RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-State Problems on Triangular Meshes

Abstract

In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical $L^2$ projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.

Funding

National Natural Science Foundation of China(11872210)

http://dx.doi.org/10.13039/501100001809(12071392)

AFOSR(FA9550-20-1-0055)

NSF(DMS-2010107)

NSFC(MCMS-I-0120G01)