1. A method for simulating and analyzing fluid ejection from a channel, there being a boundary between a first fluid that flows through the channel and a second fluid, the method comprising: (a) transforming, for a given channel geometry, a quadrilateral grid in a physical space to a uniform rectangular grid in a computational space; (b) performing finite difference analysis on the uniform rectangular grid to solve equations governing the flow of at least the first fluid through the channel, wherein the finite element analysis of an incompressible continuity equation of the equations, for projection of fluid velocity of at least the first fluid, is formulated by a two-dimensional (2-D)-five-point-stencil-based non-finite-element-method (non-FEM) discretization to obtain and solve a linear system whose coefficient matrix has an average bandwidth of five; (c) inverse transforming results of the finite difference analysis back to the quadrilateral grid in the physical space; and (d) simulating the flow of the first fluid through at least a portion of the channel, and ejection therefrom, based on the results of the finite difference analysis and the inverse transform of the results of the finite difference analysis.