Two-dimensional exponential fitting and applications to drift-diffusion models
SIAM Journal on Numerical Analysis
Monotonicity Considerations for Saturated--Unsaturated Subsurface Flow
SIAM Journal on Scientific Computing
Finite Element Approximation of the Diffusion Operator on Tetrahedra
SIAM Journal on Scientific Computing
The continuous Galerkin method is locally conservative
Journal of Computational Physics
SIAM Journal on Numerical Analysis
ADER schemes on adaptive triangular meshes for scalar conservation laws
Journal of Computational Physics
Journal of Computational Physics
| Hi-index | 31.46 |
A novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium. The computational domain is descretized using triangular meshes and the governing PDEs are discretized using a lumped in the edge centres numerical technique. The dependent unknown variable of the problem is the piezometric head. A fractional time step methodology is applied for the solution of the original system, solving consecutively a prediction and a correction problem. A scalar potential of the flow field exists and in the prediction step a MArching in Space and Time (MAST) formulation is applied for the sequential solution of the Ordinary Differential Equation of the cells, ordered according to their potential value computed at the beginning of the time step. In the correction step, the solution of a large linear system with order equal to the number of edges is required. A semi-analytical procedure is also proposed for the solution of the prediction step. The computational performance, the order of convergence and the mass balance error have been estimated in several tests and compared with the results of other literature models.