A numerical procedure based on the Arbitrary Lagrangian-Eulerian (ALE) description of Bow is developed to simulate free surface problems. The conservation equations are rewritten using a referential kinematic description where the grid points move independently of the fluid particles. In all the applications considered in this work, the fluid domain is bounded below by a rigid impermeable wall and above by a vapor-liquid moving interface, The free surface is taken to be resting on vertical spines and the grid points slide up and down along the vertical spines, The two-dimensional unsteady Navier-Stokes equations are discretized in time using Chorin type Projection scheme and pressure is determined from the Poisson equation. Galerkin Finite Element Method with three node triangular elements has been used for spatial discretization. Hydraulic jump with inlet supercritical Froude number 2.0 is solved. The turbulence is modeled using a two-equation k-epsilon closure model. The surface roller and small recirculation zone near the foot of the jump are found to influence the turbulence characteristics of the jump significantly. The next application considered is the combined buoyancy-driven and thermocapillary-induced convective flows in crystal growth melts. The influence of various parameters on the Bow field and free surface deformation is studied. Lastly, the instabilities in the thin film flows draining down an inclined plane are studied. The results are compared with the available linear stability and non-linear evolution equation results, The phase transition from supercritical to subcritical is investigated in greater detail.
