Abstract
A set of improvements of a well-balanced scheme for the model of fluid flows in a nozzle with variable cross-section is presented. Relying on the well-balanced method introduced in our earlier work, we use the steady state solutions to absorb the nonconservative term. The underlying numerical fluxes operating on these steady states are obtained as convex combinations of the numerical fluxes of a first-order and a second-order schemes. The improvements are still well-balanced schemes. Then, we present many numerical tests, which establishes the efficiency of these numerical schemes. These schemes can provide us with very desirable approximations for any initial data: data in supersonic or subsonic regions, and data in both of these two kinds of regions. All the tests also show that the accuracy of the method by the improvements is improved.
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