期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 227, 期 15, 页码 7069-7076出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2008.03.034
关键词
upwind methods; PPM; limiters
We present a new limiter for the PPM method of Colella and Woodward [P. Colella, P.R. Woodward, The Piecewise Parabolic Method (PPM) for gas-dynamical simulations, Journal of Computational Physics 54 (1984) 174-201] that preserves accuracy at smooth extrema. It is based on constraining the interpolated values at extrema (and only at extrema) using non-linear combinations of various difference approximations of the second derivatives. Otherwise, we use a standard geometric limiter to preserve monotonicity away from extrema. This leads to a method that has the same accuracy for smooth initial data as the underlying PPM method without limiting, while providing sharp, non-oscillatory representations of discontinuities. (c) 2008 Published by Elsevier Inc.
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