Computational Methods in Engineering

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The present work introduces a modified scheme for the solution of compressible 2-D full Navier-Stokes equations, using Flux Vector Splitting method. As a result of this modification, numerical diffusion is reduced. The computer code which is developed based on this algorithm can be used easily and accurately to analyze complex flow fields with discontinuity in properties, in cases such as shock wave boundary layer interactions. This scheme combines advantages of both Advective Upstream Splitting (AUSM) and Low Diffusion Flux Vector Splitting (LDFVS) Methods. To increase accuracy and monotonicity, the conservative variables are extrapolated at the cell interfaces by using the MUSCL approach with limiter. This algorithm has been used to solve four sample problems. It has been shown that the numerical diffusion has been reduced and the results are in good agreement with published numerical and/or experimental data. Keywords: Compressible Navier Stokes Equations, Flux Vector splitting, Advective upwind, Numerical diffusion

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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 study 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.