  An improved numerical solver for the unified solution of compressible and
incompressible fluids involving interfaces is proposed. The present method is
based on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified
Procedure) method, which is a pressure-based semi-implicit solver for the Euler
equations of fluid flows. In Part I of this series of articles [M. Ida, Comput.
Phys. Commun. 132 (2000) 44], we proposed an improved scheme for the convection
terms in the equations, which allowed us discontinuous descriptions of the
density interface by replacing the cubic interpolation function used in the CIP
scheme with a quadratic extrapolation function only around the interface. In
this paper, as Part II of this series, the multi-time-step integration
technique is adapted to the CIP-CUP integration. Because the CIP-CUP treats
different-nature components in the fluid equations separately, the adaptation
of the technique is straightforward. This modification allows us flexible
determinations of the time interval, which results in an efficient and accurate
integration. Furthermore, some additional discussion on our methods is
presented. Finally, the application results to composite flow problems such as
compressible and incompressible Kelvin-Helmholtz instabilities and the dynamics
of two acoustically coupled deformable bubbles in a viscous liquid are
provided.
