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- W2952658966 abstract "During the upstroke of a normal eye blink, the upper lid moves and paints a thin tear film over the exposed corneal and conjunctival surfaces. This thin tear film may be modeled by a nonlinear fourth-order PDE derived from lubrication theory. A challenge in the numerical simulation of this model is to include both the geometry of the eye and the movement of the eyelid. A pair of orthogonal and conformal maps transform a square into an approximate representation of the exposed ocular surface of a human eye. A spectral collocation method on the square produces relatively efficient solutions on the eye-shaped domain via these maps. The method is demonstrated on linear and nonlinear second-order diffusion equations and shown to have excellent accuracy as measured pointwise or by conservation checks. Future work will use the method for thin-film equations on the same type of domain." @default.
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- W2952658966 date "2017-04-05" @default.
- W2952658966 modified "2023-09-27" @default.
- W2952658966 title "Simulation of Parabolic Flow on an Eye-Shaped Domain with Moving Boundary" @default.
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