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Solving Partial Differential Algebraic Equations and Reactive Transport Models

Jocelyne Erhel 1 Souhila Sabit 1 Caroline de Dieuleveult 2 
1 SAGE - Simulations and Algorithms on Grids for Environment
Inria Rennes – Bretagne Atlantique , IRISA-D1 - SYSTÈMES LARGE ÉCHELLE
Abstract : In some scientific applications, such as groundwater studies, several processes are represented by coupled models. For example, a density-driven flow model couples the flow equations with the transport of salt. A reactive transport model couples transport equations of pollutants with chemical equations. The coupled model can combine partial differential equations with algebraic equations, in a so-called PDAE system, which is in general nonlinear. A classical approach is to follow a method of lines, where space is first discretized, leading to a semi-discrete differential algebraic system (DAE). Then time is discretized by a scheme tuned for DAE, such that each time step requires solving a nonlinear system of equations. In some decoupled approaches, a fixed-point technique is used. However, a Newton method converges faster in general and is more efficient, even though each iteration is more CPU-intensive. In this talk, we deal with reactive transport models and show how a Newton method can be used efficiently. Numerical experiments illustrate the efficiency of a substitution technique. Moreover, it appears that using logarithms in the chemistry equations lead to ill conditioned matrices and increase the computational cost.
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Submitted on : Tuesday, May 28, 2013 - 10:15:04 AM
Last modification on : Thursday, January 20, 2022 - 4:16:16 PM


  • HAL Id : hal-00826660, version 1


Jocelyne Erhel, Souhila Sabit, Caroline de Dieuleveult. Solving Partial Differential Algebraic Equations and Reactive Transport Models. The Third International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, May 2013, PECS, Hungary. ⟨hal-00826660⟩



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