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In , the Ghost Fluid Method (GFM) was developed to capture the boundary conditions at a contact discontinuity in the inviscid com-pressible Euler equations. In , related techniques were used to develop a boundary condition capturing approach for the variable coefficient Poisson equation on domains with an embedded interface. In this paper, these new… (More)
In this paper, we consider the variable coefficient Poisson equation with Dirichlet boundary conditions on an irregular domain and show that one can obtain second order accuracy with a rather simple dis-cretization. Moreover, since our discretization matrix is symmetric, it can be inverted rather quickly as opposed to the more complicated nonsymmetric… (More)
In this paper, we propose a new numerical method for treating two phase incompressible flow where one phase is being converted into the other, e.g. the vaporization of liquid water. We consider this numerical method in the context of treating discontinuously thin flame fronts for incompressible flow. This method was designed as an extension of the Ghost… (More)
We reproduce the general behavior of complicated bubble and droplet motions using the variational level set formulation introduced by the authors earlier. Our approach here ignores inertial effects; thus the motion is only correct as an approximation for very viscous problems. However, the steady states are true equilibrium solutions. Inertial forces will… (More)
We develop a fast method to localize the level set method of Osher and Sethian (1988, J. Comput. Phys. 79, 12) and address two important issues that are intrinsic to the level set method: (a) how to extend a quantity that is given only on the interface to a neighborhood of the interface; (b) how to reset the level set function to be a signed distance… (More)
We present a level set based numerical algorithm for simulating a model of epitaxial growth. The island dynamics model is a continuum model for the growth of thin films. In this paper, we emphasize the details of the numerical method used to simulate the island dynamics model.
PURPOSE To introduce a novel, digital, three-dimensional (3D) reconstruction of the optic nerve head (ONH) and to use this method to evaluate the 3D configuration of the lamina cribrosa (LC) in patients with primary open-angle glaucoma. METHODS Optic discs of 137 eyes of 137 patients with open-angle glaucoma were scanned with enhanced depth-imaging… (More)