Upwinding in the method of lines

The method of lines (MOL) is a procedure for the numerical integration of p artial differential equations (PDEs). Briefly, the spatial (boundary value) derivatives of the PDEs are approximated algebraically using, for example, finite differences (FDs). If the PDEs have only one initial value variable , typically time, then a system of initial value ordinary differential equa tions (ODEs) results through the algebraic approximation of the spatial der ivatives. If the PDEs are strongly convective (strongly hyperbolic), they can propaga te sharp fronts and even discontinuities, which are difficult to resolve in space. Experience has demonstrated that for these systems, some form of up winding is generally required when replacing the spatial derivatives with a lgebraic approximations. Here we investigate the performance of various for ms of upwinding to provide some guidance in the selection of upwind methods in the MOL solution of strongly convective PDEs. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.