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Proceedings of the 25th National and 3rd International ISHMT-ASTFE Heat and Mass Transfer Conference (IHMTC-2019)

ISSN: 2688-7231 (Online)

Flux Difference Splitting Methods Based on High Resolution Scheme for Unsteady, Viscous, Compressible flow

Uttam Singh Rajput
Department of Mechanical and Industrial Engineering, IIT Roorkee, 247667, India

Krishna Mohan Singh
Department of Mechanical and Industrial Engineering, IIT Roorkee, 247667, India

DOI: 10.1615/IHMTC-2019.1160
pages 693-698

Abstract

In this paper performance assessment of seventh order weighted essentially non-oscillatory scheme (WENO) with four flux difference splitting scheme (FDS) for unsteady viscous compressible flow is presented. We have used Harten-Lax-van-Leer (HLL), Roe solver, Harten-Lax-van Leer-Contact (HLLC), and Rusanov methods and compared results of these methods 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, to avoid spurious oscillation. We have considered supersonic and hypersonic viscous flow over a flat plate, to access the performance of FDS schemes. An explicit third order TVD Runge-Kutta method is used for the advancement of the solution in time. The present results are compared with available numerical and theoretical solutions. WENO-HLLC has good shock capturing capabilities as compare to WENO-Roe, WENO-HLL and WENO-Rusanov methods. WENO-HLLC provides best results inside and outside the boundary layer.

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