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Transonic flow simulations using an upstream centered scheme of Godunov in finite elements. (English) Zbl 0592.76081
Summary: A new first-order upwind scheme is presented and analysed. The scheme is simple to program and robust. The extension to a multi-dimensional FEM/FVM formulation is straightforward. The accuracy is demonstrated in two classical test cases. Results are obtained that do not contain unphysical oscillations even when FEM-type two-dimensional triangulations are used.

76H05 Transonic flows
76M99 Basic methods in fluid mechanics
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[1] Angrand, F.; Dervieux, A., Int. J. numer. methods fluids, 4, 749, (1984)
[2] Angrand, F.; Boulard, V.; Dervieux, A.; Periaux, J.; Vijayasundaram, G., (), 83
[3] Beam, R.M.; Warming, R.F., J. comput. phys., 22, 87, (1976)
[4] Borrel, M.; Morice, P.H., ()
[5] Courant, R.; Isaacson, E.; Rees, M., Commun. pure appl. math., 5, 243, (1952)
[6] Glowinski, R.; Periaux, J., ()
[7] Godunov, S.K., Mat. sb., 47, 271, (1959)
[8] Lerat, A., J. mec. theor. appl., 2, 185, (1983), No. 2
[9] Lerat, A.; Sides, J., (), 142
[10] Moretti, F., Comput. fluids, 7, 191, (1979)
[11] Osher, S., C. R. acad. sci. Paris ser. A, 290, 819, (1980)
[12] Osher, S.; Solomon, F., J. math. comput., (1982)
[13] Rizzi, A.; Viviano, H., ()
[14] Roe, P.L., ()
[15] Sod, G.A., J. comput. phys., 27, 1, (1978)
[16] Steger, J.; Warming, R.F., J. comput. phys., 40, 263, (1981)
[17] Stoufflet, B., ()
[18] {\scB. Stoufflet}, Contribution to the Workshop on Numerical Methods for the Euler Equations for Compressible Inviscid Flows (R. Glowinski, Ed.).
[19] Van Leer, B., J. comput. phys., 23, 263, (1977)
[20] Vijayasundaram, G., Résolution numérique des equations d’Euler pour des écoulements transoniques avec un schéma to Godunov en élément finis, ()
[21] Whitham, G.B., Linear and nonlinear waves, () · Zbl 0373.76001
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