The Constrained Interpolation Profile Method for Multiphase Analysis

We present a review of the constrained interpolation profile (CIP) method that is known as a general numerical solver for solid, liquid, gas, and plasmas. This method is a kind of semi-Lagrangian scheme and has been extended to treat incompressible flow in the framework of compressible fluid. Since it uses primitive Euler representation, it is suitable for multiphase analysis. The recent version of this method guarantees the exact mass conservation even in the framework of a semi-Lagrangian scheme. We provide a comprehensive review of the strategy of the CIP method, which has a compact support and subcell resolution, including a front-capturing algorithm with functional transformation, a pressure-based algorithm, and other miscellaneous physics such as the elastic–plastic effect and surface tension. Some practical applications are also reviewed, such as milk crown or coronet, laser-induced melting, and turbulent mixing layer of liquid–gas interface.