Well ballanced Q-scheme for nozzle flow equations

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Abstract

Hyperbolic systems with geometrical source terms arise in various applications. One such application is fluid flow with cross section area variations, which arise naturally in the study of fluid flow phenomena in ducts, pipes, shock tubes, and nozzles. In such applications the source term may have low regularity, which causes numerical difficulty particularly when steady state solutions are computed. The fix for this numerical difficulty is to approximate the source term using decomposition and upwinding, thus creating balance between numerical flux gradient and numerical source term. In this paper we introduce extension of the Q-schemes proposed in [1] to nozzle flow equations, i.e., Euler equations with geometrical source term.

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