CIMP Software Status: 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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