Regularization of the Material Discontinuities in the Two Phase Flow Simulatin

Abstract: Proper understanding of flow involving more than one phase is essential in understanding many physical phenomena. One such is the crystal growth where the convection on the surface produces an increase in the uncontrollable number of dislocations leading to defects. Geometry and physical condition of the inter-facial layer separating the two phases is crucial in controlling such physical evolution. On the microscopic scale, the inter-facial layer is of microscopic width such that there is a continuous transition of fluid properties like density from one phase to the other. More over the molecules on the inter-facial layer are unevenly pulled by the surrounding molecules resulting in the inter-facial tension. On the macroscopic scale, the continuous approximation of fluids replaces the inter-facial layer of microscopic width by a sharp mathematical interface across which there is a jump discontinuous change from density 1 to density 2. Since the motion of multi phase flow is governed by the Navier-Stokes equations by which the fluid properties like density and viscosity and the dependent variables like velocity and pressure should be smooth, fluid properties are generally smeared out properly. In such formulation, inter-facial tension effects in the equations are introduced by framing force terms. One such method of properly capturing interfacial effects on the fluid motion is the conservative level set method. But the formulation made by the conservative level set method on the fluid properties and on the force term becomes bad on modeling the physical system involving motion due to the inter-facial tension gradient. Aim of this thesis is to emphasize the importance of formulation to smoothen the jump discontinuity of fluid properties across the interface and framing the force term correctly to capture the inter-facial tension effects in the fluid motion. Here the simple physical system involving marangoni convection is taken as a model. Then it is solved with jump conditions across the interface. The fluid properties and the force term when smoothened by the conservative level set function results in the solution deviating from the physical model. So the fluid properties and the force term are reformulated to get an approximate solution matching the exact solution.