IMPES and Fully Implicit
Two Ways to Step Forward
A simulator advances in time by one of two schemes. IMPES (implicit pressure, explicit saturation) solves the pressure field implicitly each step but updates saturation with an explicit formula, so each step is cheap.
The Explicit Limit
The explicit saturation update is stable only below a timestep limit, the CFL condition, so a large step must be chopped into many small ones. IMPES therefore floors out: it cannot run cheaper than the CFL-limited step count.
Fully Implicit
Fully implicit solves pressure and saturation together by Newton iteration. Each step costs several linear solves, but it is stable at any size. Beyond the crossover, taking big implicit steps beats running many small explicit ones, which is why field-scale runs are usually fully implicit.