Fundamental Study of Smoothed Particle Hydrodynamics

-Treatment of Two-Phase Flow in Case of Different-Size Particles-

Abstract

In our preceding report, we proposed relaxation equations for the smoothed particle hydrodynamics (SPH) method suited to suppress the numerical disorder around the interface of different materials such as gas and liquid. However, when the dimensions of particles are not the same, numerical disorder appears again. Additionally, there was difficulty in that the momentum conservation is not satisfied in the relaxation equation for acceleration when the smoothing lengths of 2 particles are not the same. In this work, we study the problem of the numerical disorder caused by the difference in dimension between particles, and we propose a new smoothing method to suppress the numerical disorder. Additionally, we discuss the treatment of smoothing length, which was not clearly discussed previously, and we propose a revised relaxation equation, in which the momentum of particles is conserved.