Title: High resolution schemes for genuinely two-dimensional HLLE Riemann solver

Authors: J.C. Mandal; N. Arvind

Addresses: Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India ' Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India

Abstract: In this paper, two higher order solution reconstruction techniques based on SDWLS gradients and Barth-Jespersen limiter are investigated to obtain higher order accuracy for a genuinely multidimensional Riemann solver. Due to use of vertex-based framework in the multidimensional Riemann solver, straight forward application of conventional TVD limiters becomes difficult and confusing. Several test examples are solved in order to establish order of accuracy and to demonstrate the efficacy of the proposed reconstruction techniques. The SDWLS gradient technique is found to produce consistently higher order solution accuracy and maintain multidimensional nature of the solutions as compared to Barth-Jespersen limiter.

Keywords: genuinely multidimensional Riemann solver; higher order reconstruction; Euler equations; SDWLS gradients; Barth-Jespersen limiter; high resolution.

DOI: 10.1504/PCFD.2014.063863

Progress in Computational Fluid Dynamics, An International Journal, 2014 Vol.14 No.4, pp.205 - 220

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 24 Jul 2014 *

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