n this paper the iterative MSFV method is extended to include the
sequential implicit simulation of time dependent problems involving
the solution of a system of pressure-saturation equations. To control
numerical errors in simulation results, an error
estimate, based on the residual of the MSFV approximate pressure field,
is introduced. In the initial time steps in simulation iterations
are employed until a specified accuracy in pressure is achieved.
This initial solution is then used to improve the localization assumption
at later time steps. Additional iterations in pressure solution are
employed only when the pressure residual becomes larger than a specified
threshold value. Efficiency of the strategy and the error control
criteria are numerically investigated. This paper also shows that
it is possible to derive an a-priori estimate and control based on
the allowed pressure-equation residual to guarantee the desired accuracy
in saturation calculation.