Variable resolution for SPH in three dimensions: Towards optimal splitting and coalescing for dynamic adaptivity

摘要: Abstract As smoothed particle hydrodynamics (SPH) becomes increasingly popular for complex flow analysis the need to improve efficiency particularly 3-D problems is becoming greater. Automatic adaptivity with variable size therefore desirable. In this paper, a novel splitting and coalescing algorithm developed which minimizes density error while conserving both mass momentum using variational principle. Accuracy increased in refined areas unaffected by coarser distributions elsewhere. For splitting, key criteria are number of split (daughter) particles, their distribution, spacing kernel size. Four different arrangements investigated including cubic stencil 8 an additional 6 located at face centres, icosahedron-shaped arrangement 14 dodecahedron-shaped 20 particles where vertices. The also examines whether retaining centre necessary revealing that regardless adopted, minimize daughter should be placed same position original particle. optimum configuration found commonly used smoothing kernels such as quintic splines Wendland produce similar errors, so optimal refinement effectively independent choice. A new scheme completes resolution can either or reduced locally. SPH scheme, tested Poiseuille showing negligible loss convergence accuracy area lid driven cavity wide range Reynolds good agreement reference solutions again local defined distribution.