Summary
A fully implicit relaxation technique is developed to accelerate convergence of current multigrid solvers. The flux Jacobians are efficiently recomputed during iteration. The implicit operator allows increasing CFL numbers of the basic explicit scheme to O(100), and it properly addresses the stiffness in the discrete equations associated with highly stretched meshes. Compared to a well tuned, standard reference code, computation times are more than halved.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abarbanel, S. and Gottlieb, D., “Optimal Splitting for Two and Three Dimensional Navier-Stokes Equations with Mixed Derivatives”, ICASE Report No. 80-6, Feb. 18th, 1980.
Baldwin, B. and Lomax, H., “Thin Layer Approximation and Algebraic Turbulence Model for Separated Turbulent Flows”, AIAA-Paper 78-257, 1987.
Cook, P. H., McDonald, M. A., and Firmin, M. C. P., “Aerofoil RAE2822 Pressure Distributions and Boundary Layer and Wake Measurements”, AGARD-AR-138, 1979.
Faßbender, J., “Improved Robustness of Numerical Simulation of Turbulent Flows around Civil Transport Aircraft at Flight Reynolds Numbers”, Ph.D. Thesis, Technical University of Braunschweig, http://opus.tu-bs.de/opus/volltexte/2004/579, 2004.
Jameson, A., “Multigrid Algorithms for Compressible Flow Calculations”, in Second European Conference on Multigrid Methods, Cologne, 1985, ed. W. Hackbusch and U. Trottenberg, [Lecture Notes in Mathematics, Vol. 1228], Springer Vedag, Berlin, 1986.
Martinelli, L., “Calculations of Viscous Flow with a Multigrid Method”, Ph.D. Thesis, Princeton University, 1987.
Radespiel, R., Rossow, C.-C., and Swanson, R.C., “An Efficient Cell-Vertex Multigrid Scheme for the Three-Dimensional Navier-Stokes Equations”, AIAA J., Vol. 28, No.8, 1998, pp.423–459.
Roe, P.L., “Approximate Riemann Solvers, Parameter Vectors and Difference Schemes”,,J. Comput. Phys., Vol. 43, 1981, pp.357–372.
Rossow, C.-C., “A Flux Splitting Scheme for Compressible and Incompressible Flows”, J. Comput. Phys., Vol. 164, 2000, pp.104–122.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rossow, CC. (2006). Toward efficient solution of the compressible Navier-Stokes equations. In: Rath, HJ., Holze, C., Heinemann, HJ., Henke, R., Hönlinger, H. (eds) New Results in Numerical and Experimental Fluid Mechanics V. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 92. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33287-9_49
Download citation
DOI: https://doi.org/10.1007/978-3-540-33287-9_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33286-2
Online ISBN: 978-3-540-33287-9
eBook Packages: EngineeringEngineering (R0)