Mathematics – Numerical Analysis
Scientific paper
2001-10-10
Comput. Phys. Commun. 143/2 pp.142-154 (2002)
Mathematics
Numerical Analysis
17 pages, 8 figures, accepted for publication in Comput. Phys. Commun., Some misprint corrected
Scientific paper
10.1016/S0010-4655(01)00441-6
The semi-Lagrangian method using the hybrid-cubic-rational interpolation function [M. Ida, Comput. Fluid Dyn. J. 10 (2001) 159] is modified to a conservative method by incorporating the concept discussed in [R. Tanaka et al., Comput. Phys. Commun. 126 (2000) 232]. In the method due to Tanaka et al., not only a physical quantity but also its integrated quantity within a computational cell are used as dependent variables, and the mass conservation is completely achieved by giving a constraint to a forth-order polynomial used as an interpolation function. In the present method, a hybrid-cubic-rational function whose optimal mixing ratio was determined theoretically is employed for the interpolation, and its derivative is used for updating the physical quantity. The numerical oscillation appearing in results by the method due to Tanaka et al. is sufficiently eliminated by the use of the hybrid function.
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