Abstract
Compact differencing techniques have been shown to be applicable to simple first order advection equations. A second-order accurate compact upwind scheme has been derived which is identically equivalent to Keller's box method. Two fourth order compact analogs of Lax-Wendroff methods have also been shown. The accuracy of any of these compact methods is superior to a standard second-order method, even for one quarter of the nodes in the case of the fourth-order schemes.
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References
Hirsh, R. S., “Higher Order Accurate Difference Solutions of Fluid Mechanics Problems by a Compact Differencing Technique,” J. Comp. Phys., 19, 90–109, 1975.
Ciment, M. and Leventhal, S. H., ”Higher Order Compact Implicit Schemes for the Wave Equation,” Math. Comp., 29, 985–994, 1975.
Bontoux, P., Forestier, B. and Roux, B., “Analysis of Higher Order Methods for the Numerical Simulation of Confined Flows,” Paper presented at the Sixth International Conference on Numerical Methods in Fluid Dynamics, June 20–25, 1978, Tbilisi, U.S.S.R.
Leventhal, S. H., “A Two-Dimensional Operator Compact Implicit Method for Parabolic Equations,” Paper presented at SIAM 1979 Fall Meeting, November 12–14, 1979, Denver, Colorado.
Keller, H. B., “A New Difference Scheme for Parabolic Problems,” in J. Bramble (ed.), Numerical Solutions of Partial Differential Equations, Vol. II, Academic Press, New York, 1970.
Gottlieb, D. and Turkel, E., “Dissipative Two-Four Methods for Time Dependent Problems,” ICASE Report No. 75-22, October 1975.
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© 1981 Springer-Verlag
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Hirsh, R.S., Ferguson, R.E. (1981). Compact differencing schemes for advective problems. In: Reynolds, W.C., MacCormack, R.W. (eds) Seventh International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10694-4_30
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DOI: https://doi.org/10.1007/3-540-10694-4_30
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