Adrian Sescu, Abdollah A. Afjeh, Ray Hixon
Abstract:
In numerical solutions to hyperbolic partial differential equations
in multidimensions, in addition to dispersion and dissipation errors,
there is a grid-related error (referred to as isotropy error or
numerical anisotropy) that affects the directional dependence of
the wave propagation.
Difference schemes are mostly analyzed and optimized in one
dimension, wherein the anisotropy correction may not be effective enough.
In this work, optimized multidimensional difference schemes with
arbitrary order of accuracy are designed to have improved isotropy
compared to conventional schemes. The derivation is performed based
on Taylor series expansion and Fourier analysis. The schemes are
restricted to equally-spaced Cartesian grids, so the generalized
curvilinear transformation method and Cartesian grid methods are
good candidates.
Published April 15, 2009.
Math Subject Classifications: 76Q05, 65M06, 65M20, 65Q05.
Key Words: Computational aeroacoustics; isotropy error; difference methods.
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| Adrian Sescu University of Toledo, Toledo, OH 43606, USA email: asescu@utnet.utoledo.edu |
| Abdollah A. Afjeh University of Toledo, Toledo, OH 43606, USA email: aafjeh@utnet.utoledo.edu |
| Ray Hixon University of Toledo, Toledo, OH 43606, USA email: dhixon@utnet.utoledo.edu |
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