Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Transitional waves for conservation laws
SIAM Journal on Mathematical Analysis
Fully Discrete Finite Element Analysis of Multiphase Flow in Groundwater Hydrology
SIAM Journal on Numerical Analysis
Corrected Operator Splitting for Nonlinear Parabolic Equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Fundamentals of Numerical Reservoir Simulation
Fundamentals of Numerical Reservoir Simulation
The sequential method for the black-oil reservoir simulation on unstructured grids
Journal of Computational Physics
Three-phase immiscible displacement in heterogeneous petroleum reservoirs
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
Hi-index | 0.00 |
We describe an efficient numerical simulator, based on an operator splitting technique, for three-phase flow in heterogeneous porous media that takes into account capillary forces, general relations for the relative permeability functions and variable porosity and permeability fields. Our numerical procedure combines a non-oscillatory, second order, conservative central difference scheme for the system of hyperbolic conservation laws modeling the convective transport of the fluid phases with locally conservative mixed finite elements for the approximation of the parabolic and elliptic problems associated with the diffusive transport of fluid phases and the pressure-velocity calculation. This numerical procedure has been used to investigate the existence and stability of nonclassical waves (also called transitional or undercompressive waves) in heterogeneous two-dimensional flows, thereby extending previous results for one-dimensional problems.