Development of numerical methods for the reactive transport of chemical species in a porous media : a nonlinear conjugate gradient method

摘要

In the framework of the evaluation of nuclear waste disposal safety, the French Atomic Energy Commission (CEA) is interested in modelling the reactive transport in porous media. At a given time step, the equation system of reactive-transport can be written as a system of nonlinear coupled equations F(x) = 0. In the computational code which is presently used, this system is solved using classical sequential iterative algorithms (SIA). We are currently investigating nonlinear conjugate gradient methods to improve the resolution of the system. Indeed, the handling of the coupling is improved by numerical derivation along the descent direction. The original feature of this method is the use of an explicit formula for the descent parameter. We choose an approach involving two distinct codes, that is one code for the chemistry and one code for the transport equations.