Simulation of high density ratio interfacial flows on cell vertex/edge-based staggered octree grids with second-order discretization at irregular nodes

A numerical code has been developed for the simulation of unsteady incompressible interfacial flows with large density ratios, based on discretizing the conservation equations on a rectangular adaptive grid with a graded octree data structure, in which the pressure and velocity components are stored at the cell vertices and edges, respectively. With this arrangement, which is novel for octree grids, node alignment simplifies the Poisson equation discretization at nodes common to cells with different refinement levels (irregular nodes), while the staggered storage of variables avoids the pressure-velocity coupling difficulties associated with collocated grids. Three different discretization approaches at irregular nodes are proposed: second- and first-order schemes, and an efficient scheme based on a linear interpolation from the surrounding nodes. A grid refinement test in two dimensions, and 3D deformation and static bubble tests were carried out to assess the accuracy and efficiency of the proposed discretization methods at irregular nodes, the performance of the different schemes used to solve the level set transport equation and the capability of the numerical code to reduce spurious currents. The results of the tests are discussed and compared with results available in the literature. Finally, the ability of the code to accurately simulate the complex phenomena involved in the impact of a water drop on a free surface is demonstrated by thoroughly comparing numerical and experimental results.