Two-phase flows on interface refined grids modeled with VOF, staggered finite volumes, and spline interpolants

A two-phase 2D model that combines the volume of fluid (VOF) method with im plicit staggered finite volumes discretization of the Navier-Stokes equatio n is presented. Staggered finite volumes are developed on the basis of nonc onforming Crouzeix-Raviart finite elements. where all components of the vel ocity lie in the middle of the element edges and the pressure degrees of fr eedom are found in the centers of mass of the elements. Staggered finite Vo lumes extend marker and cell (MAC) regular staggered grids to unstructured mesh. A linear saddle point problem. resulting from either the discretizati on or the Newton method, is solved for all unknown pressures and velocities . Interface is represented with spline interpolants which follow the VOF di stribution. Adaptive mesh refinement is used to obtain a high level of unif orm refining at the domain of dependence of the interface. The aligned grid is obtained by irregular refining of the cells which are intersected by a curve. The boundaries of its elements coincide with the slope segments goin g through the intersections of the curve with the underlying regular elemen ts boundary. The deformable computational grids are used only to discretize the Navier-Stokes equation. The advection of volume fractions is done on t he advection mesh, which corresponds to highest regular refining on the com putational grid. Approximation of the surface tension on spline interpolant s offers a straightforward way to describe correctly the pressure jumps on interface-fitted staggered grids. This allows deletion of the anomalous cur rents around a statical bubble and their effective reduction in real simula tions. On the aligned grid, the continuity of the viscous stress is modeled exactly due to the finite volume approach. Using the proposed numerical te chniques. single bubble rise is analyzed. (C) 2001 Academic Press.