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• W1920565795 abstract "We present a fast and accurate algorithm for the Poisson equation in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson equations with interfaces across which the solution is discontinuous (of the type arising in multi-fluid flows). The algorithm is based on a combination of the Correction Function Method (CFM) and Boundary Integral Methods (BIM). Interface and boundary conditions can be treated in a fast and accurate manner using boundary integral equations, and the associated BIM. Unfortunately, BIM can be costly when the solution is needed everywhere in a grid, e.g. fluid flow problems. We use the CFM to circumvent this issue. The solution from the BIM is used to rewrite the problem as a series of Poisson equations in rectangular domains --- which requires the BIM solution at interfaces/boundaries only. These Poisson equations involve discontinuities at interfaces, of the type that the CFM can handle. Hence we use the CFM to solve them (to high order of accuracy) with finite differences and a Fast Fourier Transform based fast Poisson solver. We present 2D examples of the algorithm applied to problems involving boundary conditions over complex geometries (with 4th order accuracy), and to a Poisson equation with interfaces across which the solution is discontinuous (with 3rd order accuracy)." @default.
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• W1920565795 date "2014-01-31" @default.
• W1920565795 modified "2023-09-24" @default.
• W1920565795 title "Fast and accurate solution of the Poisson equation in an immersed setting" @default.
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