2009
DOI: 10.1007/s10596-009-9173-7
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A parallel global-implicit 2-D solver for reactive transport problems in porous media based on a reduction scheme and its application to the MoMaS benchmark problem

Abstract: In this article, an approach for the efficient numerical solution of multi-species reactive transport problems in porous media is described. The objective of this approach is to reformulate the given system of partial and ordinary differential equations (PDEs, ODEs) and algebraic equations (AEs), describing local equilibrium, in such a way that the couplings and nonlinearities are concentrated in a rather small number of equations, leading to the decoupling of some linear partial differential equations from th… Show more

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Cited by 31 publications
(26 citation statements)
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“…We check convergence in our numerical experiments and focus on specific behaviour such as numerical oscillations. This benchmark is also studied by other participants [4,16,19,22]. Our results are in good agreement with theirs.…”
Section: Introductionsupporting
confidence: 91%
“…We check convergence in our numerical experiments and focus on specific behaviour such as numerical oscillations. This benchmark is also studied by other participants [4,16,19,22]. Our results are in good agreement with theirs.…”
Section: Introductionsupporting
confidence: 91%
“…5). As presented by Hoffmann et al [11], these oscillations are dependent Figure 4 shows that a good convergence is achieved for a number of cells greater than 2,050. Nevertheless, it can be seen in Fig.…”
Section: Advective Casementioning
confidence: 55%
“…For this reason, we think that further developments about the numerical methods used for reactive transport should deal with time step and mesh adaptation. The actual way used for time step adaptation is a heuristic one [11,14]: if the iterative procedure (between transport and chemistry for sequential iterative approaches or for solving the reactive transport system for global approaches) converges father (resp. lower) than a prescribed value, the time step is increased (resp.…”
Section: Resultsmentioning
confidence: 99%
“…Application of (a) and (b) leads to a decoupling of the linear PDEs; this decoupling in combination with (c) leads to a reduction of the size of the nonlinear system (see Kräutle and Knaber [22], Hoffmann et al [19], and the references therein for details). The system of equations is handled in the spirit of a global implicit approach (one-step method) and avoids operator splitting.…”
Section: Code Of Hoffmann Et Almentioning
confidence: 99%
“…We use four test cases, from the so-called Easy test case collection of the MoMaS reactive transport benchmark. Additional simulation results for these test cases and other test cases [10] are documented in the contributions by the individual participants [6,12,19,23,26].…”
Section: Introductionmentioning
confidence: 99%