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: unreliable volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing especially in meshfree collocation methods. Using these, we introduce an artificial compression or expansion in the fluid to rectify errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour, even for complex industrial test cases such as automotive water crossing.

翻译：自由表面流动模拟的拉格朗日无网格框架不保证流体体积守恒。诸如SPH（光滑粒子流体动力学）等无网格粒子方法不具备仿射特性，即离散质量守恒并不意味着离散体积守恒。另一方面，无网格配点方法通常不涉及质量概念，从而导致其在离散层面上既非质量守恒也非体积守恒。本文系统总结了不同无网格方法中守恒误差的多种来源，并聚焦于一个具体问题：不可靠的体积与质量定义。我们引入了代表性质量和密度的概念，这对于精确后处理（尤其是在无网格配点方法中）至关重要。基于这些概念，我们通过人为压缩或膨胀流体来校正体积守恒误差。数值实验表明，所提出的框架显著改善了体积守恒行为，即使对于汽车涉水等复杂工业测试案例也是如此。