Exactly Conservative Semi-Lagrangian Scheme (CIP-CSL) in One-Dimension

"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.