ABSTRACT
We present unprecedented, high throughput simulations of cloud cavitation collapse on 1.6 million cores of Sequoia reaching 55% of its nominal peak performance, corresponding to 11 PFLOP/s. The destructive power of cavitation reduces the lifetime of energy critical systems such as internal combustion engines and hydraulic turbines, yet it has been harnessed for water purification and kidney lithotripsy. The present two-phase flow simulations enable the quantitative prediction of cavitation using 13 trillion grid points to resolve the collapse of 15'000 bubbles. We advance by one order of magnitude the current state-of-the-art in terms of time to solution, and by two orders the geometrical complexity of the flow. The software successfully addresses the challenges that hinder the effective solution of complex flows on contemporary supercomputers, such as limited memory bandwidth, I/O bandwidth and storage capacity. The present work redefines the frontier of high performance computing for fluid dynamics simulations.
- R. Abgrall and S. Karni. Computations of compressible multifluids. Journal of Computational Physics, 169(2):594--623, 2001. Google ScholarDigital Library
- N. Adams and S. Schmidt. Shocks in cavitating flows. In C. F. Delale, editor, Bubble Dynamics and Shock Waves, volume 8 of Shock Wave Science and Technology Reference Library, pages 235--256. Springer Berlin Heidelberg, 2013.Google Scholar
- A. S. Almgren, J. B. Bell, M. J. Lijewski, Z. Lukić, and E. V. Andel. Nyx: A massively parallel amr code for computational cosmology. The Astrophysical Journal, 765(1):39, 2013.Google ScholarCross Ref
- AMD Inc. Software Optimization Guide for the AMD 15h Family, 2011.Google Scholar
- T. B. Benjamin and A. T. Ellis. The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 260(1110):221--240, 1966.Google ScholarCross Ref
- M. Berger and P. Colella. Local adaptive mesh refinement for shock hydrodynamics. Journal of Computational Physics, 82(1):64--84, 1989. Google ScholarDigital Library
- M. J. Berger and J. Oliger. Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys., 53(3):484--512, 1984.Google ScholarCross Ref
- M. Berzins, J. Luitjens, Q. Meng, T. Harman, C. A. Wight, and J. R. Peterson. Uintah: a scalable framework for hazard analysis. In Proceedings of the 2010 TeraGrid Conference, TG '10, pages 3:1--3:8. ACM, 2010. Google ScholarDigital Library
- J. R. Blake, M. C. Hooton, P. B. Robinson, and R. P. Tong. Collapsing cavities, toroidal bubbles and jet impact. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 355(1724):537--550, 1997.Google ScholarCross Ref
- C. E. Brennen. Cavitation and bubble dynamics. Oxford University Press, USA, 1995.Google Scholar
- C. E. Brennen. An introduction to cavitation fundamentals. Technical report, In: WIMRC Forum 2011 -- Cavitation: Turbo-machinery & Medical Applications, 2011.Google Scholar
- A. Cohen, I. Daubechies, and P. Vial. Wavelets on the interval and fast wavelet transforms. Applied and Computational Harmonic Analysis, 1(1):54--81, 1993.Google ScholarCross Ref
- A. Cucheval and R. Chow. A study on the emulsification of oil by power ultrasound. Ultrasonics Sonochemistry, 15(5):916--920, 2008.Google ScholarCross Ref
- J. Dear and J. Field. A study of the collapse of arrays of cavities. J. Fluid Mech, 190(409):172, 1988.Google Scholar
- N. G. Dickson, K. Karimi, and F. Hamze. Importance of explicit vectorization for cpu and gpu software performance. Journal of Computational Physics, 230(13):5383--5398, 2011. Google ScholarDigital Library
