Central Difference Level Set Projection for Ink-Jet Simulation
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Solution Overview
Problem
Existing simulation models for ink ejection from piezoelectric print heads face challenges in complexity, code implementation, and memory requirements, particularly when dealing with non-Newtonian fluid flows and the need for increased numerical resolution.
Innovation Solution
A central difference scheme for the coupled level set projection method on uniform rectangular grids, using staggered cell averages and discrete projection operators, which simplifies code implementation and reduces memory requirements by alternating the location of velocities and level sets between time steps, and employing multi-grid-compatible finite difference and finite element projection operators.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Godunov upwind scheme is used to evaluate convection terms, then numerical resolution is improved, but code complexity increases
Solution Approach 1:
The patent extracts the complex Godunov upwind procedure (including Taylor's extrapolation in time and space, and local Riemann problem solving) from the simulation framework and replaces it with a simpler central difference scheme that achieves adequate numerical resolution without the excessive code complexity
Solution Approach 2:
The patent changes the numerical scheme parameters from Godunov upwind (with its complex extrapolation and Riemann solving) to central difference, altering the computational approach to reduce complexity while maintaining simulation accuracy for ink-jet flows
2Manufacturing precision
If Godunov upwind procedure is implemented, then grid viscosity is reduced, but implementation difficulty increases
Solution Approach 1:
The patent adopts a simpler central difference scheme that is easier to implement and maintain, trading off some of the low grid viscosity benefits of Godunov upwind for significantly reduced implementation difficulty and computational overhead
3Measurement precision
If Taylor's expansion in time and space is performed, then velocity extrapolation accuracy is improved, but computational overhead increases
Solution Approach 1:
The patent removes the dual extrapolation in time and space from the computational framework, replacing it with a central difference approach that reduces computational overhead while maintaining sufficient accuracy for the application
Data Source
AI summary
A coupled level set projection method is incorporated into a finite-difference-based ink-jet simulation method to make the simulation easier and faster to run and to decrease the memory requirements. The coupled level set projection method is based on a central difference discretization on uniform rectangular grids. A constructed numerical projection operator, in the form of either a finite difference projection operator or a finite element projection operator, can be used in the central difference scheme, in which case the resulting linear systems can be solved by a multi-grid method. The finite difference projection operator is used when the fluid velocity is located at grid points and the pressure at cell centers, whereas the finite element projection operator is used when the fluid velocity is located at cell centers and the pressure at grid points.