Optimised High-Order Compact Difference Schemes for Internal Acoustics Problems On Curvilinear Domains

Abstract

A numerical framework is presented for the solution of 2D and 3D internal acoustics problems using a high-order accurate fully staggered formulation on curvilinear domains. Optimised compact finite difference schemes previously obtained in our previous paper are used for spatial discretisation, while a free parameter linear multistep method is used for temporal discretisation. The resulting scheme does not require any numerical filtering, and several benchmark cases are provided which demonstrate the significantly reduced phase velocity errors, and greater resolving efficiency compared to existing methods. Curvilinear domains are generated with the CRDT algorithm by Driscoll, with an 8th order accurate ODE solver. The governing equations for the curvilinear problem are based on a novel transformation of the decoupled velocity pressure wave equations, with simplifications made to reduce the need to interpolate derivatives at undefined locations which occur on staggered grids. The resulting transformed equations are valid only for orthogonal grids, but are computationally efficient and do not result in loss of accuracy or stability due to grid skewness. Finally, a potential application is shown, demonstrating the solution of a generated acoustic field within a crucible of liquid aluminium by a top loaded electromagnetic induction coil. Generated pressure fields agree with results shown in previous work, and demonstrate the potential use of this contactless electromagnetic excitation method as an alternative to the immersed sonotrode for the ultrasonic treatment of alloys.