Volume tracking with adaptive refinement

A novel piecewise-linear interface calculation (PLIC) volume tracking method is implemented on an adaptively-refined structured mesh, to accurately simulate the behavior of interfacial flow phenomena when the length scales and local curvatures of the interfaces vary significantly. The PLIC volume tracking method is a robust and widely-used technique for tracking interfaces, but previous PLIC implementations have been on uniform grids. This is a limitation; because fine resolution is needed to resolve the multiscale features of interfacial flows. Adaptive refinement can be used to resolve the multiscale features of the flow by using adaptive hierarchical grids consisting of quadtrees, which are recursively subdivided on a cartesian mesh. The criteria for refinement and coarsening are related to the local curvature of the interface and to a measure of well-resolvedness. Results are presented of the scheme and compared with corresponding simulations on fixed meshes. In terms of computational expense, to reach an error norm; this approach is faster vis-a-vis a fixed mesh, but as the interface moves, the grid must be updated at every time step. Some new test cases have also been developed, and their features explored, to assess the capabilities of the algorithrn.