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A COMPARISON BETWEEN SEQUENTIAL ITERATIVE AND GLOBAL METHODS

A COMPARISON BETWEEN SEQUENTIAL ITERATIVE AND GLOBAL METHODS FOR A REACTIVE TRANSPORT NUMERICAL MODEL. J. Erhel INRIA - RENNES - FRANCE SIAM conference on Geosciences AVIGNON - June 2005. Geochemistry and transport models Numerical methods standard iterative method

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A COMPARISON BETWEEN SEQUENTIAL ITERATIVE AND GLOBAL METHODS

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  1. A COMPARISON BETWEEN SEQUENTIAL ITERATIVE AND GLOBAL METHODS FOR A REACTIVE TRANSPORT NUMERICAL MODEL J. Erhel INRIA - RENNES - FRANCE SIAM conference on Geosciences AVIGNON - June 2005

  2. Geochemistry and transport models Numerical methods standard iterative method global method Results and comparison Outline

  3. Secondary species and chemical components Aqueous and fixed species No precipitation in a first step Action laws involving stoechiometric matrices Mass conservation laws Geochemistry modelequilibrium chemistry model

  4. Convection dispersion Transport model Convection Dispersion Transport model for each component Initial condition Boundary conditions

  5. Coupled reactive transport model System of Differential Algebraic Equations

  6. Numerical discretization Cell-centered finite volume scheme for mass local conservation Implicit time scheme because of stiffness Set of nonlinear equations at each time step

  7. Sequential iterative method Time step n NONINEAR TRANSPORT F T NONLINEAR CHEMISTRY Time step n + 1 Euler implicit time scheme Nonlinear Gauss-Seidel iterative method Global Newton method for chemistry

  8. Global method Time step n LINEARIZED TRANSPORT T,c,s or C,F,c,s LINEARIZED CHEMISTRY Time step n + 1

  9. User-defined function and Jacobian Variable time step and order Newton nonlinear method Sparse direct linear solver In Matlab, function ode15s modified to use UMFPACK Global method with DAE solver

  10. Test cases Ion exchange Pyrite 4 components, 39 aqueous species and 13 fixed species. Somehow artificial with no precipitation.

  11. Chemistry solver Ion exchange Global Newton method

  12. Ion exchange Sequential iterative method 1 Newton iteration 30 Newton iterations

  13. Pyrite Sequential iterative method

  14. Pyrite Sequential iterative method

  15. Ion exchange Global method

  16. Pyrite – comparison between both methods Global method Sequential iterative method

  17. Pyrite – comparison of CPU time

  18. In our tests, the global method is faster and more robust than the sequential iterative method. However, the direct linear solver requires to couple transport and chemistry model and is memory consuming. We plan to do more experiments and to design an iterative linear solver which can decouple both models. Conclusion

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