A parameter-free Total Lagrangian Smooth Particle Hydrodynamics algorithm applied to problems with free surfaces

Lowa, K. W.Q., Lee, C. H. , Gil, A. J., Haider, J. and Bonet, J. (2021) A parameter-free Total Lagrangian Smooth Particle Hydrodynamics algorithm applied to problems with free surfaces. Computational Particle Mechanics, 8(4), pp. 859-892. (doi: 10.1007/s40571-020-00374-x)

Abstract

This paper presents a new Smooth Particle Hydrodynamics computational framework for the solution of inviscid free surface flow problems. The formulation is based on the Total Lagrangian description of a system of first-order conservation laws written in terms of the linear momentum and the Jacobian of the deformation. One of the aims of this paper is to explore the use of Total Lagrangian description in the case of large deformations but without topological changes. In this case, the evaluation of spatial integrals is carried out with respect to the initial undeformed configuration, yielding an extremely efficient formulation where the need for continuous particle neighbouring search is completely circumvented. To guarantee stability from the SPH discretisation point of view, consistently derived Riemann-based numerical dissipation is suitably introduced where global numerical entropy production is demonstrated via a novel technique in terms of the time rate of the Hamiltonian of the system. Since the kernel derivatives presented in this work are fixed in the reference configuration, the non-physical clumping mechanism is completely removed. To fulfil conservation of the global angular momentum, a posteriori (least-squares) projection procedure is introduced. Finally, a wide spectrum of dedicated prototype problems is thoroughly examined. Through these tests, the SPH methodology overcomes by construction a number of persistent numerical drawbacks (e.g. hour-glassing, pressure instability, global conservation and/or completeness issues) commonly found in SPH literature, without resorting to the use of any ad-hoc user-defined artificial stabilisation parameters. Crucially, the overall SPH algorithm yields equal second order of convergence for both velocities and pressure.

• Item Type: Articles
• Additional Information: The firrst author would like to acknowledge the financial support of the Welsh Government, the European Regional Development Fund (ERDF) and the funding provided via the ASTUTE 2020 operation. The second author gratefully acknowledges the support provided by the EPSRC Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics - EP/R008531/1. The third author acknowledges the financial support received through the European Training Network Protechtion (Project ID: 764636).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Lee, Dr Chun Hean
• Authors: Lowa, K. W.Q., Lee, C. H., Gil, A. J., Haider, J., and Bonet, J.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Computational Particle Mechanics
• Publisher: Springer
• ISSN: 2196-4378
• ISSN (Online): 2196-4386
• Published Online: 18 January 2021
• Copyright Holders: Copyright © 2021 The Authors
• First Published: First published in Computational Particle Mechanics 8(4): 859-892
• Publisher Policy: Reproduced under a Creative Commons license

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
300129		Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics	Christopher Pearce	Engineering and Physical Sciences Research Council (EPSRC)	EP/R008531/1	ENG - Infrastructure & Environment