CN107391871A

CN107391871A - A kind of space lattice deformation method based on parallelization RBF

Info

Publication number: CN107391871A
Application number: CN201710655495.5A
Authority: CN
Inventors: 赵钟; 常兴华; 马戎; 何磊
Original assignee: Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
Current assignee: Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
Priority date: 2017-08-03
Filing date: 2017-08-03
Publication date: 2017-11-24

Abstract

The invention discloses a kind of space lattice deformation method based on parallelization RBF, comprise the following steps：Step 1: establish parallel architecture, the grid of computational fields is subjected to subregion, the corresponding process of each blockette, and each process is had the backup of a global object plane unit；Step 2: traveling through all spatial points in each process, parallel RBF deformations are carried out, wherein, each point that each spatial point is concentrated using its control point performs serial RBF deformations as control point, and solution obtains the deflection of spatial point.Compared with prior art, the positive effect of the present invention is：Versatility is good, and the parallelization RBF that the present invention uses has stronger versatility, is suitable for the application fields such as data interpolating, distortion of the mesh；Method is simple, it is only necessary to a small amount of change, it is possible to by the RBF method parallelizations of existing serialization.

Description

A kind of space lattice deformation method based on parallelization RBF

Technical field

The present invention relates to one kind based on parallelization RBF (Parallel Radial Basis Function, with Space lattice deformation method down referred to as " PRBF ").

Background technology

With the continuous development of modern numerical analogy method, the physical problem increasingly approaching to reality profile of numerical simulation, Multiple physical field, unsteady simulation are developed into from former single physical field, permanent simulation.Fluid Mechanics Computation (CFD), as A kind of effective flight vehicle aerodynamic simulation means, have also obtained more and more extensive application, have been mainly shown as unsteady simulation side Method has obtained increasing engineer applied.Real physical world is essentially all the UNSTEADY FLOW under dynamic boundary condition. In the problems such as Multi-bodies Separation of aircraft and boost motor, fluid structurecoupling problem, wing deformation, object plane profile can constantly become with the time Change, it is necessary to the mesh point in space also be changed therewith, i.e. distortion of the mesh.

Currently conventional space lattice deformation method is mainly based upon SPRING METHOD OF STONE and Radial Basis Function Method, former approach letter It is single, but poor universality；The latter's versatility is good, there is larger technical advantage in distortion of the mesh field.

RBF (Radial Basis Function, hereinafter referred to as " RBF ") method, it is that one kind utilizes distance The method that basic function carries out data interpolating, is widely used in engineering fields such as computational mathematics, numerical simulations.For example, entering Promoting the circulation of qi is dynamic/heat/structure multi- scenarios method simulation in, for the flow field variable interpolation between space cell and object plane unit；In bullet Property the Moving Boundary Problem such as deformation, Multi-bodies Separation in, by the way that the deformation of the point on object plane is interpolated into space, realize that space lattice becomes Shape.

The general principle of the existing space lattice deformation method based on RBF is：

Here, N is that (control point subset is by the multiple object plane deformation points nearest from spatial point for the number at control point subset midpoint Form), f (r) is space midpoint P_field,iDisplacement, r P_field,iPosition, r_iFor i-th of object plane control point P_surface,i Initial position, | | r-r_i| | represent P_field,iAnd P_surface,iBetween Euclidean distance,Selected RBF is represented, w_iRepresent i-th of object plane control point P_surface,iThe weight coefficient at place, by taking x directions as an example, the coefficient meets following relational expression：

Wherein, Δ x_iFor i-th of object plane control point P_surface,iDeflection,Basic functionGeneral choosing It is defined as with C2 functions：

By formula (1), by the positional displacement interpolation of object plane point to space, the deflection of spatial point is obtained.

It is so far, several although Radial Basis Function Method has obtained a large amount of uses in mesh deformation technique The application of the overwhelming majority is all based on serial method, and this is due to the matrix operation being related in RBF methods in formula (2), And the matrix in the formula right-hand vector is made up of the object plane point in global calculation domain so that RBF methods are difficult to parallelization.Although at present There are some preliminary Parallel Algorithms in academia, but be typically all to use third party's math libraries such as PETs, LAPACK, , the problem of robustness is poor, efficiency is low, poor universality be present in the matrix progress parallelization in formula (2) inversion operation.

Due to being limited by computer resource, the Radial Basis Function Method of serialization make it that it is solid in Multi-bodies Separation, stream It is very restricted in the numerical simulation problems such as coupling.

The content of the invention

In order to overcome the disadvantages mentioned above of prior art, the present invention proposes a kind of space based on parallelization RBF Grid deforming method.

