Computation of nonlinear acoustic waves using smoothed particle hydrodynamics

Abstract

A Lagrangian approach for solving nonlinear acoustic wave problems is presented with direct computation from smoothed particle hydrodynamics. The traditional smoothed particle hydrodynamics method has been applied to solve linear acoustic wave propagations. However, nonlinear acoustic problems are common in medical ultrasonography, sonic boom research, and acoustic levitation. Smoothed particle hydrodynamics is a Lagrangian meshfree particle method that shows advantages in modeling nonlinear phenomena, such as the shock tube problem, and other nonlinear problems with material separation or deformable boundaries. The method is used to solve the governing equations of fluid dynamics for simulating nonlinear acoustics. The present work also tests the method in solving the nonlinear simple wave equation based on Burgers’ equation. Effects of initial particle spacing, kernel length, and time step are then discussed based on the wave propagation simulation. Different kernel functions are also evaluated. The res...