A control volume finite element approach to NAPL groundwater contamination
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
On locking and robustness in the finite element method
SIAM Journal on Numerical Analysis
Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media
Journal of Computational Physics
Finite Element Approximation of the Diffusion Operator on Tetrahedra
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Metric tensors for anisotropic mesh generation
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
Preserving monotonicity in anisotropic diffusion
Journal of Computational Physics
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
Journal of Computational Physics
Journal of Computational Physics
Bad behavior of Godunov mixed methods for strongly anisotropic advection-dispersion equations
Journal of Computational Physics
Hi-index | 31.45 |
Anisotropic problems arise in various areas of science and engineering, for example groundwater transport and petroleum reservoir simulations. The pure diffusive anisotropic time-dependent transport problem is solved on a finite number of nodes, that are selected inside and on the boundary of the given domain, along with possible internal boundaries connecting some of the nodes. An unstructured triangular mesh, that attains the Generalized Anisotropic Delaunay condition for all the triangle sides, is automatically generated by properly connecting all the nodes, starting from an arbitrary initial one. The control volume of each node is the closed polygon given by the union of the midpoint of each side with the ''anisotropic'' circumcentre of each final triangle. A structure of the flux across the control volume sides similar to the standard Galerkin Finite Element scheme is derived. A special treatment of the flux computation, mainly based on edge swaps of the initial mesh triangles, is proposed in order to obtain a stiffness M-matrix system that guarantees the monotonicity of the solution. The proposed scheme is tested using several literature tests and the results are compared with analytical solutions, as well as with the results of other algorithms, in terms of convergence order. Computational costs are also investigated.