The technical solution adopted for the present invention to solve the technical problems is：A kind of space based on parallelization RBF Grid deforming method, comprise the following steps：

Step 1: establishing parallel architecture, the grid of computational fields is subjected to subregion, each blockette corresponds to a process, and Each process is set to have the backup of a global object plane unit；

Step 2: traveling through all spatial points in each process, parallel RBF deformations are carried out, wherein, each spatial point is with from it Nearest multiple object plane deformation points are control point subset, perform serial RBF deformations, and solution obtains the deflection of spatial point.

Compared with prior art, the positive effect of the present invention is：

1st, versatility is good.The parallelization RBF that the present invention uses has stronger versatility, is suitable for data and inserts The application fields such as value, distortion of the mesh；

2nd, method is simple.Only need to change on a small quantity, it is possible to by the RBF method parallelizations of existing serialization.

Brief description of the drawings

Examples of the present invention will be described by way of reference to the accompanying drawings, wherein：

Fig. 1 is the flow chart of the inventive method.

Embodiment

A kind of space lattice deformation method based on parallelization RBF, as shown in figure 1, comprising the following steps：

Step 1, parallel architecture is established, the parallel architecture of establishing comprises the following steps：

Step 101, the partitioning algorithm (as called METIS) using routine, are n blockette by the mesh generation of computational fields Z={ Z₁、Z₂、Z₃······Z_n, the corresponding process P={ P of each block₁、P₂、P₃······P_n}；Here Subregion block number n determined by initial mesh scale and calculator memory, typically make the grid cell in each subregion after scoring area Number is less than 1,000,000.

Step 102, by each blockette Z_iOn object plane unit send to corresponding server processes P_i；

All object plane cell S={ s that step 103, server processes will be collected into₁、s₂、s₃······s_lAssembling For whole object plane S；Here, l<=n.

Step 104, server processes will include all object plane cell S={ s₁、s₂、s₃······s_lIt is whole Object plane is sent to each process P_iSo that each process P_iThere is the backup of a global object plane cell S；

Step 2, the institute for traveling through space a little, carry out parallel RBF deformations.For each process P_iIn each spatial point P_field,iDeformation：

In step 201, the object plane control point on whole object plane unit collection S, search from spatial point P_field,iNearest is N number of Control point (N typically takes 10~30), form P_field,iControl point subset { c_i}；

Step 202, to spatial point P_field,i, the control point subset { c that is possessed based on it_iAnd these control points deflection, According to formula (1), formula (2), solution obtains spatial point P_field,iDeformation.

Table 1 be using the present invention space lattice deformation method based on parallelization RBF with it is traditional based on string The efficiency comparative of row RBF space lattice deformation method.It can be seen that either for simple profile, or for as transporting A kind of wing deformation of machine, calculating time of the invention all significantly shorten, and obtain good effect.

The efficiency comparative of the present invention of table 1 and conventional method

	Serial RBF	Parallel RBF
			Cube rotates	78 minutes	4.2 minutes (8 core)
JSM transporters wing deforms	8.5 hour	17 minutes (2048 core)

Claims

A kind of 1. space lattice deformation method based on parallelization RBF, it is characterised in that：Comprise the following steps：

Step 1: establishing parallel architecture, the grid of computational fields is subjected to subregion, the corresponding process of each blockette, and make every Individual process has the backup of a global object plane unit；

Step 2: traveling through all spatial points in each process, parallel RBF deformations are carried out, wherein, each spatial point is with its nearest neighbours Multiple object plane deformation points be control point subset, perform serial RBF deformation, solution obtains the deflection of spatial point.
2. a kind of space lattice deformation method based on parallelization RBF according to claim 1, its feature exist In：1,000,000 are less than to the number of meshes in each subregion after grid progress subregion described in step 1.
3. a kind of space lattice deformation method based on parallelization RBF according to claim 1, its feature exist In：The object plane unit on corresponding blockette that global object plane unit described in step 1 is collected into by each server processes forms.
4. a kind of space lattice deformation method based on parallelization RBF according to claim 1, its feature exist In：The number at the control point subset midpoint is 10~30.
5. a kind of space lattice deformation method based on parallelization RBF according to claim 1, its feature exist In：The method of solution room point deformation amount is as follows：The displacement of spatial point is calculated as follows：

Wherein：N is the number at control point subset midpoint, and f (r) is spatial point P_field,iDisplacement, r is spatial point P_field,i's Position, r_iFor i-th of object plane control point P_surface,iInitial position, | | r-r_i| | represent P_field,iAnd P_surface,iBetween Europe Formula distance,Represent selected RBF, w_iRepresent i-th of object plane control point P_surface,iThe weight coefficient at place.
6. a kind of space lattice deformation method based on parallelization RBF according to claim 5, its feature exist In：The weight coefficient w_iMeet following relational expression：

Wherein, △ x_iFor i-th of object plane control point P_surface,iDeflection,