The equations are solved by an iterative approach.
Iterative Solver
The basic idea of an iterative method is to
Start with some initial guess for the unknown values
Improve the current values in each iterative step
Repeat the iterative process until one of the stopping criteria is reached.
The iterative process is controlled by setting the values and activation for Enter value, Maximal Iterations, and Maximal Run Time (h). The stopping criteria apply for each computational direction individually.
If multiple stopping criteria are selected, the first criterion that is reached causes the solver to stop.
The stopping criterion that has been reached can be viewed in the Result Viewer of the GeoDict result file (*.gdr) under the Results Report tab.
The default stopping criterion of the LIREnter valuesolver, Error Bound, uses the result of previous iterations, and predicts the final solution based on linear and quadratic extrapolation. The solver stops if the relative difference between computed and predicted solution 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.
If the Krylov method (under LIR - Advanced Options) is activated, Enter valuethe definition of Error Bound is somewhat different. Here, no prediction is made, instead the continuity between neighboring cells and the conservation of mass is checked. The maximal value is normalized by the mean flow and if this value is smaller than the Error Bound the simulation stops.
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.
The Tolerance stopping criterion, the default stopping criterion for EJ, 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.
In each iteration, the solver checks for the current computed value against the values of the last 100 iterations if there are any changes.
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The computation is stopped if the maximal 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. The drawback of this criterion is that the solver sometimes might stop too early in case of slow convergence rate or at local extrema of oscillatory convergence curves.
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.
When the Residual stopping criterion is used, the iteration is stopped if the solution satisfies the equation up to the required accuracy.
By setting the stopping criterion to Residual, the computations terminate as soon as the relative norm drops below the selected residual threshold. The relative norm of the Schur Complement residual is computed and displayed in the console window during the calculations. The console is visible by clicking the double arrow button on the lower right corner in the progress dialog.
The recommendation to choose Tolerance or Residual for the EJ solver is based on the structure’s porosity. Both give similar results for highly porous structures. For dense structures, if using the Schur Complement Residual, the relative norm of the residual may be small even though the correct permeability has not been reached. So, when in doubt, use the Tolerance criteria – the default option.
Use the Maximum Iterations value or the Maximum Run Time (h) stopping criteria causes the solver to stop if the maximal number of iterations and/or the maximal run time (in hours) is exceeded.
When the solver stops because one of these criteria has been reached, no guarantee on the quality of solution can be given. In this case, a warning is printed into the report. The following possibilities might help:
Check the corresponding .log file to see how large the residual values and permeability values are. If permeability values are in reasonable range and they do not have changed during the last iterations, you may decide to use the current result.
Double-check the structure and parameter values. Unphysical parameters or too rough resolution of the structure (leading, e.g., to artificial unconnected components) can cause an iterative solver to fail.
Know how! We recommend to use the Error Bound criterion for the LIR and SimpleFFT solver. This stopping criterion approximates the “relative deviation from the final solution”.
Error Bound (LIR and SimpleFFT)