Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media
Journal of Computational Physics
Solving diffusion equations with rough coefficients in rough grids
Journal of Computational Physics
A local support-operators diffusion discretization scheme for quadrilateral r-z meshes
Journal of Computational Physics
Robust convergence of multi point flux approximation on rough grids
Numerische Mathematik
Monotonicity of control volume methods
Numerische Mathematik
A Multipoint Flux Mixed Finite Element Method
SIAM Journal on Numerical Analysis
A cell-centered diffusion scheme on two-dimensional unstructured meshes
Journal of Computational Physics
Enriched multi-point flux approximation for general grids
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
An efficient cell-centered diffusion scheme for quadrilateral grids
Journal of Computational Physics
Local flux mimetic finite difference methods
Numerische Mathematik
A cell functional minimization scheme for parabolic problem
Journal of Computational Physics
The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes
Journal of Computational Physics
A nine-point scheme with explicit weights for diffusion equations on distorted meshes
Applied Numerical Mathematics
SIAM Journal on Scientific Computing
An improved monotone finite volume scheme for diffusion equation on polygonal meshes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
In this paper, we employ the so-called linearity preserving method, which requires that a difference scheme should be exact on linear solutions, to derive a nine-point difference scheme for the numerical solution of diffusion equation on the structured quadrilateral meshes. This scheme uses firstly both cell-centered unknowns and vertex unknowns, and then the vertex unknowns are treated as a linear combination of the surrounding cell-centered unknowns, which reduces the scheme to a cell-centered one. The weights in the linear combination are derived through the linearity preserving approach and can be obtained by solving a local linear system whose solvability is rigorously discussed. Moreover, the relations between our linearity preserving scheme and some existing schemes are also discussed, by which a generalized multipoint flux approximation scheme based on the linearity preserving criterion is suggested. Numerical experiments show that the linearity preserving schemes in this paper have nearly second order accuracy on many highly skewed and highly distorted structured quadrilateral meshes.