SIAM Journal on Scientific and Statistical Computing
A local support-operators diffusion discretization scheme for quadrilateral r-z meshes
Journal of Computational Physics
A finite volume method for the approximation of diffusion operators on distorted meshes
Journal of Computational Physics
Robust convergence of multi point flux approximation on rough grids
Numerische Mathematik
Mesh locking effects in the finite volume solution of 2-D anisotropic diffusion equations
Journal of Computational Physics
Analysis of accuracy of a finite volume scheme for diffusion equations on distorted meshes
Journal of Computational Physics
A cell-centered diffusion scheme on two-dimensional unstructured meshes
Journal of Computational Physics
Monotone finite volume schemes for diffusion equations on polygonal meshes
Journal of Computational Physics
A Nine Point Scheme for the Approximation of Diffusion Operators on Distorted Quadrilateral Meshes
SIAM Journal on Scientific Computing
Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes
Journal of Computational Physics
Local flux mimetic finite difference methods
Numerische Mathematik
Construction and Convergence Study of Schemes Preserving the Elliptic Local Maximum Principle
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Hi-index | 31.45 |
A new reconstruction algorithm is developed to obtain diffusion schemes with cell-centered unknowns only. The main characteristic of the new algorithm is the flexibility of stencils when the auxiliary unknowns are reconstructed with cell-centered unknowns. The stencils are selected depending on the mesh geometry and discontinuities of diffusion coefficients. Moreover, an explicit expression is derived for interpolating the auxiliary unknowns in terms of cell-centered unknowns, and the auxiliary unknowns can be defined at any point on the edge. The algorithm is applied to construct several new diffusion schemes, whose effectiveness is illustrated by numerical experiments. For anisotropic problems with or without discontinuities, nearly second order accuracy is achieved on skewed meshes.