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

Abstract

Purpose 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). Design/methodology/approach 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. Findings 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. Originality/value 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.

Accuracy analysis of different Laplacian models of incompressible SPH method improved by using Voronoi diagram

“…A new model of Laplacian operator with significant accuracy has been recently proposed which is formulated as a hybrid of ISPH with Taylor expansion and moving least-squares approach [30]. Later, the significant higher accuracy of this model in comparison with some of the well-known higher-order Laplacian SPH models was shown by Heydari et al [12]. A somewhat similar study was conducted to solve the p-Laplacian equation using a constrained-vertex variant of the mortar spectral element method [26].…”

Modified incompressible SPH method for simulating free surface problems using highly irregular multi-resolution particle configurations

“…More recently, a new kernel function with steep shape in comparison with the existing functions has been proposed to obviate the need of dummy particles in modeling solid wall boundary conditions [40][41][42]. Recently, a higher-order SPH Laplacian model has been proposed by Shobeyri [43], and later, the model was compared with some well-known higher-order models [10]. The newly proposed model shows a significant superiority in accuracy compared with the other models.…”