R. Hansen et Ms. Espedal, ON THE NUMERICAL-SOLUTION OF NONLINEAR RESERVOIR FLOW MODELS WITH GRAVITY, International journal for numerical methods in engineering, 38(12), 1995, pp. 2017-2032
Based on a two-phase fluid model for immiscible displacement in a poro
us medium, we develop and analyse numerical solution techniques for ce
rtain non-linear phenomena. Two different solution strategies for the
treatment of gravity effects, which are non-trivial to model by existi
ng solution techniques and may be of great influence in many practical
flow situations, are presented. The solution procedures are based on
an operator-splitting technique, combining the modified method of char
acteristics with finite element techniques and adaptive grid refinemen
t.