Comparisons of numerical methods with respect to convectively dominated problems
A series of numerical schemes: first-order upstream, Lax-Friedrichs; second-order upstream, central difference, Lax-Wendroff, Beam-Warming. Fromm; third-order QUICK, QUICKEST and high resolution flux-corrected transport and total variation diminishing (TVD) methods are compared for one-dimensional convection-diffusion problems. Numerical results show that the modified TVD Lax-Friedrichs method is the most competent method for convectively dominated problems with a steep spatial gradient of the variables. Copyright (C) 2001 John Wiley & Sons, Ltd.
numerical method convection total variation diminishing