Internally, the solvers in FlowDict solve several equations for values of pressure and velocity at each voxel by using iterative solvers. The basic idea of an iterative method is to:

1. Start with some initial guess for the unknown values,
2. Improve the current values in each iterative step. The improvement can be fast or extremely slow depending on problem parameters,
3. Repeat the iterative process until the stopping criteria is fulfilled.

The iterative process is controlled by setting the values and activation for Error Bound, Tolerance, Maximal Iterations, and Maximal Run Time (h).

While Maximal Iterations and Maximal Run Time can be selected simultaneously with all other stopping criteria, only one of the three criteria available from the pull-down menu can be selected at once.

The default stopping criterion for the LIR FlowDict solver is Error Bound.

The Error Bound stopping criterion uses the result of previous iterations and predicts the final solution based on linear and quadratic extrapolation. The solver stops if the relative difference in regard to the prediction is smaller than the specified error bound. The stopping criterion recognizes oscillations in the convergence behavior and prevents premature stopping at local minima or maxima. A damped convergence curve is fit through the oscillating curve and the solver stops then regarding the damped convergence curve.

The Tolerance stopping criterion looks for stagnation of the method when the process becomes stationary, i.e. the improvement in the permeability value becomes extremely small from iteration to iteration.

The iteration is stopped if the relative change is smaller than the value entered for Tolerance. When there is doubt about the quality of the solution, decrease the Tolerance value by a factor of ten for that solver. The drawback of this criterion is that flow solvers sometimes stop too early in case of slow convergence rate or at local extrema of oscillatory convergence curves.

Additionally, for the Error Bound and Tolerance stopping criterion, it is possible to choose if the stopping criterion should consider the permeability only in flow direction or in both flow and tangential directions. For flow simulations where the permeability in flow direction converges much faster than the permeability in tangential directions,  it is recommended to change from Flow permeability to Flow & tangential permeability.

For the LIR solver it is recommended to use Error Bound, as this stopping criterion approximates the “relative deviation from the final solution”.

When the solver does not stop due to the stopping criterion Error Bound, Tolerance, or Residual and instead, stops because the Maximal Iterations value or the Maximal Run Time (h) has been reached, no guarantee on the quality of solution can be given.

Which stopping criterion has occurred can be seen in the result file (*.gdr).