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Parallel Simulations of Underground Flow in Porous and Fractured Media

Parallel Simulations of Underground Flow in Porous and Fractured Media. H. Mustapha 1,2 , A. Beaudoin 1 , J. Erhel 1 and J.R. De Dreuzy 2. 1 - IRISA – INRIA de Rennes 2 - Géosciences de Rennes. Parallel Simulations of Underground Flow in Porous and Fractured Media. Outline.

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Parallel Simulations of Underground Flow in Porous and Fractured Media

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  1. Parallel Simulations of Underground Flow in Porous and Fractured Media H. Mustapha1,2, A. Beaudoin1, J. Erhel1 and J.R. De Dreuzy2 1 - IRISA – INRIA de Rennes 2 - Géosciences de Rennes

  2. Parallel Simulations of Underground Flow in Porous and Fractured Media Outline • Problem presentation • Geometrical and flow fluid model • Numerical method and parallel matrix generation • Parallel linear solver • Direct solver - PSPASES • Iterative solver – HYPRE • Results and performances • Tests and architecture • Complexity and scalability analysis with PSPASES • Comparison between PSPASES and HYPRE • Conclusions and future work H. Mustapha INRIA, Parco sept 2005

  3. Parallel Simulations of Underground Flow in Porous and Fractured Media Outline • Problem presentation • Geometrical and flow fluid model • Numerical method and parallel matrix generation • Parallel linear solver • Direct solver - PSPASES • Iterative solver – HYPRE • Results and performances • Tests and architecture • Complexity and scalability analysis with PSPASES • Comparison between PSPASES and HYPRE • Conclusions and future work H. Mustapha INRIA, Parco sept 2005

  4. Parallel Simulations of Underground Flow in Porous and Fractured Media Geometrical model 2D porous media 3D fracture network Heterogeneous hydraulic conductivity field Discrete fracture network H. Mustapha INRIA, Parco sept 2005

  5. Equations Q = - K*grad (h) div (Q) = 0 Fixed head Nul flux Parallel Simulations of Underground Flow in Porous and Fractured Media Flow fluid model • Boundary conditions 2D porous media 3D fracture network Nul flux Fixed head Fixed head Nul flux H. Mustapha INRIA, Parco sept 2005

  6. Parallel Simulations of Underground Flow in Porous and Fractured Media Outline • Problem presentation • Geometrical and flow fluid model • Numerical method and parallel matrix generation • Parallel linear solver • direct solver – PSPASES • iterative solver – HYPRE • Result and performances • tests and architecture • complexity and scalability analysis with PSPASES • comparison between PSPASES and HYPRE • Conclusions and future work H. Mustapha INRIA, Parco sept 2005

  7. Parallel Simulations of Underground Flow in Porous and Fractured Media Numerical method and parallel matrix generation • Mixed Hybrid Finite Element Method • Type of mesh • Global linear system Conforming triangular mesh Regular grid Assembled by all corresponding sub-domains linear systems H. Mustapha INRIA, Parco sept 2005

  8. Parallel Simulations of Underground Flow in Porous and Fractured Media Outline • Problem presentation • Geometrical and flow fluid model • Numerical method and parallel matrix generation • Parallel linear solver • Direct solver – PSPASES • Iterative solver – HYPRE • Results and performances • Tests and architecture • Complexity and scalability analysis with PSPASES • Comparison between PSPASES and HYPRE • Conclusions and future work H. Mustapha INRIA, Parco sept 2005

  9. Parallel Simulations of Underground Flow in Porous and Fractured Media Parallel Linear solver • Direct solver – PSPASES • sparse matrices • symmetric positive definite matrices • distributed-memory paradigm and MPI library • P (number of processors) = 2^N • Cholesky factorization • Iterative solver – HYPRE • sparse matrices • V-cycle multi-grid algorithm (SMG) • distributed-memory paradigm and MPI library H. Mustapha INRIA, Parco sept 2005

  10. Parallel Simulations of Underground Flow in Porous and Fractured Media Outline • Problem presentation • Geometrical and flow fluid model • Numerical method and parallel matrix generation • Parallel linear solver • Direct solver – PSPASES • Iterative solver - HYPRE • Results and performances • Parallel architecture • Complexity and scalability analysis with PSPASES • Comparison between PSPASES and HYPRE • Conclusions and future work H. Mustapha INRIA, Parco sept 2005

  11. Parallel Simulations of Underground Flow in Porous and Fractured Media Parallel architecture Parallel architecture distributed memory 2 nodes of 32 bi – processors (Proc AMD Opteron 2Ghz with 2Go of RAM) H. Mustapha INRIA, Parco sept 2005

  12. Parallel Simulations of Underground Flow in Porous and Fractured Media Outline • Problem presentation • Geometrical and flow fluid model • Numerical method and parallel matrix generation • Parallel linear solver • Direct solver – PSPASES • Iterative solver - HYPRE • Results and performances • Parallel architecture • Complexity and scalability analysis with PSPASES • Comparison between PSPASES and HYPRE • Conclusions and future work H. Mustapha INRIA, Parco sept 2005

  13. Parallel Simulations of Underground Flow in Porous and Fractured Media Complexity analysis with PSPASES • Test 1 : CPU time of matrix generation, linear solving and flow computation obtained with two processors H. Mustapha INRIA, Parco sept 2005

  14. Parallel Simulations of Underground Flow in Porous and Fractured Media Complexity analysis with PSPASES • Test 2 : Memory requirements for both applications H. Mustapha INRIA, Parco sept 2005

  15. Parallel Simulations of Underground Flow in Porous and Fractured Media Scalability analysis with PSPASES • Test 1 : Efficiency 2D medium 3D fracture network H. Mustapha INRIA, Parco sept 2005

  16. Parallel Simulations of Underground Flow in Porous and Fractured Media Scalability analysis with PSPASES • Test 2 : Speed-up H. Mustapha INRIA, Parco sept 2005

  17. Parallel Simulations of Underground Flow in Porous and Fractured Media Outline • Problem presentation • Geometrical and flow fluid model • Numerical method and parallel matrix generation • Parallel linear solver • Direct solver - PSPASES • Iterative solver - HYPRE • Results and performances • Parallel architecture • Complexity and scalability analysis with PSPASES • Comparison between PSPASES and HYPRE • Conclusions and future work H. Mustapha INRIA, Parco sept 2005

  18. Parallel Simulations of Underground Flow in Porous and Fractured Media Comparison between PSPASES and HYPRE • Test 1 : Linear solving time HYPRE PSPASES H. Mustapha INRIA, Parco sept 2005

  19. Parallel Simulations of Underground Flow in Porous and Fractured Media Comparison between PSPASES and HYPRE • Test 2 : Speed-up PSPASES HYPRE H. Mustapha INRIA, Parco sept 2005

  20. Parallel Simulations of Underground Flow in Porous and Fractured Media Outline • Problem presentation • Geometrical and flow fluid model • Numerical method and parallel matrix generation • Parallel linear solver • Direct solver – PSPASES • Iterative solver – HYPRE • Results and performances • Parallel architecture • Complexity and scalability analysis with PSPASES • Comparison between PSPASES and HYPRE • Conclusions and future work H. Mustapha INRIA, Parco sept 2005

  21. Parallel Simulations of Underground Flow in Porous and Fractured Media • Conclusions Scalable in the case of 2D medium Direct solver PSPASES Not scalable in the case of 3D fracture network Iterative solver HYPRE Efficient for large linear systems • Future work • A 3D extension of parallel software in the case of 2D porous media • Parallel software for simulating solute migration H. Mustapha INRIA, Parco sept 2005

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