Selectively reduced bi-cubic interpolation for ink-jet simulations on quadrilateral grids
AssigneeSeiko Epson Corporation
InventorJiun-Der Yu
Life of this patent
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Abstract
A selectively reduced bi-cubic interpolation on quadrilateral grids for level set re-distancing improves finite-difference-based ink-jet simulation. The “bi-cubic” nature of the interpolation helps the scheme conserve droplet mass. The “selectively reduced” logic prevents the higher-order simulation algorithm from introducing new instability factors.
Claims19
A method for simulating and analyzing fluid ejection from a channel having a boundary between a first fluid that flows through, and is ejected from, the channel and a second fluid, the method comprising:
- simulating the ejection of the first fluid from the channel using a level set projection algorithm that includes
- (1) creating a quadrilateral grid in a physical space, comprising a plurality of nodes at the intersections of the quadrilateral grid,
- (2) calculating a transformation matrix for transforming equations derived with respect to the quadrilateral grid for application to a uniform square grid in a computational space, the uniform square grid comprising a plurality of nodes at the intersections of the uniform square grid,
- (3) solving equations governing the first and second fluids including creating a level set representative of the boundary, and
- (4) re-distancing the level set, periodically during the simulation, by performing selectively reduced bi-cubic interpolation.
An apparatus for simulating and analyzing fluid ejection from a channel having a boundary between a first fluid that flows through, and is ejected from, the channel and a second fluid, the apparatus comprising:
- means for simulating the ejection of the first fluid from the channel using a level set projection algorithm that includes modules configured to
- create a quadrilateral grid in a physical space, comprising a plurality of nodes at the intersections of the quadrilateral grid,
- calculate a transformation matrix for transforming equations derived with respect to the quadrilateral grid for application to a uniform square grid in a computational space, the uniform square grid comprising a plurality of nodes at the intersections of the uniform square grid,
- solve equations governing the first and second fluids, and
- re-distance, periodically during the simulation, the level set for the first and second fluids by performing selectively reduced bi-cubic interpolation.
A machine-readable medium having a program of instructions for directing a machine to perform a method for simulating and analyzing fluid flow ejection from a channel having a boundary between a first fluid that flows through, and is ejected from, the channel and a second fluid, the program of instructions comprising instructions for:
- simulating the ejection of the first fluid from the channel using a level set projection algorithm that includes instructions for
- (1) creating a quadrilateral grid in a physical space, comprising a plurality of nodes at the intersections of the quadrilateral grid,
- (2) calculating a transformation matrix for transforming equations derived with respect to the quadrilateral grid for application to a uniform square grid in a computational space, the uniform square grid comprising a plurality of nodes at the intersections of the uniform square grid,
- (3) solving equations governing the first and second fluids, and
- (4) re-distancing, periodically during the simulation, the level set for the first and second fluids by performing selectively reduced bi-cubic interpolation.
Dependencies are inferred from the claim text.