Empirical versus time stepping with embedded error control for density‐driven flow in porous media

Abstract

Modeling density‐driven flow in porous media may require very long computational time due to the nonlinear coupling between flow and transport equations. Time stepping schemes are often used to adapt the time step size in order to reduce the computational cost of the simulation. In this work, the empirical time stepping scheme which adapts the time step size according to the performance of the iterative nonlinear solver is compared to an adaptive time stepping scheme where the time step length is controlled by the temporal truncation error. Results of the simulations of the Elder problem show that (1) the empirical time stepping scheme can lead to inaccurate results even with a small convergence criterion, (2) accurate results are obtained when the time step size selection is based on the truncation error control, (3) a non iterative scheme with proper time step management can be faster and leads to more accurate solution than the standard iterative procedure with the empirical time stepping and (4) the temporal truncation error can have a significant effect on the results and can be considered as one of the reasons for the differences observed in the Elder numerical results.