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1 A parallel software for a saltwater intrusion problem E. Canot IRISA/CNRS J. Erhel IRISA/INRIA Rennes C. de Dieuleveult IRISA/INRIA Rennes

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2 Outline Introduction Model of saltwater intrusion problem Parallel Implementation Results Conclusion

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3 Context Effect of pumping in coastal aquifers Necessity to predict the evolution of the water supply. Introduction

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4 Presentation of the software Simulation of density driven coupled flow and transport in a porous media Based on TVDV-2D software developped at IMFS in Strasbourg Originally sequential Introduction

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5 Goals Obtain good performances thanks to parallelism Allow large scale simulation (Future goal : extend to 3D geometry)

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6 Fluid equations Generalised Darcy law: Conservation of mass:

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7 Transport equation Solute mass conservation equation: State equations Convection Diffusion

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8 Model FLOW TRANSPORTconvection dispersion Coupled Model (MFE) (DFE)

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9 Model FLOW TRANSPORT Coupled Model concentration velocity

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10 Strong Coupling Time n FLOWTRANSPORT Velocity Concentration Density Time n+1 Coupled Model Fixed-point scheme Stopping criterion

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11 Model FLOW TRANSPORT Parallel linear solvers Parallel implementation

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12 Parallel sparse solver Use of MUMPS (« MUltifrontal Massively Parallel Solver »), a free package for solving linear systems of equations Ax=b (direct method): Adapted for sparse unsymmetric, and symmetric definite positive matrices. Three steps: symbolic factorisation, numerical factorisation and triangular solving. Parallel implementation

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13 Global parallelisation Partitioning mesh thanks to METIS, a free package for partitioning graphs, meshes and for producing fill reducing orderings for sparse matrices. Partitioning example with 5 parts Parallel implementation

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14 Test case : Henry Stable test case Results

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15 Choice of the network Tests on a Fast Eternet network (100Mb/s) with bi-processors Intel Xeon (CPU 2.4Hz, cache 512Kb) Poor results Use of a Myrinet network (2Gb/s) Results

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16 Choice of the MUMPS option Time spent in MUMPS for different methods of pivot order with mesh 254x126 elements for the Henry test case and 10 time steps. Results

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17 Parallel Results Time results with MUMPS and the Henry problem on 2D meshes. Results

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18 Conclusion - Perspectives 3D geometry Parallelisation of the visualisation Improved coupling Conclusion

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