Flux-difference-splitting (FDS) for the unsteady Euler equations are reviewed, and it is shown that any of the proposed methods can be regarded as a prescription for finding the entries in a "Riemann table", which records the effect on each flow quantity of the wave system generated by the differences between neighbouring pairs of states. For an associated finite-difference scheme to be efficient, it is first of all necessary that the table is constructed economically, and then that the information contained in it should be fully used. We describe a scheme which is efficient in both respects.
The eigen vectors, values and strengths are evaluated efficiently for Roe's method. The technique employed, which avoids the difficult task of finding the averaged Jacobian matrix, may also be applied to other similar schemes.
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Last modified: March 09.