A bounded upwinding scheme for computing convection-dominated transport problems

Abstract

A practical high resolution upwind differencing scheme for the numerical solution of convection-dominated transport problems is presented. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving the 1D/2D scalar advection equations, 1D inviscid Burgers' equation, 1D scalar convection-diffusion equation, 1D/2D compressible Euler's equations, and 2D incompressible Navier-Stokes equations. The numerical results displayed good agreement with other existing numerical and experimental data. (C) 2012 Elsevier Ltd. All rights reserved.