×

zbMATH — the first resource for mathematics

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.

MSC:
76H05 Transonic flows
76M99 Basic methods in fluid mechanics
PDF BibTeX Cite
Full Text: DOI
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.