Jérôme Carrayrou

Operator-splitting procedures for reactive transport and comparison of mass balance errors

Operator-splitting (OS) techniques are very attractive for numerical modelling of reactive transport, but they induce some errors. Considering reactive mass transport with reversible and irreversible reactions governed by a first-order rate law, we develop analytical solutions of the mass balance for the following operator-splitting schemes: standard sequential non-iterative (SNI), Strang-splitting SNI, standard sequential iterative (SI), extrapolating SI, and symmetric SI approaches. From these analytical solutions, the operator-splitting methods are compared with respect to mass balance errors and convergence rates independently of the techniques used for solving each operator. Dimensionless times, NOS, are defined. They control mass balance errors and convergence rates. The following order in terms of decreasing efficiency is proposed: symmetric SI, Strang-splitting SNI, standard SNI, extrapolating SI and standard SI schemes. The symmetric SI scheme does not induce any operator-splitting errors, the Strang-splitting SNI appears to be O(N2OS) accurate, and the other schemes are first-order accurate.

Modélisation du transport réactif en milieu poreux : schéma itératif associé à une combinaison d'éléments finis discontinus et mixtes-hybrides

The sequential iterative approach (SIA) scheme is the most efficient method for modelling reactive transport in porous media with the operator-splitting approach. A combination of finite discontinuous and finite mixed-hybrid elements is a powerful method for solving solute transport in porous media, but the use of this method for SIA scheme induces numerical difficulties. In this paper, a new method is developed to solve reactive transport by using both the SIA scheme and a combination of finite discontinuous and finite mixed elements. The proposed method is tested by modelling a column experiment. To cite this article: J. Carrayrou et al., C. R. Mecanique 331 (2003).

Comparison of linear solvers for equilibrium geochemistry computations

Equilibrium chemistry computations and reactive transport modelling require the intensive use of a linear solver under very specific conditions. The systems to be solved are small or very small (4 × 4 to 20 × 20, occasionally larger) and are very ill-conditioned (condition number up to 10100). These specific conditions have never been investigated in terms of the robustness, accuracy, and efficiency of the linear solver. In this work, we present the specificity of the linear system to be solved. Several direct and iterative solvers are compared using a panel of chemical systems, including or excluding the formation of mineral species. We show that direct and iterative solvers can be used for these problems and propose computational keys to improve the chemical solvers.