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Net-Inflow Method |
- Net-Inflow Method (8/94):
Net-Inflow Method(NIM) is to simulate time-dependent incompressible
viscous flow with moving free surface in any irregular domain.
The position of the free surface is tracked by satisfying
the Navior-Stokes equations and the free-surface boundary
conditions simultaneously. No extra marker or free-surface
kinetic equation is needed. As NIM allows one or more control
volumes to be filled or unfilled in each time step, a large
time step can be used to save computational effort. The CPU
time can be further reduced by using the optional penalty-function
method, which eliminates the pressure variables and replaces
the continuity equation as a velocity constraint. When the
Reynolds number is high (>> 1), the momentum convection in
NIM is included in the equilibrium equation by using the Donor-Cell
upwind method to avoid possible numerical instability. As
the problem is highly non-linear due to the liquid inertia,
unknown free-surface position and non-Newtonain viscosity,
the governing equations have been solved iteratively with
Newton-Raphson method and a fully-implicit time discretization.
NIM has been implemented in a six-noded fixed-mesh triangular
control-volume finite-element program to similate the free-surface
flow in two-dimentional domain or the die-filling process
in two-dimensional thin cavity. In its linear solver, only
the non-zero entries of the sparse matrix are stored to reduce
memory requirement and the linearized equations are solved
iteratively by using the Generalized Minimum Residual Method
(GMRES).
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