Solver with the differential algebraic cubic interpolated propagation scheme on massively parallel computer

A method for solving hydrodynamic equations with the differential algebraic-cubic interpolated propagation (DA-CIP) scheme on massively parallel computer is presented. The scheme uses a spatial profile interpolated with cubic polynomials within the grid cells; it is formulated straightforwardly from the equations of motion describing the system without algorithmically specific parameters, and applies the numerical integration method for the ordinary differential equations such as the Runge-Kutta integration method without using the concept of finite difference or finite volume method. Therefore, the scheme is efficiently implemented based on the Single Program Multiple Data (SPMD) model and has been applied to simulate the pressure waves in gas generated by an impulsive heating of a solid boundary on the massively parallel processor Intel Paragon.