Accuracy analysis of different higher-order Laplacian models of incompressible SPH method

This paper aims to examine the accuracy of several higher-order incompressible smoothed particle hydrodynamics (ISPH) Laplacian models and compared with the classic model (Shao and Lo, 2003).

The numerical errors in solving two-dimensional elliptic partial differential equations using the Laplacian models are investigated for regular and highly irregular node distributions over a unit square computational domain.

The numerical results show that one of the Laplacian models, which is newly developed by one of the authors (Shobeyri, 2019) can get the smallest errors for various used node distributions.

The newly proposed model is formulated by the hybrid of the standard ISPH Laplacian model combined with Taylor expansion and moving least squares method. The superiority of the proposed model is significant when multi-resolution irregular node distributions commonly seen in adaptive refinement strategies used to save computational cost are applied.