Efficient and flexible adaptive particle refinement for free-surface flows based on the regularized high-order diffusive smoothed particle hydrodynamics scheme

The aim of the present work is the investigation of an adaptive particle refinement (APR) approach that enables large variations in particle size even in the presence of a free surface. In the smoothed particle hydrodynamics (SPH) literature, the existing APR or similar multi-resolution techniques can be categorized into three main approaches, essentially driven by the discrete differential operators selected. When a conservative formulation is retained, either variable smoothing-length techniques or buffer regions are generally employed. By contrast, in formulations using accurate but non-conservative SPH operators, large variations of the particle size are achievable without requesting any specific treatment. However, because of the difficulties of such formulations in addressing the free surface, they have so far been restricted to internal flows. Recently, a regularized high-order diffusive (RHOD)-SPH approach has been derived in the context of single resolution. In this approach an accurate formulation is used inside the bulk of the fluid, whereas a conservative one is preferred in the free-surface region. In the present paper, the ingredients required in the RHOD-SPH approach are extended to APR. Specifically, the Riemann-based diffusive terms and particle shifting technique are generalized to deal with particles of different sizes. A particle-splitting procedure is employed to enlarge the range of applications of the approach. The formulation is validated on six different test cases, with comparisons to both single-resolution and reference results.