An improved weakly compressible multi-resolution SPH method for free-surface flow simulation

Abstract

This paper proposes an improved multi-resolution smooth particle hydrodynamics (SPH) method for efficiently and accurately simulating the free surface flow of viscous fluids. To address the numerical instabilities arising from interactions between coarse and fine particles due to differences in smoothing length, this study proposes a particle refinement method inspired by adaptive mesh refinement (AMR) and introduces a multi-layer background grid coupling mechanism to improve numerical accuracy while maintaining computational efficiency. To resolve physical field discontinuities at the interface between refined and non-refined regions due to the truncation of the smoothing kernel, buffer particles (including child guard and parent guard particles) are introduced on both sides of the refined region. The physical properties of hidden parent guard particles are updated by fine particles within the fine background grid, ensuring a smooth transition of physical quantities between coarse and fine particle regions. To mitigate tensile instability caused by irregular particle distribution, the particle shifting technique is further enhanced, improving the stability of multi-resolution simulations. Finally, comparisons with single-resolution simulations of dam-break flow, hydrostatic water column, and F-shaped cavity flow demonstrate that the proposed method significantly improves computational efficiency while maintaining high accuracy, thus confirming its effectiveness and robustness.