Numerical Simulation Of Oscillation Of Drops Using Level Set Method

This thesis concerns numerical techniques for two phase flow simulations, the two phases are immiscible and incompressible fluids. Strategies for accurate simulations are suggested. In particular, accurate approximations of the weakly discontinuous velocity field, the discontinuous pressure, and the surface tension force and a new model for simulations of contact line dynamics are proposed.In two phase flow problems discontinuities arise in the pressure and the gradient of the velocity field due to surface tension forces and differences in the fluids’ viscosity. In this thesis, a new finite element method which allows for discontinuities along an interface that can be arbitrarily located with respect to the mesh is presented. Using standard linear finite elements, the method is for an elliptic PDE proven to have optimal convergence order and a system matrix with condition number bounded independently of the position of the interface.The free oscillation of liquid droplet is one of the classical questions in science research, liquid drops play important role in a lot of engineering applications. Theory study of droplet oscillation mainly based on the linear method, this method is only adapted to the small-amplitude oscillatory motion of drops. Except the linear method used in this study, numerical method have been successfully applied in simulation of the free oscillation of liquid droplet. To date, the literature on simulation of oscillation of viscoelastic drops is quite sparse.In this paper, we study small-amplitude shape oscillation of viscoelastic drop in air using the numerical simulation. A spatial discretization is accomplished by the finite element method and temporal discretization by backward differentiation formula(BDF). In order to ensure the accuracy of numerical calculation, we use the conservative level set method to track the moving interface of drop. Our numerical data indicate that changing different Deborah number and Ohnesorge number exhibit different oscillation behavior; especially, for the low Deborah number the frequency increase with Ohnesorge number, reaches a maximum value, then decrease again, this behavior is not found for higher Deborah number, where the frequency is monotonic with Ohnesorge number; all these results are in line with the prediction of the linear theory for small-amplitude shape oscillation of viscoelastic drop. Finally we extend this method to solve problem for large-amplitude oscillation.