A new directional-splitting CIP interpolation with high accuracy and low memory consumption

A new directional-splitting CIP interpolation of third-order accuracy is proposed. This scheme uses only the value and first-order derivatives of the physical field as computational variables, and thus largely reduces the memory requirement. The higher-order cross derivatives are not treated as the computational variables but calculated by recursively using the local Taylor expansions within each single mesh cell, which retains the third order accuracy even for meshes of non-uniform grid spacings. The proposed directional splitting can be easily extended to solve advection equations of any multi dimensionality.