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Optimised high-order compact difference schemes for internal acoustics problems on curvilinear domains

Optimised high-order compact difference schemes for internal acoustics problems on curvilinear domains

Beckwith, Christopher, Pericleous, Koulis ORCID: 0000-0002-7426-9999 and Bojarevics, Valdis (2019) Optimised high-order compact difference schemes for internal acoustics problems on curvilinear domains. Journal of Physics: Conference Series, 1184 (1). ISSN 1742-6588 (Print), 1742-6596 (Online) (doi:https://doi.org/10.1088/1742-6596/1184/1/012005)

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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.

Item Type: Article
Additional Information: Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Uncontrolled Keywords: Internal acoustics, ultrasonics, numerical methods, high order schemes
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Centre for Numerical Modelling & Process Analysis (CNMPA)
Faculty of Architecture, Computing & Humanities > Centre for Numerical Modelling & Process Analysis (CNMPA) > Computational Science & Engineering Group (CSEG)
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 26 Apr 2019 23:51
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/23446

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