Improving the High Order Spectral Volume Formulation Using a Diffusion Regulator (Communications in Computational Physics, 2012)
The concept of diffusion regulation (DR) was originally proposed byJaisankar for traditional second order finite volume Euler solvers. This was used todecrease 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 andcontrast the original and the DR formulations. These experiments demonstrated (i)retention of high order accuracy for the new formulation, (ii) higher fidelity of the DRformulation, when compared to the original scheme for all orders and (iii) straightforward extension to Navier Stokes equations, since the DR does not interfere withthe discretization of the viscous fluxes. In general, the 2D numerical results are verypromising and indicate that the approach has a great potential for 3D flow problems.