Three-dimensional variable resolution for multi-scale modeling in Smoothed Particle Hydrodynamics

This study builds on our prior 2D variable-resolution framework for Smoothed Particle Hydrodynamics (SPH) using domain decomposition, extending it to the simulation of three-dimensional flows. We enhance the domain decomposition strategy to enable efficient mass transfer across subdomains with varying resolutions. Key improvements include a refined calculation of Eulerian fluxes at the interfaces between different subdomains, including the free surface, and the use of a first-order consistent approximation of the pressure gradient for a smooth transition of the physical variables across the different resolution zones. The model is implemented in the SPH solver DualSPHysics and validated through several 3D test cases, including flow past a sphere, water entry of a wedge, and wave-induced motion of a floating box. Simulation results indicate that our 3D multi-resolution model can capture complex fluid-structure interactions effectively, and it can offer significant computational savings over traditional uniform resolution techniques. Our advancements provide a scalable and efficient solution for simulating a wide range of multi-scale engineering applications, especially those involving fluid-structure interaction.