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Meshfree Lagrangian frameworks for free surface flow simulations do notconserve fluid volume. Meshfree particle methods like SPH are not mimetic, inthe sense that discrete mass conservation does not imply discrete volumeconservation. On the other hand, meshfree collocation methods typically do notuse any notion of mass. As a result, they are neither mass conservative norvolume conservative at the discrete level. In this paper, we give an overviewof various sources of conservation errors across different meshfree methods.The present work focuses on one specific issue: unreliable volume and massdefinitions. We introduce the concept of representative masses and densities,which are essential for accurate post-processing especially in meshfreecollocation methods. Using these, we introduce an artificial compression orexpansion in the fluid to rectify errors in volume conservation. Numericalexperiments show that the introduced frameworks significantly improve volumeconservation behaviour, even for complex industrial test cases such asautomotive water crossing.

Volume and Mass Conservation in Lagrangian Meshfree Methods