Journal of Computational Physics
The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Monotonicity of control volume methods
Numerische Mathematik
A Multipoint Flux Mixed Finite Element Method
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A quasi-positive family of continuous Darcy-flux finite-volume schemes with full pressure support
Journal of Computational Physics
Pores resolving simulation of Darcy flows
Journal of Computational Physics
A cell functional minimization scheme for parabolic problem
Journal of Computational Physics
SIAM Journal on Scientific Computing
Monotonic solution of heterogeneous anisotropic diffusion problems
Journal of Computational Physics
Hi-index | 31.47 |
This paper focuses on flux-continuous pressure equation approximation for strongly anisotropic media. Previous work on families of flux-continuous schemes for solving the general geometry-permeability tensor pressure equation has focused on single-parameter families. These schemes have been shown to remove the O(1) errors introduced by standard two-point flux reservoir simulation schemes when applied to full-tensor flow approximation. Improved convergence of the schemes has also been established for specific quadrature points. However these schemes have conditional M-matrices depending on the strength of the off-diagonal tensor coefficients. When applied to cases involving full-tensors arising from strongly anisotropic media, the point-wise continuous schemes can fail to satisfy the maximum principle and induce severe spurious oscillations in the numerical pressure solution. New double-family flux-continuous locally conservative schemes are presented for the general geometry-permeability tensor pressure equation. The new double-family formulation is shown to expand on the current single-parameter range of existing conditional M-matrix schemes. The conditional M-matrix bounds on a double-family formulation are identified for both quadrilateral and triangle cell grids. A quasi-positive QM-matrix analysis is presented that classifies the behaviour of the new schemes with respect to double-family quadrature in regions beyond the M-matrix bounds. The extension to double-family quadrature is shown to be beneficial, resulting in novel optimal anisotropic quadrature schemes. The new methods are applied to strongly anisotropic full-tensor field problems and yield results with sharp resolution, with only minor or practically zero spurious oscillations.