Advertisement

A Parallel Locally-Adaptive 3D Model on Cartesian Nested-Type Grids

  • Igor MenshovEmail author
  • Viktor Sheverdin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10421)

Abstract

The paper addresses the 3D extension of the Cartesian multilevel nested-type grid methodology and its software implementation in an application library written in C++ object-oriented language with the application program interface OpenMP for parallelizing calculations on shared memory. The library accounts for the specifics of multithread calculations of 3D problems on Cartesian grids, which makes it possible to substantially minimize the loaded memory via non-storing the grid information. The loop order over cells is represented by a special list that remarkably simplifies parallel realization with the OpenMP directives. Test results show high effectiveness of dynamical local adaptation of Cartesian grids, and increasing of this effectiveness while the number of adaptation levels becomes larger.

Keywords

Locally-adaptive nested-type Cartesian grid Shared memory parallel calculation Gas dynamics equations 

Notes

Acknowledgments

This research was supported by the grant No 17-71-30014 from Russian Scientific Fund.

References

  1. 1.
    Bramkamp, F., Lamby, P.H., Mueller, S.: An adaptive multiscale finite volume solver for unsteady and steady state flow computations. J. Comput. Phys. 197(2), 460–490 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Harten, A.: Multiresolution algorithms for the numerical solution of hyperbolic conservation laws. Comm. Pure Appl. Math. 48(12), 1305–1342 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Harten, A.: Multiresolution representation of data: a general framework. SIAM J. Numer. Anal 33(3), 1205–1256 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Zumbusch, G.: Parallel Multilevel Methods: Adaptive Mesh Refinement and Load Balancing. Advances in Numerical Mathematics. Teubner, Wiesbaden (2003)CrossRefzbMATHGoogle Scholar
  5. 5.
    Osher, S., Sanders, R.: Numerical approximations to nonlinear conservation laws with locally varying time and space grids. Math. Comp. 41, 321–336 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Vasilyev, O.V.: Solving multi-dimensional evolution problems with localized structures using second generation wavelets. Int. J. Comp. Fluid Dyn. 17, 151–168 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Menshov, I.S., Kornev, M.A.: Free_boundary method for the numerical solution of gas_dynamic equations in domains with varying geometry. Math. Models Comput. Simul. 6(6), 612–621 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Menshov, I.S., Pavlukhin, P.V.: Efficient parallel shock-capturing method for aerodynamics simulations on body-unfitted cartesian grids. Comput. Math. Math. Phys. 56(9), 1651–1664 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Menshov, I.S., Pavlukhin, P.V.: Highly scalable implementation of an implicit matrix-free solver for gas dynamics on GPU-accelerated clusters. J. Supercomput. 73, 631–638 (2017)CrossRefGoogle Scholar
  10. 10.
    Godunov, S.K.: Difference method for computing discontinuous solutions of fluid dynamics equations. Mat. Sb. 47(3), 271–306 (1959)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Van Leer, B.: Towards the ultimate conservative difference scheme: V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32, 101–136 (1979)CrossRefzbMATHGoogle Scholar
  12. 12.
    Menshov, I.S., Nikitin, V.S., Sheverdin, V.V.: Parallel three-dimensional LAD model on Cartesian grids of nested structure. Keldysh Inst. Prepr. 118, 1–32 (2016)Google Scholar
  13. 13.
    Sedov, L.I.: Propagation of strong shock waves. J. Appl. Math. Mech. 10, 241–250 (1946)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Keldysh Institute for Applied MathematicsRussian Academy of SciencesMoscowRussia
  2. 2.VNIIAMoscowRussia

Personalised recommendations