- M. O. Domingues, S. M. Gomes, O. Roussel, and K. Schneider. Space-time adaptive multiresolution methods for hyperbolic conservation laws: Applications to compressible euler equations, Sep 2009. Google ScholarDigital Library
- D. Donoho. Interpolating wavelet transforms, 1992.Google Scholar
- S. Faulk, E. Loh, M. L. D. Vanter, S. Squires, and L. Votta. Scientific computing's productivity gridlock: How software engineering can help. Computing in Science Engineering, 11(6):30--39, 2009. Google ScholarDigital Library
- R. T. Fisher, L. P. Kadanoff, D. Q. Lamb, A. Dubey, T. Plewa, A. Calder, F. Cattaneo, P. Constantin, I. T. Foster, M. E. Papka, S. I. Abarzhi, S. M. Asida, P. M. Rich, C. C. Glendenin, K. Antypas, D. J. Sheeler, L. B. Reid, B. Gallagher, and S. G. Needham. Terascale turbulence computation using the flash3 application framework on the ibm blue gene/lsystem. IBM Journal of Research and Development, 52(1--2):127--136, 2008. Google ScholarDigital Library
- Folk M., Cheng A. and Yates K. Hdf5: A file format and i/o library for high performance computing applications. In Proceedings of Supercomputing, 1999.Google Scholar
- J. P. Franc and M. Riondet. Incubation time and cavitation erosion rate of work-hardening materials. In The proceeding of the Sixth International Symposium on Cavitation, CAV2006, 2006.Google Scholar
- B. Fryxell, K. Olson, P. Ricker, F. X. Timmes, M. Zingale, D. Q. Lamb, P. MacNeice, R. Rosner, J. W. Truran, and H. Tufo. Flash: An adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes. The Astrophysical Journal Supplement Series, 131(1):273, 2000.Google ScholarCross Ref
- J.-l. Gailly and M. Adler. Zlib compression library. 2004.Google Scholar
- E. Gamma, R. Helm, R. Johnson, and J. Vlissides. Design patterns: Abstraction and reuse of object-oriented design. In O. Nierstrasz, editor, ECOOP' 93 --- Object-Oriented Programming, volume 707 of Lecture Notes in Computer Science, pages 406--431. Springer Berlin/Heidelberg, 1993. Google ScholarDigital Library
- F. R. Gilmore. The collapse and growth of a spherical bubble in a viscous compressible liquid. Technical Report 26--4, California Institute of Technology, 1952.Google Scholar
- J. A. Greenough, B. R. De Supinski, R. K. Yates, C. A. Rendleman, D. Skinner, V. Beckner, M. Lijewski, and J. Bell. Performance of a block structured, hierarchical adaptive mesh refinement code on the 64k node ibm bluegene/l computer. Computer, pages 1--12, 2005.Google Scholar
- W. Gropp, D. Kaushik, D. Keyes, and B. Smith. High-performance parallel implicit CFD. Parallel Computing, 27(4):337--362, 2001. Google ScholarDigital Library
- F. Günther, M. Mehl, M. Pögl, and C. Zenger. A cache aware algorithm for pdes on hierarchical data structures based on space filling curves. SIAM Journal on Scientific Computing, 28(5):1634--1650, 2006. Google ScholarDigital Library
- F. G. Hammitt. Damage to solids caused by cavitation. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 260(1110):245--255, 1966.Google ScholarCross Ref
- I. Hansson, V. Kedrinskii, and K. A. Morch. On the dynamics of cavity clusters. Journal of Physics D: Applied Physics, 15(9):1725, 1982.Google ScholarCross Ref
- R. Haring, M. Ohmacht, T. Fox, M. Gschwind, D. Satterfield, K. Sugavanam, P. Coteus, P. Heidelberger, M. Blumrich, R. Wisniewski, A. Gara, G.-T. Chiu, P. Boyle, N. Chist, and C. Kim. The ibm blue gene/q compute chip. Micro, IEEE, 32(2):48--60, 2012. Google ScholarDigital Library
