Level-set Method For Two-phase Incompressible Fluid Interface Dynamics

Two-phase interface dynamics plays an important role in a wide variety of technical applications, for example LOX/H₂ rocket engines or printing. The dynamics at theinterface determine the atomization process. The atomization process of liquid jets/sheets is usually divided into two consecutive steps, the primary and the secondary atomization. The initial breakup of the liquid jet/sheet into large and small structures is called the primary atomization, whereas the subsequent breakup of these structure into ever-small secondary atomization. We focus on the primary atomization, and in the secondary atomization the diameter of small drop is less than our grid diameter.M.Herrmann discussed a vortex sheet problem. [1] focuses on the motion of the interface Γ between two inviscid, incompressible fluids 1 and 2. They have the same fluid densities. The velocity u at a point is given by a line integral of the jump in tangential velocity across the interface Γ. The interface is represented by the level-set method. In [2], M.Herrmann extends the method to three dimensions.Level-set method adds dynamics to implicit surfaces. The key idea that started the level set fanfare was the Hamilton-Jacobi approach to numerical solutions of a time-dependent equation for a moving implicit surface. When we know the position of the interface, we can construct a signed distance function. Then we extend the velocity near the interface off Γ by letting the velocity be a constant along the curve normal to Γ. Using level-set equation, we can get a new signed distance. Avoiding numerical errors caused by both...