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On positivity preserving finite volume schemes for Euler equations. (English) Zbl 0857.76062
Summary: We consider the positivity preserving property of first- and higher-order finite volume schemes for one- and two-dimensional Euler equations of gas dynamics. A general framework is established which shows the positivity of density and pressure whenever the underlying one-dimensional first-order building block based on an exact or approximate Riemann solver and the reconstruction are both positivity preserving. Appropriate limitation to achieve a high-order positivity preserving reconstruction is described.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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