An h/p-adaptive algorithm for the weakly compressible SPH method

In this work, a novel smoothed particle hydrodynamics (SPH) h/p-refinement method is proposed for the first time in SPH, based on Lagrangian and high-order Eulerian formulations. The approach decomposes the computational domain into subdomains, where particle resolution (h-refinement) and kernel order (p-refinement) can be varied. Lagrangian subdomains are employed in regions with free-surfaces, fragmentation or moving boundaries, while high-order Eulerian subdomains capture internal flow structures with enhanced accuracy. The coupling between subdomains is achieved via buffer zones, allowing consistent exchange of physical quantities. The novel algorithm has been implemented in the DualSPHysics code framework to exploit the computational power of graphics processing units (GPUs). The method is validated through classical benchmarks, including a Taylor-Green vortex to obtain the convergence characteristics and a flow past an impulsively started cylinder at R e = 9500 . Finally, the advection of a three-dimensional vortex ring demonstrates the capability of the approach in complex flows. Results show that the h/p-refinement formulation achieves higher accuracy at a given resolution and can reduce the computational cost by up to an order of magnitude, compared to a classical Lagrangian SPH scheme.