Cartesian Cut-Cell Method with Local Grid Refinement for Wave Computations

Abstract

Sound generation from a vibrating circular piston is a classical acoustic problem. The goal of this paper is to simulate numerically the sound radiation produced by oscillating baffled pistons, using both linear and nonlinear model, and to consider the interplay between wave propagation and geometric complexities. The linear solution, based on the linear Euler equations, will be compared to the Rayleigh integral approximation. The nonlinear solution, based on the Navier-Stokes equations, will be compared against linear model for low speed (less than 0.01 of sound speed). A main practical interest in this problem is to capture the behavior of the waves resulting from the source pistons with other solid objects or waves. The wave's properties in terms of frequency, amplitude and wavenumber are influenced by the initial frequencies and coordinates of the pistons, and the geometry. The wave equations in Cartesian coordinate with cut-cell and local grid refinement technique are employed along with the Optimized Prefactored Compact finite volume (OPC-fv) scheme for spatial discretization, the Low-Dispersion Low-Dissipation Runge-Kutta (LDDRK) scheme for time discretization. Problems for the waves around different geometries, and with varied frequencies and amplitudes are considered and presented.