Method of lines and direct discretization, a comparison for linear advection:

Abstract: "There are two standard ways to derive numerical algorithms for multi-dimensional flow problems [12]: either by the method of lines approach, where space and time discretization are considered separately, or with dimensional splitting, starting from a fully discrete one-dimensional me...

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Bibliographic Details
Main Authors: Hundsdorfer, Willem (Author), Trompert, Ron A. (Author)
Format: Book
Language:English
Published: Amsterdam 1993
Series:Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1993,14
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Summary:Abstract: "There are two standard ways to derive numerical algorithms for multi-dimensional flow problems [12]: either by the method of lines approach, where space and time discretization are considered separately, or with dimensional splitting, starting from a fully discrete one-dimensional method. In this paper two such related schemes are compared for linear advection. The fully discrete one-dimensional scheme is obtained by direct discretization in space and time, using a four-point upwind-biased stencil. Spatial discretization for the method of lines is considered with the same stencil and same order. Both methods are considered with flux limiting to avoid oscillations and negative values in the solutions
The schemes are applied to a number of test problems, on uniform grids and with local uniform grid refinement, to compare the accuracy and computational efficiency.
Physical Description:22 S.

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