Finite difference level set projection method on multi-staged quadrilateral grids
AssigneeSeiko Epson Corporation
InventorJiun-Der Yu
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Abstract
A finite difference level set projection algorithm on multi-staged quadrilateral grids for simulation of a split liquid film between two rollers. From one stage to the next, the number of meshes in the vertical direction changes by a select factor to provide a good balance between resolution and number of meshes. Having fewer meshes at the nip (the smallest gap between the rollers), the multi-staged quadrilateral grid allows a much bigger time step and requires much less CPU time to reach the steady state.
Claims18
A non-transitory computer-readable medium encoded with instructions for a processor to perform a method for simulating a system in a simulation space comprising:
- instructions for dividing the simulation space into a plurality of quadrilateral grids, including a first grid having a first number of meshes along a vertical axis of the simulation space, and a second grid adjacent to the first grid, the second grid having twice the first number of meshes along the vertical axis of the simulation space;
- instructions for identifying a first cell and a fourth cell in the first grid, and for identifying a second cell, a third cell, a fifth cell and a sixth cell in the second grid, wherein:
- a first node is located at an intersection of the first, third, fourth and fifth cell,
- a first segment defines a boundary between the first cell and the second cell and between the first cell and the third cell, and
- a second segment defines a boundary between the fourth cell and fifth cell and between the fourth cell and the sixth cell;
- instructions for evaluating, using a finite element projection, a system variable associated with the first node using a testing function extending through a first area encompassing:
- the first, second, third, fourth, fifth, and sixth cell;
- and an interpolation function extending through a second area encompassing the first, third, fourth and fifth cell.
A non-transitory computer-readable medium encoded with instructions for a processor to perform a method for simulating a system in a simulation space comprising:
- instructions for dividing the simulation space into a plurality of quadrilateral grids, including a first grid having a first number of meshes along a vertical axis of the simulation space, and a second grid adjacent to the first grid, the second grid having twice the first number of meshes along the vertical axis of the simulation space;
- instructions for identifying a first cell in the first grid, and identifying a second cell and a third cell in the second grid,
- wherein a first segment defines a boundary between the first cell and the second cell and between the first cell and the third cell, the second cell and the third cell share a common boundary;
- and
- instructions for evaluating, using a numerical approximation method, a system variable at a second node located at the intersection of the first segment and the common boundary, which evaluation includes:
- evaluating the system variable at a third point located at a cell center of the first cell, at a fourth point located at a cell center of the second cell, and at a fifth point located at a cell center of the third cell, and
- evaluating a Jacobian located at a center of the common boundary as the sum of a Jacobian located at the fourth point and a Jacobian located at the fifth point.
Dependencies are inferred from the claim text.