Commun. Comput. Phys., 12 (2012), pp. 247-260.


Improving the High Order Spectral Volume Formulation Using a Diffusion Regulator

Ravi Kannan 1*, Zhijian Wang 2

1 CFD Research Corporation, 215 Wynn Drive, Huntsville, AL 35805, USA.
2 Iowa State University, Howe Hall, Ames, IA 50011, USA.

Received 27 March 2011; Accepted (in revised version) 6 July 2011
Available online 27 January 2012
doi:10.4208/cicp.270311.060711a

Abstract

The concept of diffusion regulation (DR) was originally proposed by Jaisankar for traditional second order finite volume Euler solvers. This was used to decrease the inherent dissipation associated with using approximate Riemann solvers. In this paper, the above concept is extended to the high order spectral volume (SV) method. The DR formulation was used in conjunction with the Rusanov flux to handle the inviscid flux terms. Numerical experiments were conducted to compare and contrast the original and the DR formulations. These experiments demonstrated (i) retention of high order accuracy for the new formulation, (ii) higher fidelity of the DR formulation, when compared to the original scheme for all orders and (iii) straightforward extension to Navier Stokes equations, since the DR does not interfere with the discretization of the viscous fluxes. In general, the 2D numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.

AMS subject classifications: 65

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Key words: Diffusion regulation, spectral volume, high-order, Rusanov flux, Navier Stokes equations.

*Corresponding author.
Email: sunshekar@gmail.com (R. Kannan), zjw@iastate.edu (Z. J. Wang)
 

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