Abstract
For the compressible Navier-Stokes equations, different methods for the discretization of the convective and viscous terms on different triangular and quadrilateral grids are compared for the flow over a flat plate boundary layer. It turns out that we obtained the best result for the improved advection upstream splitting method (AUSMDV) for the convective terms on unstructured quadrilateral grids. For the viscous terms discretizations which satisfy a discrete maximum principle are the most successful. We discuss the parallelization of such schemes and a posteriori error estimates.
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
Cockburn, B.; Coquel, F.; LeFloch, P.: An error estimate for high-order accurate finite volume methods for scalar conservation laws. Preprint of AHPCRC Institute, Minneapolis, Minnesota, 1991
Coquel, F.; Liou, M.-S.: Hybrid Upwind Splitting (HUS) by a Field-By-Field Decomposition. To be published
Dick, E.: Multigrid Methods for Steady Euler- and Navier-Stokes Equations Based on Polynomial Flux-Difference Splitting. International Series of Numer. Mathematics, Vol. 98, 1991
Geiben, M.: Convergence of MUSCL-Type Upwind Finite Volume Schemes on Unstructured Grids. Preprint 318, SFB 256, Bonn, 1993
Kroner, D.; Ohlberger, M.: A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions Preprint Nr. 2/1998, Freiburg, 1998
Lax P.D., Wendroff B.: Systems of Conservation Laws, CPAM, 13, 1960, pp. 217–237
Liou, M.-S.; Steffen, C.J.: A New Flux Splitting Scheme. Journal of Computational Physics, 107, 23–39, 1993
Schwane, R. Hanel, D.: An Implicit Flux-Vector Splitting Scheme for the Computation of Viscous Hypersonic Flow. AIAA-paper No. 89-04, 1989
Schworer, R.: Entwicklung und Parallelisierung von Finite-Volumen-Verfahren zur Losung der kompressiblen Navier-Stokes-Gleichungen in 2D. Diploma thesis, 1997
Steger, J.L.; Warming R.F.: Flux Vector Splitting of the Inviscid Gasdynamic Equations with Application to Finite-Difference Methods. Journal of Computational Physics 40 (1981), 263–293
Vijayasundaram, G.: Transonic Flow Simulations Using an Upstream Centered Scheme of Godunov in Finite Elements. Journal of Computational Physics 63 (1986), 416–433
Wada, Y.; Liou, M.-S.: A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities. AIAA-94-0083
Wierse, M.: Higher Order Upwind Schemes on Unstructured Grid for the Compressible Euler Equations in Time dependent Geometries in 3-D. PhD Thesis, Freiburg, 1994
Wierse, M.; Kröner, D.; Miiller, A.; Schupp, B.; Schwörer, R.: Simulation of a 3-D piston driven flow. Notes on Numerical Fluid Mechanics, Verlag Vieweg, 1997
Wierse, M.: Cell-centered Upwind Finite Volume Scheme on Triangles for Scalar Convection Diffusion Equations. To be published
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Egelja, A., Kröner, D., Schwürer, R. (1999). Adaptive Grids for Time Dependent Conservation Laws: Theory and Applications in CFD. In: Bungartz, HJ., Durst, F., Zenger, C. (eds) High Performance Scientific and Engineering Computing. Lecture Notes in Computational Science and Engineering, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60155-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-60155-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65730-9
Online ISBN: 978-3-642-60155-2
eBook Packages: Springer Book Archive