Geodesic
A numerical method for unsteady flows
Applications of Mathematics, Tome 40 (1995) no. 3, pp. 175-201

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A high resolution finite volume method for the computation of unsteady solutions of the Euler equations in two space dimensions is presented and validated. The scheme is of Godunov-type. The first order part of the flux function uses the approximate Riemann problem solver of Pandolfi and here a new derivation of this solver is presented. This construction paves the way to understand the conditions under which the scheme satisfies an entropy condition. The extension to higher order is done by applying ideas of LeVeque to the approximate Riemann problem solution. A detailed validation of the scheme is done on one and two dimensional test problems.
A high resolution finite volume method for the computation of unsteady solutions of the Euler equations in two space dimensions is presented and validated. The scheme is of Godunov-type. The first order part of the flux function uses the approximate Riemann problem solver of Pandolfi and here a new derivation of this solver is presented. This construction paves the way to understand the conditions under which the scheme satisfies an entropy condition. The extension to higher order is done by applying ideas of LeVeque to the approximate Riemann problem solution. A detailed validation of the scheme is done on one and two dimensional test problems.
DOI : 10.21136/AM.1995.134290
Classification : 05M25, 65M05, 76H05, 76M25
Keywords: finite volume method; Euler equations; Riemann problem 
Botta, Nicola; Jeltsch, Rolf. A numerical method for unsteady flows. Applications of Mathematics, Tome 40 (1995) no. 3, pp. 175-201. doi: 10.21136/AM.1995.134290
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