Theoretical and numerical assessment of explicit incompressible SPH method

The Explicit Incompressible SPH (EISPH) method is formulated as a fully explicit method derived from the projection-based Incompressible SPH (ISPH) framework, developed specifically to achieve a concurrent realization of the numerical stability inherent in projection-based ISPH and the computational efficiency characteristic of fully explicit algorithms. Despite its increasing application, the method’s core assumption—truncating the iterative solution of the Pressure Poisson Equation (PPE) to a single step—has not been rigorously investigated. This study addresses this gap by first establishing a theoretical analogy between EISPH and the weakly compressible δ -SPH method. This analysis reveals that conventional EISPH is equivalent to a δ -SPH method with unphysically high compressibility and excessive numerical diffusion, which compromises its accuracy and stability. Based on these findings, we provide recommendations for its appropriate application in terms of CFL condition and propose a stabilization scheme to mitigate its deficiencies. Subsequently, fundamental benchmark tests are conducted to systematically evaluate and numerically confirm these inherent limitations and the effectiveness of the proposed settings and schemes.