A Cartesian grid method for the three-dimensional numerical simulation of shock wave propagation in complex-shape domains with moving boundaries

This paper is devoted to the development and quantitative estimation of a numerical algorithm based on the Cartesian grid method for the three-dimensional mathematical simulation of shock wave propagation in domains of complex varying shapes. A detailed description of the numerical algorithm is presented. Its key element is the specification of numerical fluxes through the edges that are common for the inner regular cells of the computational domain and the outer cells intersected by the boundaries of the bodies. The efficiency of the algorithm is shown by comparing the numerical and experimental data in the problems of interaction of a shock wave with a fixed sphere and a moving particle.