Faster and just as good: the motto of adaptive methods

In the field of numerical simulation, a sufficiently accurate representation of the data associated with physical models requires, in general, a very large numerical grid that, despite existing computing power, results in excessively long calculation times.

For example, geological models, which cover extensive geographic zones, require a fine grid that can contain hundreds of millions of grid cells. Moreover, they require several additional calculations for the calibration^a of reservoir properties^b from experimental data. Therefore, the process chain that follows for a single simulation can render the calculation time exorbitant.

To overcome this problem, IFPEN develops and implements acceleration strategies. Adaptive mesh refinement is a judicious solution both in terms of saving memory resources and reducing calculation times, while maintaining results of a satisfactory quality. For this, a “fine” resolution approach is reserved for the zones where such accuracy is required and a “coarse” approach is used elsewhere. The success of such a strategy is inextricably linked to the tool used to decide which zones require a fine approach and which do not (figure).

 

In this respect, a posteriori error estimates ^(1,2), specifically developed in recent years by IFPEN, represent an extremely efficient tool for adaptive mesh refinement algorithms.

This efficiency can be explained by the mathematical rigor of the methods used, in contrast with other more heuristic tools. In addition, they have led to the formulation of stopping criteria for linear/non-linear solvers, leading to significant CPU time savings, without impacting the precision of results.
 

^{a - Adjustment process using uncertainty analysis and optimization tools.
b - Porosities, permeabilities, fluid viscosities, capillary pressures, etc.}
 

⁽¹⁾ J.-M. Gratien, O. Ricois, S. Yousef, Oil Gas Sci. Technol (2016), 71, 59.
    DOI : 10.2516/ogst/2016009

⁽²⁾ M. Vohralík and S. Yousef. Comput. Methods Appl. Mech. Engrg. 331 (2018), 728–760.
    DOI : 10.1016/j.cma.2017.11.027
 

Scientific contact: Soleiman YOUSEF

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