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Modified Upwinding Compact Scheme for Shock and Shock Boundary Layer Interaction

Published online by Cambridge University Press:  20 August 2015

Chaoqun Liu ,
Ping Lu ,
Maria Oliveira  and
Peng Xie
Chaoqun Liu*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
Ping Lu*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
Maria Oliveira*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
Peng Xie*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
*
Corresponding author.Email:cliu@uta.edu
Email:ping.lu@mavs.uta.edu
Email:malubamol@gmail.com
Email:xiepeng.peng@gmail.com
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Abstract

Standard compact scheme and upwinding compact scheme have high order accuracy and high resolution, but cannot capture the shock which is a discontinuity. This work developed a modified upwinding compact scheme which uses an effective shock detector to block compact scheme to cross the shock and a control function to mix the flux with WENO scheme near the shock. The new scheme makes the original compact scheme able to capture the shock sharply and, more importantly, keep high order accuracy and high resolution in the smooth area which is particularly important for shock boundary layer and shock acoustic interactions. Numerical results show the scheme is successful for 2-D Euler and 2-D Navier-Stokes solvers. The examples include 2-D incident shock, 2-D incident shock and boundary layer interaction. The scheme is robust, which does not involve case related parameters.

Keywords

47.11.-j47.11.BcCompact schemeWENOshock-boundary layer interactionshock detector
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 3 , March 2012 , pp. 1022 - 1042
Copyright
Copyright © Global Science Press Limited 2012

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