A High Resolution Compact Scheme for Compressible Flows Involving Shocks and Turbulence

Speaker: Akshay Subramaniam, Stanford University
March 15, 2018

Presentation

Abstract

We present a new high-order weighted compact high resolution (WCHR) scheme based on the idea of weighted compact nonlinear schemes (WCNS’s) for shock capturing in compressible flows that has improved resolution properties compared to previous WCNS’s. This is achieved by using a compact (or spatially implicit) form instead of the explicit form used in WCNS’s for the interpolation in conjunction with a compact finite difference scheme. Since compact interpolation and derivative schemes tend to have better resolution properties compared to standard finite difference schemes, this new scheme has the ability to resolve more fine scale features while still providing sufficient dissipation to capture shocks and discontinuities robustly. Approximate dispersion relation characteristics of this scheme shows the superior resolution properties of the scheme compared to other WCNS’s of similar orders of accuracy. Different test cases demonstrate the ability of this scheme to capture discontinuities in a robust and stable manner while also localizing the required numerical dissipation to regions with discontinuities and high wavenumber features and hence preserving smooth flow features better in comparison to WCNS’s. Finally, we describe some aspects of the numerical implementation of the scheme with respect to optimization for algorithmic and computational efficiency.

Biography

Akshay Subramaniam is a Ph.D. candidate in the Department of Aeronautics and Astronautics at Stanford University, working under the supervision of Prof. Sanjive Lele. His research interests are in the areas of shock induced multi-material interfacial instabilities, shock turbulence interaction, Eulerian simulations of high-deformation elastic-plastic flows, and high-order numerical methods. Akshay received his Masters degree in Aeronautics and Astronautics from Stanford University in 2014 and his Bachelors degree in Aerospace Engineering from the Indian Institute of Technology, Madras in 2012.

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