A universal cubic interpolation solver for compressible and incompressible fluids

A universal numerical solver commonly usable for compressible and incompressible fluids is proposed. The method approaches the MAC algorithm at very high sound speed and continuously approaches the algorithm for compressible fluid with decreasing sound speed. The advection term is treated by the CIP algorithm which was previously proposed. A single program is applied to one- and two-dimensional shock-tube problems, and two-dimensional liquid flow inside a cavity at high Reynolds number.