Simulation of compressible flow using a semi-implicit TVD scheme

Total variation diminishing (TVD) scheme is a kind of robust high-resolution approach, which removes the undesirable oscillations generated by numerical solution. The present work proposes a new implementation of the TVD scheme into a density-based semi-implicit finite-volume procedure to solve the inviscid and viscous flow equations. The proposed algorithm uses a simple linearization technique for convective fluxes. In order to enhance the accuracy of the algorithm, a high-resolution TVD scheme is employed in the discretization of the governing equations. This procedure has a simple implementation compared to other explicit and implicit schemes. The present scheme is first examined for some inviscid and viscous steady-state flows at several Mach numbers from subsonic to the supersonic regime. In addition, the inviscid and viscous unsteady flows are simulated and compared with experimental and numerical results, so that an acceptable correspondence was obtained. Results from this study indicate that the proposed algorithm is accurate for a wide range of Mach numbers