Editorial Type:
Article
Article Type:
Research Article

A Two-Step Scheme for the Advection Equation with Minimized Dissipation and Dispersion Errors

Lawrence L. Takacs M/A-COM Sigma Data, Inc., Goddard Laboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, MD 20771

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Print Publication:
01 Jun 1985
DOI:
https://doi.org/10.1175/1520-0493(1985)113<1050:ATSSFT>2.0.CO;2
Page(s):
1050–1065
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Abstract

A two-step advection scheme of the Lax-Wendroff type is derived which has accuracy and phase characteristics similar to that of a third-order scheme. The scheme is exactly third-order accurate in time and space for uniform flow. The new scheme is compared with other currently used methods, and is shown to simulate well the advection of localized disturbances with steep gradients. The scheme is derived for constant flow and generalized to two-dimensional nonuniform flow.

Abstract

A two-step advection scheme of the Lax-Wendroff type is derived which has accuracy and phase characteristics similar to that of a third-order scheme. The scheme is exactly third-order accurate in time and space for uniform flow. The new scheme is compared with other currently used methods, and is shown to simulate well the advection of localized disturbances with steep gradients. The scheme is derived for constant flow and generalized to two-dimensional nonuniform flow.

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