Towards higher-order accuracy on arbitrary grids
Several ways of achieving higher order accuracy on arbitrary grids are explored. These include polynomial reconstructions based on point and cell average values and the Discontinuous Galerkin method, in which the solution is expanded within a cell, and evolution equations are derived for the expansion coefficients. The polynomial reconstruction scheme based on cell averages is also extended to deal with unsteady viscous flows to higher order accuracy.
KeywordsMass Matrix Discontinuous Galerkin Discontinuous Galerkin Method Order Accuracy Riemann Solver
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- H. L. Atkins and C. Shu. AIAA Paper 96-1683, May 1996.Google Scholar
- T. J. Barth and P. O. Fredrickson. AIAA Paper 90-0013, Jan. 1990.Google Scholar
- T. J. Barth and D. C. Jespersen. AIAA Paper 89-0366, Jan. 1989.Google Scholar
- F. Bassi and S. Rebay, CFD CONF., 39 (1996), pp. 1879–1888.Google Scholar
- K. S. Bey and J. T. Oden. AIAA Paper 91-1575CP, July 1991.Google Scholar
- M. Delanaye, P. Geuzaine, J. A. Essers, and P. Rogiest. AGARD Conf. Proceedings 578: Progress and Challenges in CFD Methods and Algorithms, Apr. 1996.Google Scholar
- A. Harten and S. Chakravarthy. ICASE Report No. 91-76, 1991.Google Scholar
- R. B. Lowerie, P. L. Roe, and. B. van Leer, A space-time discontinuous Galerkin method for the time-accurate numerical solution of hyperbolic conservation laws. AIAA Paper 95-1658CP, June 1995.Google Scholar
- K. W. Morton, Proc. 8th ICNMFD, Aachen, Germany, Berlin/New York, 1982, Springer-Verlag, p. 77.Google Scholar
- J. J. W. van der Vegt and H. van der Ven. AGARD Conf. Proceedings 578: Progress and Challenges in CFD Methods and Algorithms, Apr. 1996.Google Scholar
- V. Venkatakrishnan and D. J. Mavriplis. AIAA-95-1705-CP, 1995, to appear in J. Comp. Phys.Google Scholar