A Finite Volume Scheme for Three-Dimensional Diffusion Equations (Communications in Computational Physics, 2018)
The extension of diamond scheme for diffusion equation to three dimensionsis presented. The discrete normal flux is constructed by a linear combination ofthe directional flux along the line connecting cell-centers and the tangent flux along thecell-faces. In addition, it treats material discontinuities by a new iterative method. Thestability and first-order convergence of the method are proved on distorted meshes. Thenumerical results illustrate that the method appears to be approximate second-orderaccuracy for solution.