does not approach in the Delaunay ball on limit in any topology, then this point is joined in triangular mesh the quality and yardstick of improving this unit.Finally will meet the external triangular of quality requirements, in step 230, each hybrid grid unit generated together form the overall two-dimentional hybrid grid calculated for boundary-layer.
In sum, following two examples are provided.First model be input as closed concave curve, as shown in Figure 9; Figure 10 is the restriction Delaunay triangulation network lattice utilizing the complicated Delaunay of restriction Triangulation Algorithm to generate, and as can be seen from the figure curve has been embedded in triangle gridding completely, and the topology that boundary line, outside is input curve approaches limit set; According to given step-length, outwards advanced by curved boundary, in first time in the 4th progradation, the topological structure of boundary curve does not all change, as shown in figure 11; Figure 12 shows that situation is intersected on the border occurred after border advances for the 5th time, Figure 13 is the topological diagram of the outer boundary caught after intersecting, by the seizure to new border, make wall scroll closed curve border after self intersection, split into two closed curve borders, also reflected that the method that the present invention provides can process self intersection situation in concave curve verge advance process simultaneously, the hybrid grid situation of fill area after border the 5th time advances by Figure 14, obtains quadrilateral that frontier point is connected to form naturally and the polygonal region that change in topology region is formed; Figure 15 gives the filling situation of hybrid grid in change in topology region; The final hybrid grid generated after finally adding border outer triangle gridding, as shown in figure 16.
The closed curve being input as two simulation air-foils of second model, Figure 17 gives the result of the Delanay triangulation under original input closed curve and curve constraint; Figure 18 gives the generation situation of the propelling regional structure quadrilateral mesh after first three verge advance, can find out and topology conflict does not now occur; Figure 19 gives the topological conflict situations after advancing for the 4th time; Figure 20 be topological conflict area detail view and topology conflict automatic Reconstruction after outer boundary figure; Figure 21 gives the polygonal element of topological conflict area and the result after filling hybrid grid thereof; Figure 22 is that final hybrid grid generates result figure.
In a word, the present invention is simply easy to realize, good reliability, automatically can process the boundary topology change in progradation and collision problem; For initial two-dimentional closed curve without particular/special requirement; Adapt to the large computing grid of flow field velocity graded around boundary-layer and required close requirement, and generating dimensional variation destructuring triangular mesh more flexibly away from boundary-layer place, high-quality grid can be provided for Fluid Mechanics Computation.
Certainly; the present invention can also have other various embodiments; when not deviating from the present invention's spirit and essence thereof; those of ordinary skill in the art are when making various corresponding change and distortion according to the present invention, but these change accordingly and are out of shape the protection domain that all should belong to the claim appended by the present invention.
Claims (7)
1., towards the two-dimentional hybrid grid automatic generating method that boundary-layer calculates, its feature comprises the following steps:
Steps A: input one or more of closed two-dimensional curve;
Step B: generate the Delaunay triangulation network lattice under the restriction of above-mentioned two-dimensional curve, two-dimensional curve is embedded in triangle gridding, and is the triangle gridding unit that boundary marker closes two-dimensional curve inside with two-dimensional curve;
Step C: the triangle gridding unit of the two-dimensional curve be embedded in triangle gridding together with inside is advanced along direction of propulsion, to generate after advancing on curve new Delaunay triangulation network lattice a little, and ball detection of attribute is closed to obtain the topological structure advancing rear curve by topology, finally identify in new triangle gridding and drop on the rear curvilinear inner of propelling and outside triangle;
Step D: fill hybrid grid between curve at two-dimensional curve with after advancing, if also need outside propelling, is then set to two-dimensional curve by curve after propelling and returns step C, otherwise, complete boundary-layer structured grid and generate, perform step e;
Step e: the triangle gridding of curved exterior after advancing in extraction step C, the generation of the overall hybrid grid that finished surface calculates to boundary-layer.
