Commun. Comput. Phys., 11 (2012), pp. 1022-1042.

Modified Upwinding Compact Scheme for Shock and Shock Boundary Layer Interaction

Chaoqun Liu 1*, Ping Lu 1, Maria Oliveira 1, Peng Xie 1

1 Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA.

Received 25 January 2010; Accepted (in revised version) 16 February 2011
Available online 18 November 2011


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.

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PACS: 47.11.-j, 47.11.Bc
Key words: Compact scheme, WENO, shock-boundary layer interaction, shock detector.

*Corresponding author.
Email: (C. Liu), (P. Lu), (M. Oliveira), (P. Xie)

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