Preconditioned HLLC scheme for incompressible viscous flow simulation

Abstract

A new HLLC approximate Riemann solver with preconditioning technique based on the pseudo-compressibility formulation for numerical simulation of the incompressible viscous flows has been proposed, which follows the HLLC Riemann solver (Harten, Lax and van Leer solver with contact resolution modified by Toro) for the compressible flow system. In the authors' previous work, the preconditioned Roe's Riemann solver was applied to the finite difference discretization of the inviscid flux. Although the Roe's Riemann solver is found to be an accurate and robust scheme in various numerical computations, the HLLC Riemann solver is more suitable for the pseudo-compressible Navier- Stokes equations, in which the inviscid flux vector is a non-homogeneous function of degree one of the flow field vector; however the Roe's solver is restricted to the homogeneous problems. Numerical investigations have been performed in order to demonstrate the efficiency and accuracy of the present procedure. The present results are found to be good agreement with the exact solutions, existing numerical results or experimental data. © 2012 WIT Press.