DOI: https://doi.org/10.26089/NumMet.v16r117

An implementation of vortex methods for modeling 2D incompressible flows using the CUDA technology

Authors

  • S.R. Grechkin-Pogrebnyakov
  • K.S. Kuzmina
  • I.K. Marchevsky

Keywords:

graphics processor unit (GPU)
CUDA technology
parallel computing
Navier-Stokes equations
viscous incompressible medium
method of viscous vortex domains
discrete vortex method
Blasius problem

Abstract

The possibility of computation speedup in the vortex element method (a meshfree Lagrangian method of computational fluid dynamics) using the graphics accelerators is studied. An algorithm based on the authors’ modification of the vortex element method is implemented; this algorithm allows one to perform all the necessary computations directly on a GPU using the CUDA technology. The speed of solving a typical problem on a single GeForce GTX 970 or Tesla C2050 accelerator is comparable with the speed of solving a similar problem on a cluster containing 30-40 cores with the use of the MPI technology. The numerical results obtained confirm a high efficiency of using graphics accelerators when solving the problems of hydrodynamics with vortex methods.

New computational technologies

Downloads

Published

2015-04-04

Issue

Vol. 16 (2015): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biographies

S.R. Grechkin-Pogrebnyakov

Bauman Moscow State Technical University,
Faculty of Fundamental Sciences
• Student

K.S. Kuzmina

Bauman Moscow State Technical University,
Faculty of Fundamental Sciences
• Student

I.K. Marchevsky

Bauman Moscow State Technical University,
Faculty of Fundamental Sciences
• Associate Professor

References

  1. S. M. Belotserkovsky and I. K. Lifanov, Method of Discrete Vortices (CRC Press, Boca Raton, 1994).
  2. I. K. Lifanov, Singular Integral Equations and Discrete Vortices (Yanus, Moscow, 1995; VSP, Utrecht, 1996).
  3. G. Ya. Dynnikova, Vortex Methods to Study Unsteady Flows of Viscous Incompressible Fluids , Doctoral Dissertation in Mathematics and Physics (Zhukovsky Air Force Engineering Acad., Moscow, 2011).
  4. V. A. Aparinov and A. V. Dvorak, “Method of Discrete Vortices with Closed Vortex Frames,” Tr. VVIA im. Prof. Zhukovskogo, No. 1313, 424-432 (1986).
  5. I. K. Marchevskii and G. A. Shcheglov, “Model of Symmetrical Vortex-Segment for Numerical Modeling of 3D Flows of Ideal Incompressible Medium,” Vestn. Bauman Mosk. Tekh. Univ., Ser.: Natural Sci., No. 4, 62-71 (2008).
  6. G. Ya. Dynnikova, “Fast Technique for Solving the N-Body Problem in Flow Simulation by Vortex Methods,” Zh. Vychisl. Mat. Mat. Fiz. 49 (8), 1458-1465 (2009) [Comput. Math. Math. Phys. 49 (8), 1389-1396 (2009)].
  7. V. V. Lukin, I. K. Marchevskii, V. S. Moreva, et al., “Computing Cluster for Training and Experiments. Part 2. Examples of Solving Problems,” Vestn. Bauman Mosk. Tekh. Univ., Ser.: Natural Sci., No. 4, 82-102 (2012).
  8. I. K. Marchevsky and G. A. Scheglov, “Application of Parallel Algorithms for Solving Hydrodynamic Problems by the Vortex Element Method,” Vychisl. Metody Programm. 11 (1), 105-110 (2010).
  9. G. Ya. Dynnikova and D. A. Syrovatskii, “Three-Dimensional Meshfree Simulation of Unsteady Flows on Hybrid Supercomputing Systems with Graphics Accelerators,” in Proc. Lomonosov Readings, Moscow, April 22-24, 2012 (Mosk. Gos. Univ., Moscow, 2012), pp. 71-72.
  10. G. Ya. Dynnikova and D. A. Syrovatskii, “Numerical Simulation of Unsteady Flow by an Ideal Fluid around Thin Lifting Surfaces Using the Meshfree Methods of Dipole Domains,” in Proc. 17th Conference on Modern Problems of Aerohydrodynamics, Sochi, Russia, August 20-30, 2014 (Mosk. Gos. Univ., Moscow, 2014), p. 55.
  11. W. M. Van Rees, D. Rossinelli, P. Hadjidoukas, and P. Koumoutsakos, “High Performance CPU/GPU Multiresolution Poisson Solver,” in Parallel Computing: Accelerating Computational Science and Engineering (CSE). Advances in Parallel Computing (IOS Press, Amsterdam, 2014), Vol. 25, pp. 481-490.
  12. P. R. Andronov, S. V. Guvernyuk, and G. Ya. Dynnikova, Vortex Methods of Calculation of Unsteady Hydrodynamic Loads (Mosk. Gos. Univ., Moscow, 2006) [in Russian].
  13. S. Li and W. K. Liu, Meshfree Particle Methods (Springer, Berlin, 2004).
  14. I. P. Christiansen, “Numerical Simulation of Hydrodynamics by the Method of Point Vortices,” J. Comp. Phys. 13 (3), 363-379 (1973).
  15. V. S. Moreva and I. K. Marchevsky, “Vortex Element Method for 2D Flow Simulation with Tangent Velocity Components on Airfoil Surface,” in Proc. 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Vienna, Austria, September 10-14, 2012 (Vienna Univ. Technol., Vienna, 2012), pp. 5952-5965.
  16. I. K. Marchevsky and V. S. Moreva, “The POLARA Package to Model the Profile Flow and to Study the Computational Scheme of the Vortex Element Method,” in Proc. Int. Conf. on Parallel Computational Technologies, Novosibirsk, Russia, March 26-30, 2012 (Inst. Comput. Math. Math. Geophys., Novosibirsk, 2012), pp. 236-247.
  17. M. E. Makarova, I. K. Marchevsky, and V. S. Moreva, “Flow Simulation around a Thin Plate Using a Modified Numerical Scheme of the Vortex Element Method,” in Science and Education (Bauman Moscow Tech. Univ., Moscow, 2013), Vol. 9, pp. 233-242.
  18. K. S. Kuzmina and I. K. Marchevsky, “Estimation of Computational Complexity of the Fast Numerical Algorithm for Calculating Vortex Influence in the Vortex Element Method,” in Science and Education (Bauman Moscow Tech. Univ., Moscow, 2013), Vol. 10, pp. 399-414.
  19. K. S. Kuzmina and I. K. Marchevsky, “On Computation Speeding up when Solving Two-Dimensional Hydroelastic Coupled Problems by Using Vortex Methods,” Vestn. Perm Politekh. Univ., Ser.: Aerokosm. Tekh., No. 39, 145-163 (2014).
  20. R. Yokota and L. A. Barba, “Hierarchical N-Body Simulations with Autotuning for Heterogeneous Systems,” Comput. Sci. Eng. 14 (3), 30-39 (2012).