The Finite Volume Formulation for 2D Second-Order Elliptic Problems with Discontinuous Diffusion/Dispersion Coefficients

Stefano Ferraris; Ivan Bevilacqua; Davide Canone; Davide Pognant; Maurizio Previati

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The Finite Volume Formulation for 2D Second-Order Elliptic Problems with Discontinuous Diffusion/Dispersion Coefficients

机译：具有不连续扩散/扩散系数的二维二阶椭圆问题的有限体积公式

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摘要

We propose a finite volume method for the numerical resolution of two-dimensional steady diffusion problems with possibly discontinuous coefficients on unstructured polygonal meshes. Our numerical method is cellcentered, secondorder accurate on smooth solutions and based on a special numerical treatment of the diffusion/dispersion coefficients that makes its application possible also when such coefficients are discontinuous. Numerical experiments confirm the convergence of the numerical approximation and show a good behavior on a set of benchmark problems in two space dimensions.

机译：对于非结构化多边形网格上可能具有不连续系数的二维稳态扩散问题，我们提出了一种有限体积方法。我们的数值方法是基于中心点的，在光滑解上是二阶精度的，并且基于对扩散/弥散系数的特殊数值处理，这使得在系数不连续时也可以应用。数值实验证实了数值逼近的收敛性，并在二维空间的一系列基准问题上表现出良好的行为。

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《Mathematical Problems in Engineering》 |2012年第4期|p.187634.1-187634.23|共23页
作者
Stefano Ferraris; Ivan Bevilacqua; Davide Canone; Davide Pognant; Maurizio Previati;
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Dipartimcnto di Economia e Ingcgneria Agraria, Forestale e Ambientnle (DEIAFA) Sez, Idrautlica, Via Leonardo da Vinci 44, 10095 Crugliasco, Italy;

Dipartimcnto di Economia e Ingcgneria Agraria, Forestale e Ambientnle (DEIAFA) Sez, Idrautlica, Via Leonardo da Vinci 44, 10095 Crugliasco, Italy;

Dipartimcnto di Economia e Ingcgneria Agraria, Forestale e Ambientnle (DEIAFA) Sez, Idrautlica, Via Leonardo da Vinci 44, 10095 Crugliasco, Italy;

Dipartimcnto di Economia e Ingcgneria Agraria, Forestale e Ambientnle (DEIAFA) Sez, Idrautlica, Via Leonardo da Vinci 44, 10095 Crugliasco, Italy;

Dipartimcnto di Economia e Ingcgneria Agraria, Forestale e Ambientnle (DEIAFA) Sez, Idrautlica, Via Leonardo da Vinci 44, 10095 Crugliasco, Italy;

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The Finite Volume Formulation for 2D Second-Order Elliptic Problems with Discontinuous Diffusion/Dispersion Coefficients

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