- N. A. Hawker and Y. Ventikos. Interaction of a strong shockwave with a gas bubble in a liquid medium: a numerical study. Journal of Fluid Mechanics, 701:59--97, 2012.Google ScholarCross Ref
- B. Hejazialhosseini, D. Rossinelli, C. Conti, and P. Koumoutsakos. High throughput software for direct numerical simulations of compressible two-phase flows. Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, pages 16:1--16:12, 2012. Google ScholarDigital Library
- B. Hejazialhosseini, D. Rossinelli, and P. Koumoutsakos. 3D shock-bubble interactions at mach 3. Physics of Fluids (Gallery of Fluid Motion), 2013.Google Scholar
- R. Hickling and M. S. Plesset. Collapse and rebound of a spherical bubble in water. Physics of Fluids, 7(1):7--14, 1964.Google ScholarCross Ref
- M. Holmström. Solving hyperbolic pdes using interpolating wavelets. SIAM Journal on Scientific Computing, 21(2):405--420, 1999. Google ScholarDigital Library
- X. Y. Hu, B. C. Khoo, N. A. Adams, and F. L. Huang. A conservative interface method for compressible flows. Journal of Computational Physics, 219(2):553--578, Dec 10 2006. Google ScholarDigital Library
- Y. Hu, A. Cox, and W. Zwaenepoel. Improving fine-grained irregular shared-memory benchmarks by data reordering. In Supercomputing, ACM/IEEE 2000 Conference, pages 33--33, 2000. Google ScholarDigital Library
- IBM. A2 Processor User's Manual for Blue Gene/Q, 2012.Google Scholar
- T. Ikeda, S. Yoshizawa, M. Tosaki, J. S. Allen, S. Takagi, N. Ohta, T. Kitamura, and Y. Matsumoto. Cloud cavitation control for lithotripsy using high intensity focused ultrasound. Ultrasound in Medicine & Biology, 32(9):1383--1397, 2006.Google ScholarCross Ref
- Intel Corporation. Intel® 64 and IA-32 Architectures Optimization Reference Manual. Intel Corporation, 2009.Google Scholar
- G. Jiang and C. Shu. Efficient implementation of weighted ENO schemes. Journal of Computational Physics, 126(1):202--228, Jun 1996. Google ScholarDigital Library
- E. Johnsen and T. Colonius. Implementation of WENO schemes in compressible multicomponent flow problems. Journal of Computational Physics, 219(2):715--732, Dec 10 2006. Google ScholarDigital Library
- E. Johnsen and T. Colonius. Numerical simulations of non-spherical bubble collapse. Journal of Fluid Mechanics, 629:231--262, 5 2009.Google ScholarCross Ref
- E. Johnsen and F. Ham. Preventing numerical errors generated by interface-capturing schemes in compressible multi-material flows. Journal of Computational Physics, 231(17):5705--5717, 2012. Google ScholarDigital Library
- D. Kelly. A software chasm: Software engineering and scientific computing. Software, IEEE, 24(6):120--119, 2007. Google ScholarDigital Library
- N. K. R. Kevlahan and O. V. Vasilyev. An adaptive wavelet collocation method for fluid-structure interaction at high reynolds numbers. SIAM Journal on Scientific Computing, 26(6):1894--1915, 2005. Google ScholarDigital Library
- B.-J. Kim and W. Pearlman. An embedded wavelet video coder using three dimensional set partitioning in hierarchical trees (spiht). In Data Compression Conference, 1997. DCC '97. Proceedings, pages 251--260, 1997. Google ScholarDigital Library
- R. T. Knapp. Recent investigations of the mechanics of cavitations and cavitation damage. Trans. ASME, 77, 1955.Google Scholar
- T. Kodama and K. Takayama. Dynamic behavior of bubbles during extracorporeal shock-wave lithotripsy. Ultrasound in Medicine & Biology, 24(5):723--738, 1998.Google ScholarCross Ref
