Coupled quadrilateral grid level set scheme for piezoelectric ink-jet simulation

A method for simulating and analyzing two-phase fluid flow through at least a portion of, and ejection from, a channel through at least the portion of which an interface between a first fluid in a first phase and a second fluid in a second phase moves, the method comprising the steps of:

• (a) deriving partial differential equations, including a level set convection equation having a level set function, applicable to a quadrilateral grid in a physical space, including deriving a viscosity term, a surface tension term, and a level set convection equation for two-phase flows;
• (b) calculating a transformation for transforming the derived partial differential equations for application to a uniform square grid in a computational space;
• and
• (c) solving the derived and transformed partial differential equations to determine the flow of the first fluid through at least the portion of, and ejection from, the channel, wherein the level set function takes into consideration the interface as it moves.

An apparatus for simulating and analyzing two-phase fluid flow through at least a portion of, and ejection from, a channel through at least the portion of which an interface between a first fluid in a first phase and a second fluid in a second phase moves, the apparatus comprising:

• means for deriving partial differential equations, including a level set convection equation having a level set function, applicable to a quadrilateral grid in a physical space, including deriving a viscosity term, a surface tension term, and a level set convection equation for two-phase flows;
• means for calculating a transformation for transforming the derived partial differential equations for application to a uniform square grid in a computational space;
• and
• means for solving the derived and transformed partial differential equations to determine the flow of the first fluid through at least the portion of, and ejection from, the channel, wherein the level set function takes into consideration the interface as it moves.

A storage medium having a program of instructions for directing a machine to perform a method for simulating and analyzing two-phase fluid flow through at least a portion of, and ejection from, a channel through which at least the portion of which an interface between a first fluid in a first state and a second fluid in a second state moves, the program of instructions comprising instructions for:

• (a) deriving partial differential equations, including a level set convection equation having a level set function, applicable to a quadrilateral grid in a physical space, including deriving a viscosity term, a surface tension term, and a level set convection equation for two-phase flows;
• (b) calculating a transformation for transforming the derived partial differential equations for application to a uniform square grid in a computational space;
• and
• (c) solving the derived and transformed partial differential equations to determine the flow of the first fluid through at least the portion of, and ejection from, the channel, wherein the level set function takes into consideration the interface as it moves.