Oevermann, M. and Klein, R.
(2006)
*A cartesian grid finite volume method for the solution of the Poisson equation with variable coefficients and embedded interfaces.*
JCP
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## Abstract

We present a finite volume method for the solution of the two-dimensional Poisson equation r· ((x)ru(x)) = f(x) with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz function on Cartesian grids for the solution u(x) resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. The method achieves second order of accuracy in the L1 and L2 norm.

Item Type: | Article |
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Uncontrolled Keywords: | Poisson equation, finite volume methods, embedded interface, variable and discontinuous coefficients, discontinuous solution |

Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group |

ID Code: | 504 |

Deposited By: | Ulrike Eickers |

Deposited On: | 01 Jul 2009 13:03 |

Last Modified: | 01 Jul 2009 13:03 |

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