扩展欧拉光滑粒子流体动力学及其有限体积法的实现
Extended Eulerian SPH and its realization of FVM
AI总结：
本文通过引入粒子松弛、核修正矩阵和耗散限制器等扩展，使欧拉SPH与FVM严格等价，并在SPHinXsys中实现网格FVM，从而实现了两种方法的严格性能比较。
摘要：
欧拉光滑粒子流体动力学（Eulerian SPH）被认为是计算流体力学（CFD）中传统欧拉网格方法（即有限体积法，FVM）的一种潜在无网格替代方案。尽管研究人员已经分析了这两种方法之间的差异，但由于欧拉SPH框架中成对粒子相互作用中与界面法线方向相关的约束，对其性能和计算效率的严格比较受到阻碍。为了解决这一约束并提高数值精度，我们引入了欧拉SPH的扩展，包括满足零阶一致性的粒子松弛、确保一阶一致性并解除界面法线方向相关约束的核修正矩阵，以及增强数值精度的耗散限制器，这些扩展使欧拉SPH与FVM严格等价。此外，我们通过开发一个解析器，从使用商业软件ICEM以MESH格式导出的网格文件中提取必要信息，在开源SPH库SPHinXsys中实现了基于网格的FVM。因此，这些综合方法使得这两种方法之间能够进行严格的比较。
英文摘要：
Eulerian smoothed particle hydrodynamics (Eulerian SPH) is considered as a potential meshless alternative to a traditional Eulerian mesh-based method, i.e. finite volume method (FVM), in computational fluid dynamics (CFD). While researchers have analyzed the differences between these two methods, a rigorous comparison of their performance and computational efficiency is hindered by the constraint related to the normal direction of interfaces in pairwise particle interactions within Eulerian SPH framework. To address this constraint and improve numerical accuracy, we introduce Eulerian SPH extensions, including particle relaxation to satisfy zero-order consistency, kernel correction matrix to ensure first-order consistency and release the constraint associated with the normal direction of interfaces, as well as dissipation limiters to enhance numerical accuracy and these extensions make Eulerian SPH rigorously equivalent to FVM. Furthermore, we implement mesh-based FVM within SPHinXsys, an open-source SPH library, through developing a parser to extract necessary information from the mesh file which is exported in the MESH format using the commercial software ICEM. Therefore, these comprehensive approaches enable a rigorous comparison between these two methods.
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