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Keywords: GPU computing, hybrid architecture, multiphase porous media flow, kinetic schemes, explicit finite difference schemes, stability condition, hyperbolic system of equations.

Summary

The proposed approach is aimed at implementation by explicit difference schemes having a simple structure. By the analogy with the kinetically-consistent finite difference schemes and the quasi-gas dynamic system of equations [1,2] the classical model of slightly compressible fluid flows in porous media is modified taking into account the minimal scales of averaging on space and on time. As a result the regularizing term and the time derivation of the second order with small parameters are present in the continuity equation. Transformation of this equation from the parabolic to hyperbolic type provides the sufficient scheme stability. In comparison with traditional approaches this approach increases the time step and reduces substantially computational costs.

The infiltration of dense non-aqueous phase liquid (e.g. tetrachloroethylene) into a reservoir filled with fully water saturated sand is used as a test problem for verification of the algorithm developed while running on GPUs. The data partitioning strategy is chosen to parallelize the algorithm.

Computations are performed with double precision on the hybrid cluster MVS-Express. Each node of the cluster includes four-core CPU (AMD Opteron 2.6 GHz) and a graphics accelerator NVIDIA GeForce 295GTX supporting the CUDA technology. The original library Shmem-Express has been developed in the Keldysh Institute of Applied Mathematics. Its distinguishing feature is the single-ended data exchange between the nodes.

To estimate efficiency of GPU employment the running time on a single CPU core has been compared with the running time on a single graphics card and on four cards belonging to different nodes. In the first case the highest speedup is achieved at the grid size 1024x1024 and comes to 48 times. In the second case at the grid of 12288x2048 it comes to 82 times.

References

1: B.N. Chetverushkin, "Kinetic schemes and Quasi-Gas Dynamic system of equations", CIMNE, Barcelona, Spain, 2008.
2: M.A. Trapeznikova, N.G. Churbanova, B.N. Chetverushkin, "A New Approach to Porous Media Flow Simulation using Adaptive Mesh Refinement", in Ph. Bouillard, P. Diez, (Editors), "ADMOS 2009, Proc. of the IV Int. Conf. on Adaptive Modeling and Simulation", CIMNE, Barcelona, Spain, 197-200, 2009.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 95 PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING Edited by: Paper 19 An Explicit Algorithm for Porous Media Flow Simulation using GPUs D.N. Morozov¹, B.N. Chetverushkin², N.G. Churbanova² and M.A. Trapeznikova² ¹Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Region, Russia ²Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia doi:10.4203/ccp.95.19 purchase the full-text of this paper Full Bibliographic Reference for this paper D.N. Morozov, B.N. Chetverushkin, N.G. Churbanova, M.A. Trapeznikova, "An Explicit Algorithm for Porous Media Flow Simulation using GPUs", in , (Editors), "Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 19, 2011. doi:10.4203/ccp.95.19 Keywords: GPU computing, hybrid architecture, multiphase porous media flow, kinetic schemes, explicit finite difference schemes, stability condition, hyperbolic system of equations. Summary The proposed approach is aimed at implementation by explicit difference schemes having a simple structure. By the analogy with the kinetically-consistent finite difference schemes and the quasi-gas dynamic system of equations [1,2] the classical model of slightly compressible fluid flows in porous media is modified taking into account the minimal scales of averaging on space and on time. As a result the regularizing term and the time derivation of the second order with small parameters are present in the continuity equation. Transformation of this equation from the parabolic to hyperbolic type provides the sufficient scheme stability. In comparison with traditional approaches this approach increases the time step and reduces substantially computational costs. The infiltration of dense non-aqueous phase liquid (e.g. tetrachloroethylene) into a reservoir filled with fully water saturated sand is used as a test problem for verification of the algorithm developed while running on GPUs. The data partitioning strategy is chosen to parallelize the algorithm. Computations are performed with double precision on the hybrid cluster MVS-Express. Each node of the cluster includes four-core CPU (AMD Opteron 2.6 GHz) and a graphics accelerator NVIDIA GeForce 295GTX supporting the CUDA technology. The original library Shmem-Express has been developed in the Keldysh Institute of Applied Mathematics. Its distinguishing feature is the single-ended data exchange between the nodes. To estimate efficiency of GPU employment the running time on a single CPU core has been compared with the running time on a single graphics card and on four cards belonging to different nodes. In the first case the highest speedup is achieved at the grid size 1024x1024 and comes to 48 times. In the second case at the grid of 12288x2048 it comes to 82 times. References 1 B.N. Chetverushkin, "Kinetic schemes and Quasi-Gas Dynamic system of equations", CIMNE, Barcelona, Spain, 2008. 2 M.A. Trapeznikova, N.G. Churbanova, B.N. Chetverushkin, "A New Approach to Porous Media Flow Simulation using Adaptive Mesh Refinement", in Ph. Bouillard, P. Diez, (Editors), "ADMOS 2009, Proc. of the IV Int. Conf. on Adaptive Modeling and Simulation", CIMNE, Barcelona, Spain, 197-200, 2009. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £85 +P&P)
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