Multigrid Method for Solving Euler and Navier-Stokes Equations in two and three Dimensions
In this paper we describe the multigrid method we use for solving Euler and Navier-Stokes equations and which is based upon the method proposed by Ni  . Because the multigrid acceleration technique used for the Navier-Stokes equations is straightforwardly derived from that used for the Euler equations, the main part of the presentation is dedicated to the Euler multigrid solver. Comparisons between calculations performed on a 3D complex inviscid flow allow us to optimize the convergence rate of the multigrid process by modifying the transfer operator. We indicate how the multigrid method can be easily extended to the solution of the Navier-Stokes equations.
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- Ni R.H., A Multiple-Grid Scheme for Solving the Euler Equations, AIAA J., vol. 20, n o 11, (1982).Google Scholar
- Ni R.H. and Bogoian J.C., Prediction of 3D Multi-Stage Turbine Flow Field Using a Multiple-Grid Euler Solver, AIAA Paper n o 89-0203, (1989).Google Scholar
- Davis R.L., Ni R.H. and Carter J.E., Cascade Viscous Flow Analysis Using the Navier-Stokes Equations, AIAA Paper n o 86-0033, (1986).Google Scholar
- Cambier L., Couaillier V. and Veuillot J.P., Numerical Solution of the Navier-Stokes equations by a Multigrid Method, La Recherche Aérospatiale n o 1988-2, pp. 23-42 (English Edition).Google Scholar
- Viviand H. and Veuillot J.P., Méthodes pseudo-instationnaires pour le calcul d’écoulements transsoniques, ONERA Publication n o 1978-4, (English translation, ESA TT 561).Google Scholar
- Vuillot A.M., A Multi-Domain 3D Euler Solver for Flows in Turbomachines, Proceedings of the 9th ISABE Symposium, Athens (Sept. 1989).Google Scholar
- Couaillier V., Solution of the Euler Equations: Explicit Scheme Acceleration by a multigrid Method, 2nd European Conference on Multigrid Methods, GAMM Cologne, Oct. 1985, GMD-Studien n o 110 and ONERA TP n o 1985-129.Google Scholar
- Eriksson L.E., Boundary Conditions for Artificial Dissipation Operators, FFA TN 1984-53.Google Scholar
- Rizzi A., Spurious Entropy Production and Very Accurate Solutions to the Euler Equations, AIAA paper n o 84-1644, (1984).Google Scholar
- Couaillier V. and Peyret R., Theoretical and Numerical Study of the Ni’s Multigrid Method, La Recherche Aérospatiale, n 1985–5, French and English Editions.Google Scholar
- Usab W.J., Embedded Mesh Solutions of the Euler Equations Using a Multiple-Grid Method, Ph.D. Thesis, Dept. of Aeronautics and Astronautics, MIT (1983).Google Scholar
- Veuillot J.P. and Cambier L., Computation of High Reynolds Number Flows around Airfoils by Numerical Solution of the Navier-Stokes equations, 11th International Conference on Numerical Methods in Fluid Dynamics, Williamsburg, Virginia, (June 1988).Google Scholar
- Cambier L. and Escande B., Navier-Stokes Simulation of a Shock Wave-Turbulent Boundary Layer Interaction in a Three-Dimensional Channel, AIAA 20th Fluid Dynamics and Lasers Conference, Buffalo (N.Y.), (June 1989).Google Scholar