High Order Schemes for Resolving Waves: Number of Points per Wavelength

Authors:
Leland Jameson
Affiliations:
Lawrence Livermore National Laboratory, University of California, P.O. Box 808, MS L-312, Livermore, California 94551. jameson3@llnl.gov
Venue:
Journal of Scientific Computing
Year:
2000

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Abstract

For energetic flows there are many advantages of high order schemes over low order schemes. Here we examine a previously unknown advantage. It is commonly thought that the number of points per wavelength in order to obtain a given error in a numerical approximation depends only on runtime and the order of the approximation. Using truncation error arguments and examples we will show that it is not a constant and depends also on the wavenumber. This dependence on the numerical order and wavenumber strongly favors high order schemes for use in flows which have significant energy in the high modes such at Rayleigh–Taylor and Richtmyer–Meshkov instabilities.