Issues in the Application of High Order Schemes
We argue, in this paper, that the type of simulations to be carried out in the next decade will entail the use of high order schemes.
A discussion of some issues in the application of those schemes to time dependent problems are discussed. In particular we will review spectral shock capturing techniques and the asymptotic behavior of high order compact schemes.
KeywordsShock Wave Spectral Method Fourier Coefficient High Order Scheme Hyperbolic Problem
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- S. Abarbanel and D. Gottlieb, “Information content in spectral calculations”, in Progress and Supercomputing in Computational Fluid Dynamics, edited by E. Murman and S. Abarbanel, (1984), Birkhauser, pp. 345–356.Google Scholar
- W. Cai, “Spectral methods for shock wave calculations”, Ph.D. thesis, Brown University 1989.Google Scholar
- W. Cai, D. Gottlieb and A. Harten, “Cell averaging Chebyshev methods for hyperbolic problems”, Comput. and Math. with Appli. 1990.Google Scholar
- Mark H. Carpenter, David Gottlieb and Saul Abarbanel, “The stability of numerical boundary treatments for compact highorder finite difference schemes”, ICASE report 91-71, september 1991.Google Scholar
- D. Gottlieb and E. Tadmor, “Recovering pointwise values of discontinuous data”, in Progress and Supercomputing in Computational Fluid Dynamics, editedGoogle Scholar
- Gottlieb D. Shu, C.W., Solomonof A., Vandeven H. “On the Gibbs Phenomenon I” to appear in Applied Numerical Mathematics.Google Scholar
- Kriess H.O. and Wu L. “On the stability definitions of difference approximations for Initial Boundary valur problems”, Comm. Pure Appl. Math. to appear.Google Scholar
- K. R. Sreenivasan, “Transition and turbulent wakes and chaotic dynamical systems”, in S. H. Davis and J. L. Lumley, eds, Frontiers in Fluid Mechanics ( Springer, New York, 1985 ), pp. 41–67.Google Scholar
- B. Strand- Ph.D thesis Uppsala University, to appear.Google Scholar