A second-order accurate, component-wise TVD scheme for nonlinear, hyperbolic conservation laws

In this paper, we present a two-step, component-wise TVD scheme for nonline ar, hyperbolic conservation laws, which is obtained by combining the scheme s of Mae Cormack and Warming-Beam. The scheme does not necessitate the char acteristic decompositions of the usual TVD schemes. It employs component-wi se limiting: hence the programming is much simpler, especially for complica ted coupled Systems. For Euler systems of conservation laws, we found the s cheme is two times faster in computation than the usual TVD schemes based o n field-by-field decomposition limiting. A lot of numerical results show pr imarily the value of the new method. (C) 2001 Academic Press.