Domain Decomposition Technique for Solution of Acoustic Wave Scattering

Abstract

A novel domain decomposition technique is applied that couples nonlinear and linear Euler solvers to model acoustic scattering of waves in the vicinity of high-velocity gradients and large-amplitude waves to reduce numerical resources. The linear solver is applied in domains in which the wave amplitude is small and linearization is applicable, whereas the nonlinear solver is used in the vicinity of high wave amplitudes and stagnation points. Three numerical models are compared in this paper: 1) a linear Euler, 2) a nonlinear Euler, and 3) the domain decomposition technique. For all three models, the finite difference dispersion relation preserving scheme is applied to all spatial derivatives and the low-dissipation–dispersion Runge–Kutta scheme is applied for the temporal integration. A perfectly matched layer is applied at the edges of the computational domain to absorb outgoing waves and minimize reflections. To include complex bodies and geometries, an overset mesh is applied. After model validation, the technique is applied to the acoustic scattering of a pulse and a periodic source from a circular cylinder in flow. The results conclude that a thin zone around a complex body is sufficient to accurately account for nonlinear effects in the vicinity of stagnation points and that the domain decomposition technique accurately predicts both the unsteady field and integral unsteady forces about bluff bodies compared with full nonlinear simulations. The results suggest that there is a 40% reduction in computational time using the domain decomposition technique compared with full nonlinear calculations.