Abstract
Hyperbolic first order systems with a high degree of unsymmetry are ill conditioned for numerical computation. The principles for symmetrization are discussed and applied to the Euler equations at low Mach numbers. A new class of implicit one-step methods is introduced.
Similar content being viewed by others
References
Guerra, J., and Gustafsson, B. (1986a). A semi-implicit method for hyperbolic problems with different time-scales,SIAM J. Numer. Anal. 23, 734–749.
Guerra, J., and Gustafsson, B. (1986b). A numerical method for incompressible and compressible flow problems with smooth solutions,J. Comp. Phys. 63, 377–397.
Gustafsson, B. (1985). A semi-implicit method for almost incompressible flow problems on parallel computers, Proc. International symposium on computational fluid dynamics, Tokyo.
Gustafsson, B. (1980a). Asymptotic expansions for hyperbolic problems with different time-scales,SIAM J. Numer. Anal. 17, 623–634.
Gustafsson, B. (1980b). Numerical solution of hyperbolic systems with different time-scales using asymptotic expansions,J. Comp. Phys. 36, 209–235.
Warming, R. F., Beam, R. M., and Hyett, B. J. (1975). Diagonalization and simultaneous symmetrization of the gasdynamic matrices.Math. Comp. 29, 1037–1045.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gustafsson, B. Unsymmetric hyperbolic systems and the Euler equations at low Mach numbers. J Sci Comput 2, 123–136 (1987). https://doi.org/10.1007/BF01061482
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01061482