基于能量守恒的SPH边界条件
Boundary conditions for SPH through energy conservation
AI总结：
本文提出一种基于能量守恒的新型SPH壁面边界条件，在Boundary Integrals框架下将SPH的无条件稳定性扩展至含壁面边界的问题，并通过多项流体动力学案例验证了其有效性。
摘要：
在Smoothed Particle Hydrodynamics (SPH) 中处理边界条件存在显著困难，这实际上是SPHERIC Grand Challenges之一。特别是，自SPH从天体物理学发展到更广泛的流体动力学模拟以来，壁面边界条件在SPH模型发展中一直至关重要。尽管研究人员对此给予了极大关注，并有大量文献致力于建立和评估壁面边界条件，但鲜有研究涉及能量守恒这一关键方面。本研究提出了一种新型边界条件，将能量守恒作为首要考量，从而有效地将SPH的无条件稳定性扩展至涉及壁面边界条件的问题中。该结果在Boundary Integrals技术框架下构建。该提议在多个案例中进行了测试：对壁面的法向冲击、活塞的绝热振荡、溃坝以及航天器的水上着陆。
英文摘要：
Dealing with boundary conditions in Smoothed Particle Hydrodynamics (SPH) poses significant difficulties, indeed being one of the SPHERIC Grand Challenges. In particular, wall boundary conditions have been pivotal in SPH model development since it evolved from astrophysics to more generic fluid dynamics simulations. Despite considerable attention from researchers and numerous publications dedicated to formulating and assessing wall boundary conditions, few of them have addressed the crucial aspect of energy conservation. This work introduces a novel boundary condition designed with energy conservation as a primary consideration, effectively extending the unconditional stability of SPH to problems involving wall boundary conditions. The result is formulated within the framework of the Boundary Integrals technique. The proposal is tested on a number of cases: normal impact against a wall, adiabatic oscillations of a piston, dam break, and the water landing of a spacecraft.
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