  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.
