Multiphase Dynamics in Arbitrary Geometries on Fixed Cartesian Grids

In this work, a mixed Eulerian-Lagrangian algorithm, calledELAFINT(Eulerian Lagrangian algorithm for interface tracking) is developed further and applied to compute flows with solid-fluid and fluid-fluid interfaces. The method is capable of handling fluid flows in the presence of both irregularly shaped solid boundaries and moving boundaries on a fixed Cartesian grid. The field equations are solved on the underlying fixed grid using a collocated variable, pressure-based formulation. The moving boundary is tracked explicitly by the Lagrangian translation of marker particles. The moving boundary passes through the grid and the immersed boundary technique is used to handle its interaction with the underlying grid. The internal solid boundaries are dealt with by using a cut-cell technique. Particular attention is directed toward conservation and consistency in the vicinity of both phase boundaries. The complex geometry feature has been tested for a variety of flow problems. The performance of the immersed boundary representation is demonstrated in the simulation of Newtonian liquid drops. The combination of the two features is then employed in the simulation of motion of drops through constricted tubes. The capabilities developed here can be useful for solving flow problems involving moving and stationary complex boundaries.