Modifications to the Lax-Wendroff scheme for hyperbolic systems with source terms

For wave phenomena in one spatial dimension, governed by hyperbolic partial differential equations with source terms, the standard Lax-Wendroff scheme leads to oscillations at discontinuous wavefronts even if the Courant-Frie drich-Lewy (CFL) number is set equal to unity. We modify the Lax-Wendroff s cheme for hyperbolic systems with source terms based on characteristic anal ysis to preserve the wave profile correctly when the CFL number is set equa l to 1. The new scheme can be used as easily as the original Lax-Wendroff s cheme since the calculation of the characteristics is not introduced in the new scheme. Thus, additional computations of characteristics are not neces sary. We also extend our method for higher spatial dimensions and illustrat e our approach by numerical examples. Copyright (C) 1999 John Wiley & Sons, Ltd.