The use of adapting quadtree grids for simulating moving interface and viscous fluid free surface flows

The new method presented in this paper involves the application of adaptive hierarchical grids to CFD calculations where the fluid interface is moving, such as the collapse of a dam. Adapting quadtree grids are combined with a volume of fluid approach, in which the CICSAM [1] scheme is used for advection of the interface and PLIC (piecewise linear interface construction) is used to reconstruct and interpolate the volume fraction field during adaptation of the quadtree grid. The combination of high resolution adaptive hierarchical remeshing and CICSAM interface advection is shown to overcome the problems of interface smearing and high CPU intensivity inherent in most VoF schemes. The result is a combination of the two main approaches to free surface problems: the free surface is effectively tracked by the adapting refinements in the quadtree grid, a sharp interface is achieved and the advantages of both interface tracking and capturing are realised. The new method is demonstrated for interface advection in a shearing flow field and shown to provide high resolution at the interface at low computational cost. The saving in grid size is also apparent when the new quadtree VoF scheme is combined with a Navier Stokes solver and used to simulate the collapse of a water column. The grids are adapted in this case to provide resolution at the free surface. The calculations are made on uniform and adapting quadtree grids and the accuracy of the quadtree calculations is shown to be the same as those made on the equivalent uniform grids. The adaptive quadtree results are in excellent agreement with experimental and other numerical data, a sharp interface is maintained at the free surface and a considerable saving is made in the size of the computational grid.