Grand Challenge of CIP towards Universal Solver from Nano-Scale to Astrophysical Scale

摘要

We review some recent progress of the 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 multi-phase analysis. This method was also applied to the magnetohydrodynamic equation in astrophysical jet formation and to the Shroedinger equation. In the Shroedinger equation, the CIP achieved the accuracy by a few orders of magnitude higher than the conventional schemes. This method is recently extended to almost mesh-free system that is called "soroban grid" that ensures the third order accuracy both in time and space with the help of the CIP method.