Finite volume method (FVM) is a widely used mesh-based technique, renowned for its computational efficiency and accuracy but it bears significant drawbacks, particularly in mesh generation and handling complex boundary interfaces or conditions. On the other hand, smoothed particle hydrodynamics (SPH) method, a popular meshless alternative, inherently circumvents the mesh generation and yields smoother numerical outcomes but at the expense of computational efficiency. Therefore, numerous researchers have strategically amalgamated the strengths of both methods to investigate complex flow phenomena and this synergy has yielded precise and computationally efficient outcomes. However, algorithms involving the weak coupling of these two methods tend to be intricate, which has issues pertaining to versatility, implementation, and mutual adaptation to hardware and coding structures. Thus, achieving a robust and strong coupling of FVM and SPH in a unified framework is imperative. Due to differing boundary algorithms between these methods in Wang's work, the crucial step for establishing a strong coupling of both methods within a unified SPH framework lies in incorporating the FVM boundary algorithm into the Eulerian SPH method. In this paper, we propose a straightforward algorithm in the Eulerian SPH method, algorithmically equivalent to that in FVM, grounded in the principle of zero-order consistency. Moreover, several numerical examples, including fully and weakly compressible flows with various boundary conditions in the Eulerian SPH method, validate the stability and accuracy of the proposed algorithm.

翻译：有限体积法(FVM)是一种广泛使用的基于网格的计算技术，以其计算效率和精度著称，但在网格生成以及处理复杂边界界面或条件方面存在显著缺陷。另一方面，光滑粒子流体动力学(SPH)方法作为一种流行的无网格替代方法，天然规避了网格生成问题并能得到更平滑的数值结果，但代价是计算效率较低。因此，众多研究者策略性地融合了两种方法的优势来研究复杂流动现象，这种协同作用已取得了精确且计算高效的结果。然而，涉及这两种方法弱耦合的算法往往较为复杂，存在通用性、实现难度以及硬件与编码结构相互适配等问题。因此，在统一框架内实现FVM和SPM的鲁棒性强耦合至关重要。由于Wang等人的研究中这两种方法的边界算法存在差异，在统一SPH框架内建立二者强耦合的关键步骤在于将FVM边界算法引入欧拉SPH方法。本文提出了一种基于零阶一致性原理的欧拉SPH方法简化算法，该算法在算法层面与FVM等效。此外，通过多个数值算例（包括欧拉SPH方法中具有多种边界条件的完全可压缩流与弱可压缩流），验证了所提算法的稳定性与精度。