Abstract
Theoretical and experimental convergence results are presented for multigrid and iterative defect correction applied to finite volume discretizations of the steady, 2D, compressible Navier-Stokes equations. Iterative defect correction is introduced for circumventing the difficulty in finding a soiution of discretized equations with a second- or higher-order accurate convective pari As a smoothing -echnique, use is made of point Gauss-Seidel relaxation with inside the latter, Newton iteration as a basic Solution method. The multigrid echnique appears to be very efficient for smooth as well as non-smooth problems. Iterative defect correction appears to be very efficient for smooth problems only, though still reasonably efficient for non-smooth Problems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
W. Hackbusc. (1985). Multigrid Methods and Applications. Springer, Berlin.
R.J. HAkkinen, I. Greber, L. Trilling and S.S. Abarbane. (1958). The Interaction of an Oblique Shock Wave with a Laminar Boundary Layer. NASA-memorandum 2-18-59 W.
P.W. Hemke. (1986). Defect Correction and Higher Order Scheines for the Multi Grid Solution of the Steady Euler Equations. Proceedings of the 2nd European Conference on Multigrid Methods, Cologne 1985, Springer, Berlin.
P.W. Hemkeand B. Kore. (1986). A Non-linear Multigrid Method for the Steady Euler Equations. Proceedings GAMM-Workshop on the Numerical Simulation of Compressible Euler Flows, Rocquencourt 1986, Vieweg, Braunschweig.
P.W. Hemkeand and S.P. Spekreijs. (1986). Multiple Grid and Osher’s Scheme for the Efficient Solution of the Steady Euler Equations. Appl. Num. Math. 2, 475–493.
B. Kore. (1988). Euler Flow Solutions for a Transonic Wind Tunnel Section. Proceedings High Speed Aerodynamics II, Aachen 1987 (to appear).
B. Kore (1988). Defect Correction and Multigrid for an Efficient and Accurate Computation of Airfoil Flows. J. Comput. Phys. (to appear).
B. Kore (1988). First-Order Upwind Schemes and Multigrid for the Steady Navier-Stokes Equations. CWI report NM-R88xx (to appear).
B. Kore (1988). Higher-Order Upwind Schemes and Defect Correction for the Steady Navier-Stokes Equations. CWI report NM-R88yy (to appear).
B. Kore (1988). Upwind Schemes for the Navier-Stokes Equations. Proceedings Second International Conference on Hyperbolic Problems, Aachen, 1988 (to appear).
B. Kore and S.P. Spekreijs. (1988). Solution of the Steady Euler Equations by a Multigrid Method. Proceedings Third Copper Mountain Conference on Multigrid Methods, Copper Mountain, 1987 (to appear).
B. van Lee. (1982). Flux-Vector Splitting for the Euler Equations. Proceedings 8th International Conference on Numerical Methods in Fluid Dynamics, Aachen 1982, Springer, Berlin.
B. van Lee (1985). Upwind-Dijference Methods for Aerodynamic Problems governed by the Euler Equa tions. Proceedings 15th AMS -SIAM Summer Seminar on Applied Mathematics, Scripps Institution of Oceanography 1983, AMS, Providence. Rhode Island.
S. Oshe. and F. Solomo. (1982). Upwind-Dijference Schemes for Hyperbolic Systems of Conser vation Laws. Math. Comp. 38, 339–374.
R. Peyre. and T.D. Taylo. (1983). Computational Methods for Fluid Flow. Springer, Berlin.
H. Schlichtin. (1979). Boundary-Layer Theory. McGraw-Hill, New York.
S.P. Spekreijs. (1987). Multigrid Solution of Monotone Second-Order Discretizations of Hyperbolic Conservation laws. Math. Comp. 49, 135–155.
P. Wesselin. (1987). Linear Multigrid Methods. In: Multigrid Methods, SIAM, Philadelphia.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
About this chapter
Cite this chapter
Koren, B. (1989). Multigrid and Defect Correction for the Steady Navier-Stokes Equations. In: Hackbusch, W. (eds) Robust Multi-Grid Methods. Notes on Numerical Fluid Mechanics, vol 23. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-86200-6_15
Download citation
DOI: https://doi.org/10.1007/978-3-322-86200-6_15
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-08097-6
Online ISBN: 978-3-322-86200-6
eBook Packages: Springer Book Archive