- E. Lauer, X. Y. Hu, S. Hickel, and N. A. Adams. Numerical investigation of collapsing cavity arrays. Physics of Fluids, 24(5):052104, 2012.Google ScholarCross Ref
- J. Li, W.-k. Liao, A. Choudhary, R. Ross, R. Thakur, W. Gropp, R. Latham, A. Siegel, B. Gallagher, and M. Zingale. Parallel netcdf: A high-performance scientific i/o interface. In Proceedings of the 2003 ACM/IEEE conference on Supercomputing, SC '03. ACM, 2003. Google ScholarDigital Library
- J. F. Lofstead, S. Klasky, K. Schwan, N. Podhorszki, and C. Jin. Flexible io and integration for scientific codes through the adaptable io system (adios). In Proceedings of the 6th international workshop on Challenges of large applications in distributed environments, CLADE '08, pages 15--24. ACM, 2008. Google ScholarDigital Library
- J. Mellor-Crummey, D. Whalley, and K. Kennedy. Improving memory hierarchy performance for irregular applications using data and computation reorderings. International Journal of Parallel Programming, 29(3):217--247, 2001. Google ScholarDigital Library
- Q. Meng and M. Berzins. Abstract: Uintah hybrid task-based parallelism algorithm. In High Performance Computing, Networking, Storage and Analysis (SCC), 2012 SC Companion:, pages 1431--1432, 2012. Google ScholarDigital Library
- K. Mørch. Energy considerations on the collapse of cavity clusters. Applied Scientific Research, 38:313--321, 1982.Google ScholarCross Ref
- A. Myers. Stanford researchers break million-core supercomputer barrier, January 2013.Google Scholar
- P. Colella, D. T. Graves, T. J. Ligocki, D. F. Martin, D. Mondiano, D. B. Serafini, and B. Van Straalen. Chombo software package for amr applications design document. Technical report, Lawrence Berkeley National Laboratory, 2003.Google Scholar
- R. Prosser. Resolution independent lifted interpolating wavelets on an interval. 2009.Google Scholar
- D. Ranjan, J. H. J. Niederhaus, J. G. Oakley, M. H. Anderson, J. A. Greenough, and R. Bonazza. Experimental and numerical investigation of shock-induced distortion of a spherical gas inhomogeneity. Physica Scripta Volume T, 132(1):014020, Dec. 2008.Google ScholarCross Ref
- L. Rayleigh. Viii. on the pressure developed in a liquid during the collapse of a spherical cavity. Philosophical Magazine Series 6, 34(200):94--98, 1917.Google ScholarCross Ref
- S. J. Reckinger, D. Livescu, and O. V. Vasilyev. Adaptive wavelet collocation method simulations of Rayleigh-Taylor instability. Physica Scripta, T142, DEC 2010. 2nd International Conference and Advanced School on Turbulent Mixing and Beyond, Abdus Salam Int Ctr Theoret Phys, Trieste, ITALY, JUL 27-AUG 07, 2009.Google Scholar
- S. M. Reckinger, O. V. Vasilyev, and B. Fox-Kemper. Adaptive volume penalization for ocean modeling. Ocean Dynamics, 62(8):1201--1215, AUG 2012.Google ScholarCross Ref
- D. Rossinelli, B. Hejazialhosseini, D. Spampinato, and P. Koumoutsakos. Multicore/multi-gpu accelerated simulations of multiphase compressible flows using wavelet adapted grids. SIAM J. Scientific Computing, 33(2), 2011. Google ScholarDigital Library
- O. Roussel, K. Schneider, A. Tsigulin, and H. Bockhorn. A conservative fully adaptive multiresolution algorithm for parabolic pdes. Journal Of Computational Physics, 188(2):493--523, Jul 2003. Google ScholarDigital Library
