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Projection dynamics in Godunov-type schemes. (English) Zbl 0932.76059

Summary: There are two stages in the first-order Godunov-type schemes to update flow variables: the gas evolution stage for the numerical fluxes across a cell interface, and the projection stage for the reconstruction of constant state inside each cell. Ideally, the evolution stage should be based on the exact Euler solution, the so-called Riemann solver. In this paper, we show that some anomalous phenomena, such as postshock oscillations, density fluctuation in the two-dimensional shear wave, and pressure wiggles at material interface in multicomponent flow calculations, are generated by dynamical effects in the projection stage. Based on a physical model, we analyze qualitatively the averaging mechanism and compare our theoretical analysis with numerical observations. \(\copyright\) Academic Press.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics
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References:

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