A second-order accurate flux splitting scheme in two-dimensional gasdynamics
The domain of application of the proposed method is mainly unsteady flows with complex geometries. The scheme results from a combination of a spatial approximation, an upwind flux computation, and a time integration. W e have proposed a Riemann solver for flux computation because it seems to be less dependent on the homogeneity property of the flux ; but many techniques are suitable [3, 5, 8, 10], and the flux splitting techniques proposed by Van Leer seem advantageous for their computational efficiency. The scheme could also be used on a triangular finite element grid and the time integration could be improved. A three-dimensional extension is under investigation.
KeywordsTransonic Flow Riemann Solver Spatial Approximation Sonic Point Total Variation Norm
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- G. D. Van Albada, B. Van Leer, W.W. Roberts: “Comparative study of computational methods in cosmic gas dynamics”. ICASE Reports No 81-24, August 3, 1981.Google Scholar
- M. Borrel, Ph Morice: “A second order Lagrangian-eulerian method for computation of two-dimensional unsteady transonic flows”. 5th GAMM Conf. Rome 1983.Google Scholar
- P. Harten, P. Lax, B. Van Leer: “On upstream differencing and Godunov type schemes for hyperbolic conservation laws”. STAM Review, Vol. 25, No 1 Jan. 1983.Google Scholar
- B. Van Leer: “V. A second order sequel to Godunov method”. J C P 23 276–299, 1977.Google Scholar
- B. Van Leer: “Flux vector splitting for the Euler equations”. VKI 1983.Google Scholar
- A.Y. Leroux: “Approximation de quelques problmes hyperboliques non linéaires”. Thesis, Rennes University, April 1974.Google Scholar
- S. Osher: “Convergence of generalized MUSCL schemes”. ICASE Report 172306, Feb. 1984.Google Scholar
- P.L. Roe: “Approximate Riemann solvers, parameter vectors and difference schemes”. J C P 43 357–372 (1981).Google Scholar
- J.P. Veuillot, H. Viviand: “Méthodes pseudo-instationnaires pour le calcul d'écoulements transsoniques”. ONERA publication N° 1978-4 (English translation, ESA-TT-561).Google Scholar
- G. Vijayasundaram: “Résolution numérique des équations d'Euler pour des écoulements transsoniques avec un schéma de Godunov en éléments finis”. The., Paris VII, Oct. 1982.Google Scholar