- E. R. Schendel, S. V. Pendse, J. Jenkins, D. A. Boyuka, II, Z. Gong, S. Lakshminarasimhan, Q. Liu, H. Kolla, J. Chen, S. Klasky, R. Ross, and N. F. Samatova. Isobar hybrid compression-i/o interleaving for large-scale parallel i/o optimization. In Proceedings of the 21st international symposium on High-Performance Parallel and Distributed Computing, HPDC '12, pages 61--72, New York, NY, USA, 2012. ACM. Google ScholarDigital Library
- D. P. Schmidt and M. L. Corradini. The internal flow of diesel fuel injector nozzles: A review. International Journal of Engine Research, 2(1):1--22, 2001.Google ScholarCross Ref
- Schmidt et al. Assessment of the prediction capabalities of a homogeneous cavitation model fir the collapse characteristics of a vapour-bubble cloud. In WIMRC 3rd International Cavitation Forum, Coventry, U.K., 2011.Google Scholar
- K. Schneider and O. V. Vasilyev. Wavelet methods in computational fluid dynamics. Annual Review of Fluid Mechanics, 42(1):473--503, 2010.Google ScholarCross Ref
- K. Schwaber and M. Beedle. Agile Software Development with Scrum. Prentice Hall PTR, 1st edition, 2001. Google ScholarDigital Library
- J. Sermulins, W. Thies, R. Rabbah, and S. Amarasinghe. Cache aware optimization of stream programs. SIGPLAN Not., 40(7):115--126, June 2005. Google ScholarDigital Library
- J. M. Shapiro. Embedded image coding using zerotrees of wavelet coefficients. Signal Processing, IEEE Transactions on, 41(12):3445--3462, 1993. Google ScholarDigital Library
- I. B. G. team. Design of the ibm blue gene/q compute chip. IBM Journal of Research and Development, 57(1/2):1:1--1:13, 2013. Google ScholarDigital Library
- Y. Tomita and A. Shima. Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse. Journal of Fluid Mechanics, 169:535--564, Aug. 1986.Google ScholarCross Ref
- Y. Utturkar, J. Wu, G. Wang, and W. Shyy. Recent progress in modeling of cryogenic cavitation for liquid rocket propulsion. Progress in Aerospace Sciences, 41(7):558--608, 2005.Google ScholarCross Ref
- O. Vasilyev and C. Bowman. Second-generation wavelet collocation method for the solution of partial differential equations. Journal of Computational Physics, 165(2):660--693, DEC 10 2000. Google ScholarDigital Library
- T. Wen, J. Su, P. Colella, K. Yelick, and N. Keen. An adaptive mesh refinement benchmark for modern parallel programming languages. In Proceedings of the 2007 ACM/IEEE conference on Supercomputing, SC '07, pages 1--12. ACM, 2007. Google ScholarDigital Library
- B. Wendroff. Approximate Riemann solvers, Godunov schemes and contact discontinuities. In Toro, EF, editor, Godunov Methods: Theory and Applications, pages 1023--1056, 233 Spring St, New York, NY 10013 USA, 2001. London Math Soc, Kluwer Academic/Plenum Publ.Google ScholarCross Ref
- S. Williams, A. Waterman, and D. Patterson. Roofline: an insightful visual performance model for multicore architectures. Commun. ACM, 52:65--76, 2009. Google ScholarDigital Library
- J. Williamson. Low-Storage Runge-Kutta Schemes. Journal of Computational Physics, 35(1):48--56, 1980.Google ScholarCross Ref
- G. Wilson. Where's the real bottleneck in scientific computing? American Scientist, 2006.Google ScholarCross Ref
Recommendations
Eulerian–Lagrangian method for simulation of cloud cavitation
AbstractWe present a coupled Eulerian–Lagrangian method to simulate cloud cavitation in a compressible liquid. The method is designed to capture the strong, volumetric oscillations of each bubble and the bubble-scattered acoustics. The ...
Highlights- Mixture-averaged equations of motion are discretized on an Eulerian grid and the individual bubbles are tracked as Lagrangian particles at the sub-grid ...
Comments