A Finite Volume Scheme for Three-Dimensional Diffusion Equations. (14th September 2015) - Lai, Xiang; Sheng, Zhiqiang; Yuan, Guangwei
Abstract: The extension of diamond scheme for diffusion equation to three dimensions is presented. The discrete normal flux is constructed by a linear combination of the directional flux along the line connecting cell-centers and the tangent flux along the cell-faces. In addition, it treats material discontinuities by a new iterative method. The stability and first-order convergence of the method is proved on distorted meshes. The numerical results illustrate that the method appears to be approximate second-order accuracy for solution.