Numerical simulation of compressible flow with shocks using the OUCS2 upwind compact scheme

Abhishek Kundu

Abhishek Kundu Department of Mechanical Engineering, Swami Vivekananda Institute of Science and Technology, West Bengal, India

Keywords: AUSM , Compressible flow, Euler equations, Flux limiter, High Mach number

Abstract

The OUCS2 upwind compact scheme for calculation of first derivatives in the Euler and NavierStokes equations is the focus of the present paper. Derived and analyzed by Sengupta et al. and primarily meant for incompressible flow problems, the scheme has recently been applied to compressible flow with shocks. To handle shocks effectively, a combination of second and fourth derivative artificial dissipation terms were used by Sengupta et al., instead of the inbuilt sixth derivative dissipation of the OUCS2. For unsteady flow problems with shocks and vortices, use of high order numerical dissipation is desirable for proper resolution of small scale structures. In a present paper we show that when used with flux limiters, one can use the inbuilt high order dissipation in smooth regions and still bring down the scheme to small stencil formulae with low order dissipation near shocks. The basic solver is built upon the AUSM+ algorithm. OUCS2 comes in while computing the left and right states of the primitive variables at the cell faces, requiring little effort to modify an existing AUSM+ based solver to a high resolution version with the help of OUCS2. We demonstrate the procedure for a number of problems in one and two dimensions solving the Euler equations.

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