High‐order curvilinear mesh generation technique based on an improved radius basic function approach

Abstract

Summary A high‐order curvilinear hybrid mesh generation technique is developed for high‐order numerical method (eg, discontinuous Galerkin method) applications to improve the accuracy for problems with curve boundary. The grid generation technique is based on an improved radius basic function (RBF) approach by which the straight‐edge mesh is converted into high‐order curve mesh. Firstly, an initial straight‐edge mesh is prepared by traditional grid generation software. Then, high‐order interpolation points are inserted into the mesh entities such as edges, faces, and cells according to the final demand of mesh order. To preserve the original geometry, the inserted points on solid wall are then projected onto the CAD model using an open source tool “Open Cascade.” Finally, other inserted points in the field near the solid wall are moved to appropriate positions by the improved RBF approach to avoid tangled cells. If we use the original RBF approach, then the inserted points on the edge and face entities normal to the solid boundary in the region of boundary layer will move to improper positions. To overcome this problem, a weighting based on the local grid aspect ratio between normal direction and tangential direction is introduced into the baseline RBF approach. Three typical configurations are tested to validate the mesh generator. Meanwhile, a third‐order solution of subsonic flow over an analytical 3D body of revolution in the second International Workshop on High‐Order CFD Methods is supplied by a discontinuous Galerkin solver. These numerical tests demonstrate the potential capability of present technique for high‐order simulations of complex geometries.

A large‐scale parallel hybrid grid generation technique for realistic complex geometry

“…Actually, because the surface deformation induced by the surface projection is not too severe, the mesh quality and deformation are mainly determined by the closed subset of CPs. Thus different from the classic sequential RBF, the authors have proposed an improved sequential RBF approach which has been successfully applied to generate high‐order curvilinear mesh . In this improved version, 10‐50 local closest points instead of the entire surface points are chosen as the RBF control points for each volume point that needs to deform.…”

“…As a result, the efficiency of the local closest surface control points selection process can greatly influence the whole deforming time. More details can refer to Reference .…”

The Effects of Grid Accuracy on Flow Simulations: A Numerical Assessment

“…In comparison with the optimization and elasticity analogies-based techniques, their methodology reduced the computational cost while preserving the accuracy of the curved elements. Additionally, Zhao et al [22] developed a grid generation approach based on an improved radius basic function technique in order to generate a high-order curvilinear mesh. The proposed methodology was demonstrated to improve the accuracy of numerical solutions of curve-boundary problems.…”