In this work, we have carried out the assessment of a high resolution scheme for unsteady compressible flow. For high order spatial accuracy, we have used fifth order weighted essentially non oscillatory (WENO) scheme. This scheme is applied to four flux difference splitting (FDS) methods: Harten-Lax-van-Leer (HLL), Roe solver, Harten-Lax-van Leer-Contact (HLLC), and Rusanov methods. We have compared results of these flux schemes with each other. WENO scheme is used for the reconstruction of left and right state variable across the cell interface for high resolution. The reconstruction procedure is performed in terms of primitive variables instead of conservative variable, in order to avoid spurious oscillation. We have considered two test cases: shock wave reflection and supersonic viscous flow over a flat plate, to access the performance of FDS schemes. An explicit third order TVD Runge-Kutta method is used for advancement of solution in time. The present results are compared with available numerical solutions. WENO-HLLC has good shock capturing capabilities as compare to WENO-Roe, WENO-HLL and WENO-Rusanov methods. It also provides best results inside and outside the boundary layer.
This study presents the development of a fifth-order hybrid alternative mapped weighted essentially non-oscillatory scheme (HAW-M) for high-speed compressible flows. A new, improved smoothness indicator has been developed to design the HAW-M scheme. The performance of the present scheme has been evaluated through different one and two-dimensional test cases. The developed scheme shows higher accuracy and low dissipation. Further, it captures the fine-scale structures smoothly than the existing high-resolution method.
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