Volume and Mass Conservation in Lagrangian Meshfree Methods

IF 2.7 3区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY International Journal for Numerical Methods in Engineering Pub Date : 2025-01-23 DOI:10.1002/nme.7657
Pratik Suchde, Christian Leithäuser, Jörg Kuhnert, Stéphane P. A. Bordas
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Abstract

Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass conservation does not imply discrete volume conservation. On the other hand, meshfree collocation methods typically do not use any notion of mass. As a result, they are neither mass conservative nor volume conservative at the discrete level. In this paper, we give an overview of various sources of conservation errors across different meshfree methods. The present work focuses on one specific issue: inconsistent volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing in meshfree collocation methods. Using these, we introduce an artificial compressibility in the fluid to reduce errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour in meshfree collocation methods, even for complex industrial test cases such as automotive water crossing.

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来源期刊
CiteScore
5.70
自引率
6.90%
发文量
276
审稿时长
5.3 months
期刊介绍: The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems. The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
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