Two-Dimensional Numerical Analysis of Nonlinear Sound Wave Propagation Using Constrained Interpolation Profile Method Including Nonlinear Effect in Advection Equation

In this study, numerical simulations of the two-dimensional nonlinear sound wave propagation in water are performed by the constrained interpolation profile (CIP) method under the assumption of a weak shock. There are two formulations for the analysis of nonlinear sound wave propagation; one is the standard CIP formulation, in which the nonlinear advection equation is divided into the linear advection equation and the non advection term, which is called the non advection-type scheme, and the other is based on the dependence of local sound velocity on sound pressure, which is called the advection-type scheme. In this paper, the advection-type scheme is developed for the two-dimensional nonlinear sound field. Some numerical demonstrations are made for the two-dimensional nonlinear sound propagation radiated from a piston source or a focusing source, then compared with results by the conventional non advection-type scheme. It is confirmed that the advection-type scheme has the same accuracy as the non advection-type scheme for the relatively low sound pressure, while the overshoot error increases in the non advection-type scheme for the high sound pressure. It is also found that the calculation time for the advection type scheme is 1.3 times shorter than that for the non advection-type scheme in the graphics processing unit (GPU) calculation. (C) 2011 The Japan Society of Applied Physics