Reactive transport simulations using a global approach

In many environmental applications, transport of solutes is coupled with chemical reactions, either kinetic or at equilibrium. These reactions involve not only solutes, but also sorbed species and minerals. The mathematical model is a coupled set of nonlinear partial algebraic differential equations. A classical approach is to discretize first in space then in time.Since the problem is rather stiff, explicit time discretization suffers from a drastic CFL-like condition. On the other hand, implicit schemes allow large timesteps during some periods of simulation. Implicit Euler scheme is often used for monotonicity properties. At each timestep, a set of nonlinear algebraic equations must be solved. The Jacobian is computed from the transport operator and the chemical operators. In order to reduce the size of the nonlinear system, unknowns can be eliminated by a substitution approach. Moreover, conservative variables can be decoupled from others. Adaptive mesh refinement, adaptive timestep and adaptive Jacobian updates are also very efficient to reduce the computational time. Finally, computations can combine parallelism through the equations and through the chemical species. We have implemented such a global approach in the software GRT3D. This talk will present the numerical model, the software and some numerical experiments.