Mesh Deformation Method Based On Virtual Control Points And Radial Basis Functions

The mesh deformation method is widely used in numerical simulation of computational domains with moving boundaries,due to its good flexibility and adaptability.For complex deformation problems,the mesh deformation method based on radial basis functions(RBF)is considered to be a very effective method.In this method,only the position information of the points needs to be considered during the deformation process,without considering the topological connection between points,making it simple to implement and having strong deformation ability.However,for large-scale complex mesh deformation problems,the current RBF mesh deformation method still faces some challenges:(1)The current RBF method only considers the influence of boundary points displacement on internal points displacement,which leads to the accumulation of mesh elements near the moving boundary due to the lack of control from within the region.As deformation continues,the quality of mesh elements in this region deteriorates,leading to premature occurrence of inverted elements.(2)When solving large-scale deformation problems,the large number of boundary points leads to significant time consumption in computing the weight coefficient matrix.In order to address the issues with the current RBF method and enhance the mesh deformation capability,this paper presents a mesh deformation method based on virtual control points and radial basis functions(VP-RBF).Furthermore,the paper proposes an efficient mesh deformation method based on VP-RBF by incorporating three acceleration strategies to improve the efficiency of mesh deformation.The main works of this paper can be summarized as follows:1.To address the issue of mesh element accumulation near moving boundaries and to improve the adaptability of the RBF method to large deformations,this paper proposes a mesh deformation method based on VP-RBF.This method uses virtual points in the region to control the deformation from inside.The proposed method first adds virtual points near the moving boundary;and then the number of virtual points is reduced based on a quantity reduction rule;next,the preset displacement is obtained through the interpolation of virtual points by boundary points;finally,the displacement of internal points is calculated using both virtual points and boundary points.Experimental results demonstrate that this method is suitable for two-dimensional and three-dimensional mesh deformation problems and achieves significant improvements in deformation capability and mesh quality.2.To improve the efficiency of mesh deformation,this paper proposes an efficient mesh deformation method based on the VP-RBF method.The method combines three acceleration strategies: using a sparse sub-mesh to transform the large-scale mesh deformation problem into a sparse sub-mesh deformation problem;organizing mesh unit data using a tree-like spatial structure to improve the search efficiency of mesh points during deformation;and using Open MP multi-threading parallel technology to distribute the computation of the entire deformation process among multiple threads.Experimental results show that the new method significantly improves the efficiency of mesh deformation while maintaining good mesh deformation capabilities and is suitable for large-scale mesh deformation problems.