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A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

Low, Kenny W. Q., Lee, Chun Hean ORCID: 0000-0003-1102-3729, Gil, Antonio J., Haider, Jibran and Bonet, Javier ORCID: 0000-0002-0430-5181 (2021) A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces. Computational Particle Mechanics. ISSN 2196-4378 (Print), 2196-4386 (Online) (doi:

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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: Article
Additional Information: © The Author(s) 2021. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
Uncontrolled Keywords: Conservation laws · SPH · Hamiltonian · Stabilisation · Instability · Fluid
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Faculty / School / Research Centre / Research Group: Vice-Chancellor's Group
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Last Modified: 30 Apr 2021 22:04

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