Abstract
In petroleum reservoir simulations, the level of detail incorporated into the geologic model typically exceeds the capabilities of traditional flow simulators. In this sense, such simulations demand new high-performance computing techniques to deal with a large amount of data allocation and the high computational cost of computing the behavior of the fluids in the porous media. This paper presents optimizations performed on a code that implements an explicit numerical scheme to provide an approximate solution to the governing differential equation for water saturation in a two-phase flow problem with heterogeneous permeability and porosity fields. The experiments were performed on the SDumont Supercomputer using 2nd Generation Intel®Xeon®Scalable Processors (formerly Cascade Lake architecture). The paper employs a direct memory data access scheme to reduce the execution times of the numerical method. The article analyzes the performance gain using direct memory access related to indirect access memory. The results show that the optimizations implemented in the numerical code remarkably reduce the execution time of the simulations.
Supported by organization LNCC/SEPAD.
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References
Abreu, E.C.d., et al.: Modelagem e simulação computacional de escoamentos trifásicos em reservatórios de petróleo heterogêneos. Ph.D. thesis, Universidade do Estado do Rio de Janeiro (2007)
Borges, M., Furtado, F., Pereira, F., Souto, H.A.: Scaling analysis for the tracer flow problem in self-similar permeability fields. Multiscale Model. Simul. 7(3), 1130–1147 (2009)
Carneiro, I.B., Borges, M.R., Malta, S.M.C.: Aplicação de métodos de alta ordem na resolução de problemas bifásicos. Proc. Ser. Braz. Soc. Comput. Appl. Math. 6(2) (2018)
Causon, D., Mingham, C.: Introductory Finite Difference Methods for PDEs. Bookboon (2010)
Correa, M., Borges, M.: A semi-discrete central scheme for scalar hyperbolic conservation laws with heterogeneous storage coefficient and its application to porous media flow. Int. J. Numer. Meth. Fluids 73(3), 205–224 (2013)
Dagan, G.: Flow and Transport in Porous Formations. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-75015-1
Mulnix, D.L.: Intel®Xeon®processor scalable family technical overview (2017). https://www.intel.com/content/www/us/en/developer/articles/technical/xeon-processor-scalable-family-technical-overview.html
Dupuis, A., Chopard, B.: Lattice gas: an efficient and reusable parallel library based on a graph partitioning technique. In: Sloot, P., Bubak, M., Hoekstra, A., Hertzberger, B. (eds.) HPCN-Europe 1999. LNCS, vol. 1593, pp. 319–328. Springer, Heidelberg (1999). https://doi.org/10.1007/BFb0100593
Durlofsky, L.J.: Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media. Water Resour. Res. 27(5), 699–708 (1991)
Gelhar, L.W., Axness, C.L.: Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res. 19(1), 161–180 (1983)
Herrera, S., et al.: Optimizations in an numerical method code for two-phase fluids flow in porous media using the sDumont supercomputer. In: CILAMCE 2021-PANACM 2021 Proceedings of the XLII Ibero-Latin-American Congress on Computational Methods in Engineering and III Pan-American Congress on Computational Mechanics, ABMEC-IACM Rio de Janeiro, Brazil, 9–12 November 2021. CILAMCE (2021)
Herschlag, G., Lee, S., Vetter, J.S., Randles, A.: GPU data access on complex geometries for D3Q19 lattice Boltzmann method. In: 2018 IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 825–834. IEEE (2018)
Huang, C., Lawlor, O., Kalé, L.V.: Adaptive MPI. In: Rauchwerger, L. (ed.) LCPC 2003. LNCS, vol. 2958, pp. 306–322. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24644-2_20
LeVeque, R.J.: Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems. SIAM (2007)
Martys, N.S., Hagedorn, J.G.: Multiscale modeling of fluid transport in heterogeneous materials using discrete Boltzmann methods. Mater. Struct. 35, 650–658 (2002)
Osthoff, C., et al.: A arquitetura do supercomputador sDumont e os desafios da pesquisa brasileira na área de computação de alto desempenho. In: Anais da XI Escola Regional de Alto Desempenho de São Paulo, pp. 1–5. SBC (2020)
Pan, C., Prins, J.F., Miller, C.T.: A high-performance lattice Boltzmann implementation to model flow in porous media. Comput. Phys. Commun. 158(2), 89–105 (2004)
Parashar, M., Yotov, I.: An environment for parallel multi-block, multi-resolution reservoir simulations. In: Proceedings of the 11th International Conference on Parallel and Distributed Computing Systems (PDCS 98), Chicago, IL, International Society for Computers and their Applications (ISCA), pp. 230–235 (1998)
Respondek, J.: Matrix black box algorithms - a survey. Bull. Pol. Acad. Sci. Tech. Sci. 70(2), e140535 (2022)
Ryzhyk, L.: The Arm architecture. Chicago University, Illinois, EUA (2006)
Schulz, M., Krafczyk, M., Tölke, J., Rank, E.: Parallelization strategies and efficiency of CFD computations in complex geometries using lattice Boltzmann methods on high-performance computers. In: High Performance Scientific and Engineering Computing: proceedings of the 3rd International FORTWIHR Conference on HPSEC, Erlangen, 12–14 March 2001, vol. 21, pp. 115–122. Springer, Heidelberg (2002). https://doi.org/10.1007/978-3-642-55919-8_13
Shashkov, M.: Conservative Finite-Difference Methods on General Grids, vol. 6. CRC Press (1995)
Silvester, P.P., Ferrari, R.L.: Finite Elements for Electrical Engineers. Cambridge University Press (1996)
Intel Corporation Site: performance monitoring events supported by Intel performance monitoring units (PMUs). https://perfmon-events.intel.com/
Message Passing Interface Forum: MPI: a message passing interface. In: Proceedings of the 1993 ACM/IEEE Conference on Supercomputing, pp. 878–883 (1993)
Tuane, V.L.: Simulação Numérica tridimensional de escoamento em reservátorios de petróleo Heterogêneos. Master’s thesis, LNCC/MCT, Petrópolis, RJ, Brasil (2012)
Tuszyński, J., Löhner, R.: Parallelizing the construction of indirect access arrays for shared-memory machines. Commun. Numer. Meth. Eng. 14(8), 773–781 (1998)
Vázquez-Cendón, M.E.: Solving Hyperbolic Equations with Finite Volume Methods. U, vol. 90. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-14784-0
Acknowledgement
The authors acknowledge the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for providing HPC resources for the SDumont supercomputer. The use of HPC resources contributed significantly to the research results reported in this paper. URL: http://sdumont.lncc.br. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) Finance Code 001.
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Taipe, S.H.H. et al. (2023). An Evaluation of Direct and Indirect Memory Accesses in Fluid Flow Simulator. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2023. ICCSA 2023. Lecture Notes in Computer Science, vol 13956 . Springer, Cham. https://doi.org/10.1007/978-3-031-36805-9_3
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