2. a kind of two-dimentional hybrid grid automatic generating method calculated towards boundary-layer according to claim 1, it is characterized in that: described mess generation method can process automatically for the curve change in topology in boundary-layer curve progradation, and described hybrid grid comprises triangle and quadrilateral mesh; The quadrilateral mesh of generating structured in boundary-layer, grid form can be tiny and tight, meets the requirement that simulation boundary-layer velocity field graded is large; Generate destructuring triangular mesh outward at boundary-layer, become large by boundary-layer gradually to external measurement, be convenient to improve numerical evaluation efficiency.
3. a kind of two-dimentional hybrid grid automatic generating method calculated towards boundary-layer according to claim 1, it is characterized in that: described steps A comprises further, the two-dimensional curve inputted can be the closed curve of one or more mutually disjoint arbitrary shape; The form of two-dimensional curve can be arbitrary, and both can be connected with line segment the broken line formed by point, also can be the smooth two-dimentional closed curve compacted; The expression-form of two-dimensional curve also can be arbitrary, as long as correctly can describe two-dimensional curve.
4. a kind of two-dimentional hybrid grid automatic generating method calculated towards boundary-layer according to claim 1, is characterized in that; Described step B comprises further, first the quadrilateral bounding box of input two-dimensional curve is generated, using two triangles after this bounding box diagonally subdivision as initial Delaunay triangulation network lattice, whether meet topology by the antithesis Voronoi limit of detecting Delaunay triangulation network lattice and the intersection point of input two-dimensional curve to close ball attribute and constantly in Delaunay triangulation network lattice, add new summit according to rule, until its satisfied topology closes ball attribute.In final grid, the two-dimentional closed curve of every bar input is all embedded in Delaunay triangulation network lattice, namely represented by the broken line that this curve can be formed with the triangle edges of its topological homeomorphism by a group, these triangle edges are defined as topology and approach limit, can not there is the triangular element striding across input curve both sides.And identify in triangle gridding the triangle that surrounds by two-dimentional closed curve as inside triangle.
5. a kind of two-dimentional hybrid grid automatic generating method calculated towards boundary-layer according to claim 1, it is characterized in that: described step C comprises further, the topology of the two-dimensional curve be embedded in triangle gridding is approached limit as initial propelling limit, the inside triangle be communicated with associated by this limit advances to direction of propulsion together; Direction of propulsion is advance the method for the point on limit on curve to vow or direction defined by the user, and advance distance is user's appointment; If the triangular element of all curvilinear inner its leg-of-mutton three summits after propelling occur in sequence reversion change, from inside triangle set, reject this triangle; The new Delaunay triangulation network lattice on summit, all propelling limits are generated after advancing, and make the antithesis Voronoi limit in this triangle gridding meet topology relative to the region that all inner triangular grids are formed to close ball attribute by adding point operation, topology in final triangle gridding approach set that limit forms be curve advance after the topological structure of curve after new propelling, finally identify in new Delaunay triangulation network lattice drop on advance after curvilinear inner and outside triangle.
6. a kind of two-dimentional hybrid grid automatic generating method calculated towards boundary-layer according to claim 1, it is characterized in that: described step D comprises further, if initial propulsion limit still exists after propelling in new Delaunay triangulation network lattice in step C, then characterize this region topology not change, directly connect these two and advance the corresponding point on limit to form quadrilateral mesh unit.If do not exist, illustrate that this region there occurs change in topology, form change in topology band after advancing limit to collect these, fill suitable quadrilateral mesh or triangular mesh wherein; If advance number of times do not meet user setting number of times, then arranging the curve after propelling is that original two-dimensional curve returns previous step, otherwise complete boundary-layer structured grid generate carry out next step.
7. a kind of two-dimentional hybrid grid automatic generating method calculated towards boundary-layer according to claim 1, it is characterized in that: described step e comprises further, after advancing in step C, curve is the last curved boundary advanced, extract the external triangular set in the Delaunay triangulation network lattice of last curved boundary, these triangular elements with advances border to meet topological coherence for the last time, then the hybrid grid unit of generation each in all external triangular unit, step D be together form the two-dimentional hybrid grid that entirety is used for boundary-layer calculating.
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