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Author(s):
R. Tanaka, T. Nakamura and T. Yabe
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Title:
Exactly Conservative Semi-Lagrangian Scheme (CIP-CSL) in One-Dimension
Date of publication:
Feb. 2001
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Key words:
Semi-Lagrangian Schemes, Conservation, CIP, CFL, Berger's Equation
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Abstract:
Two semi-Lagrangian schemes that guarantee exactly mass conservation are proposed. Although they are in a non-conservative form, the mass of each cell is employed as an additional variable that is advaced in a conservative form. One of them (CIP-CSL4) is the direct extension of the CIP method into the 4-th order polynomial to incorporate mass conservation. In another scheme (CIP-CSL2), the CIP principle is applied to integrated mass and the interpolation of the value becomes quadratic. The latter one can be readily extended to multi-dimensions. These schemes are applied to the non-linear advection problem with large CFL number.
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