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Finite volume method (FVM) is a widely used mesh-based technique, renownedfor its computational efficiency and accuracy but it bears significantdrawbacks, particularly in mesh generation and handling complex boundaryinterfaces or conditions. On the other hand, smoothed particle hydrodynamics(SPH) method, a popular meshless alternative, inherently circumvents the meshgeneration and yields smoother numerical outcomes but at the expense ofcomputational efficiency. Therefore, numerous researchers have strategicallyamalgamated the strengths of both methods to investigate complex flow phenomenaand this synergy has yielded precise and computationally efficient outcomes.However, algorithms involving the weak coupling of these two methods tend to beintricate, which has issues pertaining to versatility, implementation, andmutual adaptation to hardware and coding structures. Thus, achieving a robustand strong coupling of FVM and SPH in a unified framework is imperative. Due todiffering boundary algorithms between these methods in Wang's work, the crucialstep for establishing a strong coupling of both methods within a unified SPHframework lies in incorporating the FVM boundary algorithm into the EulerianSPH method. In this paper, we propose a straightforward algorithm in theEulerian SPH method, algorithmically equivalent to that in FVM, grounded in theprinciple of zero-order consistency. Moreover, several numerical examples,including fully and weakly compressible flows with various boundary conditionsin the Eulerian SPH method, validate the stability and accuracy of the proposedalgorithm.

Incorporating the algorithm for the boundary condition from FVM into the framework of Eulerian SPH