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Mathematics > Numerical Analysis

arXiv:1411.4283 (math)
[Submitted on 16 Nov 2014]

Title:A higher-order finite-volume discretization method for Poisson's equation in cut cell geometries

Authors:D. Devendran, D. T. Graves, H. Johansen
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Abstract:We present a method for generating higher-order finite volume discretizations for Poisson's equation on Cartesian cut cell grids in two and three dimensions. The discretization is in flux-divergence form, and stencils for the flux are computed by solving small weighted least-squares linear systems. Weights are the key in generating a stable discretization. We apply the method to solve Poisson's equation on a variety of geometries, and we demonstrate that the method can achieve second and fourth order accuracy in both truncation and solution error for these examples. We also show that the Laplacian operator has only stable eigenvalues for each of these examples.
Subjects: Numerical Analysis (math.NA)
MSC classes: 65N08
Cite as: arXiv:1411.4283 [math.NA]
  (or arXiv:1411.4283v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1411.4283

Submission history

From: Hans Johansen [view email]
[v1] Sun, 16 Nov 2014 17:29:44 UTC (658 KB)
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