A flux splitting method for the numerical simulation of one-dimensional compressible flow

Using the technique of flux vector splitting, it is shown that one-dimensional, inviscid, compressible-flow equations possess a split conservation form. Some attractive features of this form for the design of finite-difference solution schemes are discussed. Based on the split form, two solution chemes are designed. One is a first-order accurate ‘upwind’ scheme and the other is similar to the Lax-Wendroff scheme. A hybrid scheme, based on a nonlinear weighting of these two schemes, is demonstrated to yield results superior to either of the two in the solution of an ideal shock-tube problem.