Abstract
We construct a conservative scheme which approximates gas flow through a duct by discontinuity waves, rarefaction waves and steady waves. Analytical studies on the interaction and stability of these nonlinear elementary waves are used to determine the evolution of the state variables. The scheme is consistent, admissible, and reduces to the Godunov scheme when the duct is uniform. Numerical results show that the scheme is stable and tends to a stable steady flow; it also compares favorably with a fractional Godunov scheme.
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