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Solution of the Euler equations on Cartesian grids. (English) Zbl 1146.76623
Summary: A method is presented for the solution of the two-dimensional Euler equations on Cartesian grids. The method utilizes a conservative cell vertex Euler solver with Lax-Wendroff time-stepping. Results are presented for transonic flow for Ni’s 2D channel flow problem and also for transonic flow about a circular cylinder.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76H05 Transonic flows
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[1] Ni, R.H., A multiple grid scheme for solving the Euler equations, Aiaa j., 20, 1565-1571, (1982) · Zbl 0496.76014
[2] M.G. Hall, Fast multigrid solution of the Euler equations using a finite volume scheme of Lax-Wendroff type, RAE Technical Report 84013
[3] D.K. Clarke, H.A. Hassan, M.D. Salas, Euler calculations for multielement airfoils using Cartesian grids, AIAA Paper 85-0291, 1985 · Zbl 0587.76095
[4] A.D. French, Solution of the Euler Equations on Cartesian Grids, Ph.D. Thesis, College of Aeronautics, Cranfield University, Cranfield, 1991
[5] C.M. Albone, A second order accurate scheme for the Euler equations by deferred correction of a first order upwind algorithm, RAE Tech. Report No. 88061, September 1988
[6] M.D. Salas, Recent developments in transonic Euler flow over a circular cylinder, NASA Technical Memo. 83282, April 1982
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