Adaptive mesh generation for viscous flows using delaunay triangulation
Journal of Computational Physics
A control volume finite element approach to NAPL groundwater contamination
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
Journal of Computational Physics
Journal of Computational Physics
Construction of three-dimensional improved-quality triangulations using local transformations
SIAM Journal on Scientific Computing
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
The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
Journal of Computational Physics
Delaunay mesh generation governed by metric specifications. Part I algorithms
Finite Elements in Analysis and Design
Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry
SIAM Journal on Scientific Computing
Finite Element Approximation of the Diffusion Operator on Tetrahedra
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Dihedral bounds for mesh generation in high dimensions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
A monotone finite element scheme for convection-diffusion equations
Mathematics of Computation
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Modification of A Finite Volume Scheme for Laplace's Equation
SIAM Journal on Scientific Computing
Discretization on quadrilateral grids with improved monotonicity properties
Journal of Computational Physics
Metric tensors for anisotropic mesh generation
Journal of Computational Physics
A quasi-positive family of continuous Darcy-flux finite-volume schemes with full pressure support
Journal of Computational Physics
Numerical Analysis and Its Applications
Non-negative mixed finite element formulations for a tensorial diffusion equation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
Monotonic solution of heterogeneous anisotropic diffusion problems
Journal of Computational Physics
Hi-index | 31.48 |
Multipoint flux approximation (MPFA) techniques are commonly applied for discretizing the porous media flow equations within the context of finite volume numerical procedures. Although these methods can be applied to heterogeneous, anisotropic systems on generally unstructured grids, the inverse of the resulting linear operator can suffer from a loss of monotonicity at high permeability anisotropy ratios, resulting in spurious oscillations of the pressure solution. The purpose of this paper is to develop a method for optimizing unstructured grids in two and three dimensions such that the monotonicity behavior of the MPFA technique is significantly improved. The method employs anisotropic triangulation and can be readily combined with permeability upscaling procedures. Results are presented for a variety of examples and the technique is shown to perform well on problems involving complex grid point distributions and heterogeneous permeability fields with strong anisotropy ratios (of O(100)). Oscillation free pressure solutions are achieved in all cases considered, even for examples in which the original grid shows large oscillations.