Inkjet technology is traditionally used in a general home/office printing uses. In order to increase the resolution and to explore further uses of the inkjet technology, it is important to know how the fluid droplet from the inkjet head will finally settle when they dry.
The present invention is directed towards the study of single-phase fluids. A single-phase fluid, as used in the present invention refers to a pure fluid or a mixture. A boundary encapsulates this single-phase fluid, and over time the boundary may evolve and move through space. The solution or fluid domain is restricted to an area delimited by the boundary. For the purposes of the present invention, the effect of an interface, if any that does form between elements of such a mixture may be ignored when considering the motion of the boundary.
Motion of the boundary may be governed by one or more equations. The boundary may be defined by a set of markers. For some systems the equations may include terms related to the curvature of the boundary. Prior art methods have calculated the curvature of the boundary from a cubic spline fitted to the markers that define the boundary. Small errors in the positions of the marker can cause errors in the second derivatives, which can create variations in the curvature. Under certain conditions, this variation may increase in magnitude as the boundary evolves in time. This can lead to numerically unstable simulations, which exhibit unrealistic oscillations.
Prior art methods have attempted to address the problems that arise from defining the boundary using markers by employing multi-phase fluid simulation methods (e.g., front tracking methods).
Problems may arise when handling the boundary between the two fluids. Each fluid is characterized by a set of system variables (i.e., density, viscosity, and pressure). A jump condition necessarily exists at the boundary. This jump condition is represented by a step wise change in the system variables and results in a discontinuity in system variables and their derivatives at the boundary. This discontinuity can prevent numerical solutions from converging. Further, to accommodate the complex geometry, a quadrilateral grid is needed to be set aligned with the geometry of the bank structure.