Iterative high-order weakly compressible smoothed particle hydrodynamics model for viscous fluid flows

Abstract

Smoothed particle hydrodynamics (SPH) is an efficient and robust particle-based method for large deformation problems such as strongly nonlinear free interface flow and structural damage due to its meshless characteristics. However, achieving consistent high-order accuracy remains a fundamental challenge under irregular particle distributions, which often leads to significant accuracy degradation in conventional SPH interpolation schemes. To address this issue, we propose a novel iterative high-order SPH framework to systematically improve the accuracy of gradient and Laplacian operators through multiple layers of Taylor expansions. An adaptive iteration strategy is introduced at each expansion layer, resulting in a recursive correction that utilizes high-order derivatives to improve low-order estimates, thereby improving consistency and robustness for inhomogeneous particle fields. To maintain accuracy near domain boundaries, a new high-order ghost particle extrapolation scheme is developed to ensure consistency of spatial derivatives. The proposed framework is validated on a series of typical incompressible viscous flow benchmarks, including Taylor-Green vortex, Lamb-Osing vortex, inviscid shear layer, Burggraf flow, and Lid driven flow. Results show that the proposed approach achieves up to fourth-order convergence even with irregular particle arrangements and improves simulation accuracy by two orders of magnitude compared to the conventional SPH formulation. By avoiding the use of high-order kernel functions and large matrix systems, this method provides a scalable approach for high-fidelity particle-based simulations.