10.4122/1.1000000488
Fahs, Marwan
Marwan
Fahs
fahs@imfs.u-strasbg.fr
Carrayrou, Jérôme
Jérôme
Carrayrou
carrayro@imfs.u-strasbg.fr
Younes, Anis
Anis
Younes
younes@imfs.u-strasbg.fr
Philippe, Ackerer
Ackerer
Philippe
ackerer@imfs.u-strasbg.fr
Fahs, Marwan
Marwan
Fahs
fahs@imfs.u-strasbg.fr
Comparison between global and operator splitting approaches for modeling multicomponent reactive transport in porous media
XVI International Conference on Computational Methods in Water Resources
2006
2006
Multicomponent reactive transport with chemical equilibrium reactions, involving
advective and dispersive solute transport coupled with the nonlinear reaction, is
fundamental feature of subsurface environments. At the equilibrium, the governing
system of equations is formed by the partial differential equations (PDEs) of the
transport operator and the nonlinear algebraic equations (AEs) describing the
chemical reactions. These two sets of equations are coupled and needed to be solved
using the operator splitting (OS) approach or the global approach.
With (OS), the transport and reaction equations are separated and solved
sequentially for each time step. The OS includes the Sequential non-iterative
approach (SNIA) and the Sequential iterative approach (SIA), which iterates between
transport and chemistry until convergence for each time step.
With the global approach, the governing equations of transport and reaction are
solved simultaneously. We distinguish two methods in the global approach. (i) The
Differential Algebraic Equations Approach (DAE) solves a large system formed by both
transport and chemistry equations (Miller, 1983). (ii) The direct substitution
approach (DSA) solves a reduced system obtained after substituting the chemistry
algebraic equations in the transport partial differential equations (Shen and
Nikolaidis, 1997; Jenning et al., 1982).
Since the reference work of Yeh and Tripathi (1989), the (OS) approach is widely
used to simulate reactive transport problems since it allows different numerical
methods to be used for the reactive and transport components. However, the (OS)
approach can introduce operator-splitting errors which are avoided with the global
approach.
In this work, we show that DSA and DAE have the same numerical behavior. For a fine
discretization and/or for a large number of chemical species, DSA is shown to be
more efficient then DAE.
Both DSA and SIA give accurate results. Contrarily to DSA, SIA solves sequentially
two small systems (transport and chemistry). It was shown in Saaltink (2001) that
DSA runs faster than SIA in chemically difficult cases and the SIA may become faster
than the DSA for very large, chemically simple problems. In this work, we combine
DSA with a very efficient linear solver UMFPACK. Our numerical experiments suggest
that for all cases, DSA is shown to be more efficient than SIA. DSA requires less
iteration to reach the convergence and allows large time steps contrarily to SIA.
Comparisons between DSA and SNIA show that SNIA spends less CPU time than DSA.
However OS errors introduced with SNIA are proportional to the time step size and
can therefore be significant. When SNIA is combined with an adaptative time stepping
procedure based on a posteriori control error, DSA can be more efficient then SNIA.