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 quasi-positive family of continuous Darcy-flux finite-volume schemes with full pressure support
Journal of Computational Physics
Journal of Computational Physics
Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes
Journal of Computational Physics
Non-negative mixed finite element formulations for a tensorial diffusion equation
Journal of Computational Physics
Journal of Computational Physics
Linearity preserving nine-point schemes for diffusion equation on distorted quadrilateral meshes
Journal of Computational Physics
A monotone finite volume method for advection-diffusion equations on unstructured polygonal meshes
Journal of Computational Physics
The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes
Journal of Computational Physics
Journal of Computational Physics
A fast semi-implicit method for anisotropic diffusion
Journal of Computational Physics
Construction and Convergence Study of Schemes Preserving the Elliptic Local Maximum Principle
SIAM Journal on Numerical Analysis
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
Mimetic finite difference method
Journal of Computational Physics
Hi-index | 0.08 |
Robustness of numerical methods for multiphase flow problems in porous media is important for development of methods to be used in a wide range of applications. Here, we discuss monotonicity for a simplified problem of single-phase flow, but where the simulation grids and media are allowed to be general, posing challenges to control-volume methods. We discuss discrete formulations of the maximum principle and derive sufficient criteria for discrete monotonicity for arbitrary nine-point control-volume discretizations for conforming quadrilateral grids in 2D. These criteria are less restrictive than the M-matrix property. It is shown that it is impossible to construct nine-point methods which unconditionally satisfy the monotonicity criteria when the discretization satisfies local conservation and exact reproduction of linear potential fields. Numerical examples are presented which show the validity of the criteria for monotonicity. Further, the impact of nonmonotonicity is studied. Different behavior for different discretization methods is illuminated, and simple ideas are presented for improvement in terms of monotonicity.