## Numerical Solution Of Reservoir Flow Models Based On Large Time Step Operator Splitting Algorithms (1999)

Venue: | FILTRATION IN POROUS MEDIA AND INDUSTRIAL APPLICATIONS, LECTURE NOTES IN MATHEMATICS |

Citations: | 25 - 14 self |

### BibTeX

@INPROCEEDINGS{Espedal99numericalsolution,

author = {Magne S. Espedal and Kenneth Hvistendahl Karlsen},

title = {Numerical Solution Of Reservoir Flow Models Based On Large Time Step Operator Splitting Algorithms},

booktitle = {FILTRATION IN POROUS MEDIA AND INDUSTRIAL APPLICATIONS, LECTURE NOTES IN MATHEMATICS},

year = {1999},

pages = {9--77},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

During recent years the authors and collaborators have been involved in an activity related to the construction and analysis of large time step operator splitting algorithms for the numerical simulation of multi-phase flow in heterogeneous porous media. The purpose of these lecture notes is to review some of this activity. We illustrate the main ideas behind these novel operator splitting algorithms for a basic two-phase flow model. Special focus is posed on the numerical solution algorithms for the saturation equation, which is a convection dominated, degenerate convection-diffusion equation. Both theory and applications are discussed. The general background for the reservoir flow model is reviewed, and the main features of the numerical algorithms are presented. The basic mathematical results supporting the numerical algorithms are also given. In addition, we present some results from the BV solution theory for quasilinear degenerate parabolic equations, which provides the correct ...