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

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

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

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

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

6 Fluid equations Generalised Darcy law: Conservation of mass:

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

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

9 Model FLOW TRANSPORT Coupled Model concentration velocity

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

11 Model FLOW TRANSPORT Parallel linear solvers Parallel implementation

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

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

14 Test case : Henry Stable test case Results

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

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

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

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