Numerical Simulation of Nonlinear Sound Wave Propagation Using Constrained Interpolation Profile Method: One-Dimensional Case

概要

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In this study, a numerical simulation of nonlinear sound wave propagation in the time domain is performed by the constrained interpolation profile (CIP) method. The CIP method is one kind of method of characteristics, and is a high-accuracy scheme in which numerical dispersion errors are hardly caused because not only the acoustic field values on the grid point but also their spatial derivatives are used in the scheme. Two CIP formulations are made for one-dimensional nonlinear sound wave propagation: one is the standard formulation in which the nonlinear equation is divided into the advection term and the nonadvection one corresponding to the nonlinear term, and the other is the formulation based on the dependence of local sound speed on particle velocity. In the latter method, the nonlinear term is included in the local sound speed of the advection term, which can be directly solved by the CIP method. The CIP conservative semi-lagrangian of the fourth-order (CIP-CSL4) scheme, which is a higher-order accuracy version of the CIP method, is also formulated. Some numerical demonstrations are performed for one-dimensional nonlinear sound propagation in air. The numerical results are compared with the analytical results. It is confirmed that the present formulation based on the dependence of local sound speed on particle velocity is more suitable for the simulation of nonlinear sound wave propagation.
2008-05-25