Unstructured Grid Solution of the Eikonal Equation for Acoustics

Abstract

An acoustic eikonal equation solution procedure, that is easy to implement in unstructured grid Navier-Stokes equation flow solvers, is outlined. The approach is readily parallelizable. The method is tested for the following canonical point source cases: quiescent flow; subsonic uniform flow; supersonic uniform flow and an idealized jet flow. Then, as further validation, sound propagation of a wave front through a viscous vortex is considered. For these cases, encouraging agreement is found with analytic data and a high-fidelity numerical solution of the Euler equations. Finally, as demonstration cases, the use of the approach to study the shielding of noise from a planar jet is considered along with wave propagation in a complex three-dimensional geometry. At lower Mach numbers (< 0.25), for complex geometries, robust multigrid convergence acceleration is found.

Acoustic Wave Focusing by Non-Uniform Mean Flow in a Rectangular Duct with Viscous Walls

“…There are some differences in interference patterns between the Navier-Stokes solutions for different frequencies. For high frequency, acoustic waves produce fine wave-patterns that resemble the branches of caustics typical of the geometrical acoustics (Tucker and Karabasov 2009). Nevertheless, despite these differences, the loci of acoustic wave convergence points do not change with frequency.…”

Broadband shock-associated noise modelling for high-area-ratio under-expanded jets

“…For unsteady simulation of the LTRAC jets, LES are performed and the far-field noise spectra are computed based on the FW-H method with multiple closing discs (Shur et al, 2005). In all simulations, the high-resolution CABARET method (Golovizin and Samarskii, 1998;Golovizin, 2009, Chintagunta et al, 2017) is used for solving the Navier-Stokes equations on unstructured meshes with good preservation of linear wave propagation properties (Tucker and Karabasov, 2009;Golovizin et al, 2013, Chintagunta et al, 2018. Particular features of the CABARET method include compactness of the computational stencil and asynchronous time stepping for efficient calculations on non-uniform space-time grids (Semiletov and Karabasov, 2013).…”

Cabaret Scheme for Computational Aero Acoustics: Extension to Asynchronous Time Stepping and 3D Flow Modelling

“…CABARET is a generalisation of the second-order space-time Upwind Leapfrog Scheme of Iserlis [12] and Roe [13] to nonlinear conservation laws. In the previous work, e.g., [9], [10], [14], [15] and [15], the CABARET scheme has been successfully used for a range of idealised computational aeroacoustics and hydrodynamics problems. The problems considered in the above references were largely idealised and didn't require any specific use of either non-uniform grids or local time stepping.…”