General mesh method: A unified numerical scheme

Abstract

An alternative to three existing types of mesh (structured grid, unstructured grid, and gridfree points) — general mesh — is proposed for Computational Fluid Dynamics (CFD). It includes three existing ones and the arbitrary mixing of mesh and points by using a unified framework. Different from the traditional hybrid grid/gridfree methods requiring separate numerical schemes for the respective grid and points zones, a unified numerical method — general volume scheme — is developed for the general mesh to discretize Navier–Stokes (NS) equations. This innovative scheme naturally solves not only all three existing types of mesh but also the arbitrary mixing of mesh and points without requiring overlapped zones. Compared to the existing grid and gridfree based computational methods, the general mesh method is endowed by nature with both the geometric flexibility of points (without topology connectivity) and physical accuracy of mesh (with node connectivity): 1. the meshing is as general, automated, efficient, and flexible as gridfree points but the numerical solution becomes more stable and accurate than the gridfree method; 2. the numerical scheme is as unified, compact, accurate, and robust as the unstructured grid, whereas the meshing becomes incredibly easier than the latter. Meanwhile, the proposed method is comprehensively validated by both low-speed and transonic high-Reynolds number flows. The simulation of HIRENASD demonstrates the potential to improve the convergence by converting the low-quality mesh elements into meshfree points.