Summary
This paper provides a method for solving nonlinear scalar advection problems and the conservation-law Euler equations. A recently developed genuinely multi-dimensional upwind fluctuation splitting discretization is combined with a multi-stage Runge-Kutta scheme with optimal coefficients, accelerated by a multigrid strategy. Numerical results are presented to demonstrate the merits of the proposed approach.
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
S. K. Godunov, “A finite-difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics”, Mat. Sbornik, 47, 1959, pp. 357–393.
P. L. Roe, “Characteristic-based schemes for the Euler equations”, Ann. Rev. Fluid Mech., 18, 1986, pp. 337–365.
A. Harten, S. Osher, “Uniformly high-order accurate nonoscillatory schemes, I.”, SIAM J. Numer. Anal., 24, 1987, pp. 279–309.
H. Deconinck, C. Hirsch, J. Peuteman, “Characteristic Decomposition Methods for the Multidimensional Euler Equations”, Lecture Notes in Physics, 264, Springer Verlag, 1986, pp. 216–221.
P. L. Roe, “Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics”, J. Comp. Phys., 63, 1986, pp. 458–476.
R. Struijs, P. L. Roe, H. Deconinck, “Fluctuation splitting schemes for the 2D Euler equations”, VKI-LS 1991–01, von Karman Institute, Belgium, 1991.
L. A. Catalano, H. Deconinck, “Two-dimensional optimization of smoothing properties of multi-stage schemes applied to hyperbolic equations”, Multigrid Methods: Special Topics and Applications II, GMD-Studien Nr. 189, GMD St. Augustin,. Germany, 1991, pp. 43–55.
L. A. Catalano, M. Napolitano, H. Deconinck, “Optimal multi-stage schemes for multigrid smoothing of two-dimensional advection operators”, submitted to Communications in Applied Numerical Methods.
P. De Palma, H. Deconinck, R. Struijs, “Investigation of Roe’s 2D wave decomposition models for the Euler equations”, Technical Note 172, von Karman Institute, Belgium, 1990.
P. L. Roe, “Linear advection schemes on triangular meshes”, Cranfield Institute of Technology, CoA Report No. 8720, Cranfield, Bedford, U. K., November 1987.
L. A. Catalano, H. Deconinck, “Two-dimensional optimization of smoothing properties of multistage schemes applied to hyperbolic equations”, Technical Note 173, von Karman Institute, Belgium, 1990.
A. Brandt, “Guide to multigrid development”, Lecture Notes in Mathematics 960, Springer Verlag, Berlin, 1982, pp. 220–312.
P. L. Roe, R. Struijs, H. Deconinck, “A conservative linearization of the multidimensional Euler equations”, to appear on J. Comp. Phys..
R. Struijs, H. Deconinck, P. De Palma, P. L. Roe, K. G. Powell, “Progress on Multidimensional Upwind Euler Solver for Unstructured Grids”, AIAA P 91–1550 CP, Honolulu, 1991.
L. A. Catalano, P. De Palma, G. Pascazio, “A multi-dimensional solution adaptive multigrid solver for the Euler equations”, submitted to the 13th International Conference on Numerical Methods in Fluid Dynamics, Rome, July 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Fachmedien Wiesbaden
About this paper
Cite this paper
Catalano, L.A., De Palma, P., Napolitano, M. (1992). Explicit Multigrid Smoothing for Multidimensional Upwinding of the Euler Equations. In: Vos, J.B., Rizzi, A., Ryhming, I.L. (eds) Proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanics. Notes on Numerical Fluid Mechanics (NNFM), vol 35. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-13974-4_7
Download citation
DOI: https://doi.org/10.1007/978-3-663-13974-4_7
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07635-1
Online ISBN: 978-3-663-13974-4
eBook Packages: Springer Book Archive