A New Implicit Dissipation Term for Solving 3D Euler Equations on Unstructured Grids by GMRES+LU-SGS Scheme

Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in the dissipation term by its constant spectral radius. The objective of the present &#10study is to develop a modified implicit solver based on Roe scheme so that its numerical dissipation is as much as the explicit one. In the proposed scheme, the Krylov subspace method with a LU decomposition preconditioner (GMRES+LU-SGS) is used to solve the linear systems. The efficiency of this method is shown by presenting some examples at the end.&#10