The subsurface flow problem with a free surface
is a nonlinear problem in which nonlinearities arise from the nonlinear boundary characteristics .
Unfortunately, the thin crystalline film deposited on the substrate often contains high densities of dislocations piercing the free surface
, the so-called threading dislocations (TDs), which affect adversely device properties.
As a meshless Lagrangian method, the SPH method is good at modeling Newtonian and non-Newtonian flows with a free surface
 and has been chosen for simulating the SCC flow by Kulasegaram et al.
To the authors' knowledge, the effect of surface tension at the free surface
in a two-layer fluid is yet to be known.
simulated water impact problem of a semicircular cylinder with the free surface
captured using level set method .
Monaghan, "Simulating free surface
flows with SPH," Journal of Computational Physics, vol.
it is assumed that this limitation is mainly due to the difficulties in satisfying boundary conditions at the free surface
of the ground.
Contributors also propose the design of a marine drilling riser for the deepwater environment, oxidizer nozzles for a coal gasifier, a 3D shock-capturing model for free surface
flow, and an inverse Schwartz-Christoffel panel method.
Experimental flow visualizations were carried out to exhibit the free surface
and the entire flow field at high Ca and Reynolds number (Re), which is a nondimensional number, and is the ratio of fluid inertia force and viscous force, that is Re = [rho]/[V.sub.0][l.sub.c] [eta], where [l.sub.c] represents the characteristic length, defined as [l.sub.c] = [([sigma]/ [rho]g).sup.1/2] [14, 15].
In recent years, the buoyancy and thermocapillary effects on heat transfer in free surface
enclosure have been studied and analyzed widely by a number of researchers.