High Resolution Central Scheme with Dominant Wave Dissipation for Cell Centered Unstructured Meshes

Abstract

A cell centered high resolution scheme with the dissipation term based on dominant wave approach is examined here. A simplied dominant eigenvalue expression based on the momentum equations together with low Mach number precondtioning is introduced. The dominant wave scheme was implemented in the unstructured cell centered framework capable of supporting polyhedral meshes. Second order of accuracy is achieved by using slope limiters for the primitive data reconstructed at the nite volume cell faces. The main advantage of the scheme is the resulting simplied dissipation term that does not require computation of eigenvectors while retaining the high resolution capabilities. It is shown that the dominant wave scheme has similar resolution to the ux dierence upwind scheme based on the Roe Riemann solver. In addition, the dominant wave scheme has similar resolution characteristics compared to other central schemes such as the Kurganov-Tadmor scheme, and comparison to the HLLC scheme showed similar resolution capabilities. A number of computational tests in 1D, 2D and 3D are performed in order to assess the resolution capabilities of the scheme.