Development of a VOF-Based Interface Capturing Method Using a Family of Bounded Compressive Flux Blending Schemes Within an Existing Finite Volume Flow Solver

摘要

A family of bounded compressive flux blending schemes is used as the basis for developing a VOF-based interface capturing method in an existing incompressible flow solver. An attractive feature of the method is that the interface is defined implicitly as the median value surface of a scalar volume fraction function and no explicit reconstruction of the interface is needed. The lack of any geometrical reconstruction of the interface greatly simplifies the implementation of the method in an existing finite volume flow solver using general polyhedral unstructured meshes. Several NVD-based convection schemes are presented for a cell-centered finite volume implementation of the method. Several important implementation details are discussed such as the evaluation of the 'far upwind1 point of the upwind-biased numerical stencil, the implementation of the face flux prescription as a 'deferred correction' to the first-order upwind flux and limiting of the volume fraction function to physically meaningful values in a multi-dimensional discretization. The resulting compressive VOF-based interface capturing method is evaluated using several well-known analytic flows including a steady-state oblique step function, an obliquely translating hollow square and hollow circle and a rotating slotted disk. The method is then applied to a dam break problem to demonstrate the efficacy of the overall method when applied to a well-known two-fluid Navier-Stokes flow.