Chemistry-Transport coupling : Implicit schemes keeping a code coupling approach

Abstract

This work is linked with the field of reactive transport simulations in the context of reactive waste storage in deep geological disposals. Indeed, the evolution of the different materials and the species migration are deeply influenced by chemical, hydraulic and transport interactions. For these modeling issues it is necessary to deal with numerical codes involving combined effect of transport and multiple geochemical species within groundwater flow. Currently, many of the codes use a sequential iterative or non-iterative approach based on an operator-splitting technique between the chemistry and transport parts. One main advantage of this approach is the use of two different codes: one for the transport and one for the chemistry. More recently, some codes have developed a full implicit coupled approach dealing with chemistry and transport equations in one global resolution. These types of algorithms are more robust than the sequential ones but do not allow the use of existing geochemical codes. In this work we present the development and application of two implicit schemes keeping a code coupling approach: Newton and Nonlinear Conjugate Gradient methods. In the former method, the computation of the full Jacobian matrix is required while in the latter one, a derivation along the descent direction is used. A derivation of the chemistry operator is computed numerically by finite differences. The advantage of the Nonlinear Conjugate Gradient method in comparison with the classical Newton-Krylov algorithm is that we have only one loop of iterations and the original feature of the implementation is the use of an explicit formula for the descent parameter. Different preconditioning methods are tested. We present some comparisons of these methods in one and two space dimensions. This work is part of the Alliances project the aim of which is to produce a software platform for the simulation of nuclear waste repository storage and disposal. Alliances is jointly developing by CEA (French Atomic Energy Commission), ANDRA(French Nuclear Waste Management Agency) and EDF (French Electricity Producer).