A new numerical method that guarantees exact mass conservation is proposed to solve multi-dimensional hyperbolic equations in semi-Lagrangian form without directional splitting. The method is based on a concept of CIP scheme and keep the many good characteristics of the original CIP scheme. The CIP strategy is applied to the integral form of variable. Although the advection and non-advection terms are separately treated, the mass conservation is kept in a form of spatial profile inside a grid cell. Therefore, it retains various advantages of the semi-Lagrangian schemes with exact conservation that has been beyond the capability of conventional semi-Lagrangian schemes.
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