An algorithm for the incorporation of relevant FVM boundary conditions in the Eulerian SPH framework

The finite volume method (FVM) is widely recognized as a computationally efficient and accurate mesh-based technique. However, it has notable limitations, particularly in mesh generation and handling complex boundary interfaces or conditions. In contrast, the smoothed particle hydrodynamics (SPH) method, a popular meshless alternative, inherently circumvents the challenges of mesh generation and yields smoother numerical outcomes. Nevertheless, this approach comes at the cost of reduced computational efficiency. Consequently, researchers have strategically combined the strengths of both methods to investigate complex flow phenomena, producing precise and computationally efficient outcomes. However, algorithms involving the weak coupling of these two methods tend to be intricate and face challenges regarding versatility, implementation, and mutual adaptation to hardware and coding structures. Thus, achieving a robust and strong coupling of FVM and SPH within a unified framework is essential. A mesh-based FVM has recently been integrated into the SPH-based library SPHinXsys. However, due to the differing boundary algorithms between these methods, the crucial step for establishing a strong coupling of both methods within a unified SPH framework is to incorporate the FVM boundary algorithm into the Eulerian SPH method. In this paper, we propose a straightforward algorithm within the Eulerian SPH method, which is algorithmically equivalent to that in FVM and based on the principle of zero-order consistency. Moreover, several numerical examples, including compressible and incompressible flows with various boundary conditions in the Eulerian SPH method, demonstrate the stability and accuracy of the proposed algorithm.