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New implicit time integration schemes combining high frequency damping with high second order accuracy

Wulf Dettmer Orcid Logo, Eman Alhayki

Journal of Computational Physics, Volume: 514, Start page: 113260

Swansea University Authors: Wulf Dettmer Orcid Logo, Eman Alhayki

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DOI (Published version): 10.1016/j.jcp.2024.113260

Abstract

It is shown that weighted linear combinations of the generalised-α method and certain related higher order schemes allow for the formulation of unconditionally stable single step time integration methods with improved second order accuracy and more targeted high-frequency damping. It is also shown t...

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Published in: Journal of Computational Physics
ISSN: 0021-9991
Published: Elsevier BV 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa67063
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Abstract: It is shown that weighted linear combinations of the generalised-α method and certain related higher order schemes allow for the formulation of unconditionally stable single step time integration methods with improved second order accuracy and more targeted high-frequency damping. It is also shown that, if the user controlled high frequency damping parameter is set to zero, the new schemes can be expressed as linear multistep backward difference formulae and, in a particular case, recover Park's method. The performance of the proposed methods is illustrated in terms of mathematical analysis and a number of linear and nonlinear numerical examples including finite element based solutions of the incompressible Navier-Stokes equations.
Keywords: Implicit numerical time integration; Generalised-α method; Backward difference formulae; Unconditional stability; Accuracy
College: Faculty of Science and Engineering
Funders: Swansea University
Start Page: 113260

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