Skip to main content
SpringerLink
Log in

A Characteristic-Based Spectral Element Method for Moving-Domain Problems

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript

Abstract

In this paper, we present a characteristic-based numerical procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an efficient and stable numerical scheme. Using the spectral element method and an arbitrary Lagrangian–Eulerian formulation, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of our scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Demirdžić, I., Perić, M.: Finite volume method for prediction of fluid flow in arbitrarily shaped domains with moving boundaries. Int. J. Numer. Methods Fluid. 10(7), 771 (1990)

    Article  MATH  Google Scholar 

  2. Tezduyar, T., Behr, M., Liou, J.: A new strategy for finite element computations involving moving boundaries and interfaces-the DSD/ST procedure, I: the concept and the preliminary numerical tests. Comput. Methods Appl. Mech. Eng. 94(3), 339 (1992)

    Article  MATH  Google Scholar 

  3. Tezduyar, T.E., Behr, M., Mittal, S., Liou, J.: A new strategy for finite element computations involving moving boundaries and interfacesthe deforming-spatial-domain/space-time procedure, II: computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput. Methods Appl. Mech. Eng. 94(3), 353 (1992)

    Article  MATH  Google Scholar 

  4. Donea, J., Huerta, A., Ponthot, J.P., Rodrguez-Ferran, A.: Arbitrary LagrangianEulerian methods. Encycl. Comput. Mech. 1, 14 (2004). https://doi.org/10.1002/0470091355.ecm009

    Google Scholar 

  5. Arcoumanis, C., Whitelaw, J.: Fluid mechanics of internal combustion engines a review. Proc. Inst. Mech. Eng. Part C. J. Mech. Eng. Sci. 201(1), 57 (1987)

    Article  Google Scholar 

  6. Kuo, T.W., Yang, X., Gopalakrishnan, V., Chen, Z.: Large Eddy Simulation (les) for IC Engine Flows. Oil Gas Sci. Technol.-Rev, IFP Energies nouvelles (2012)

  7. Schiffmann, P., Gupta, S., Reuss, D., Sick, V., Yang, X., Kuo, T.W.: TCC-III engine benchmark for large-eddy simulation of IC engine flows. Oil Gas Sci. Technol. 71(1), 3 (2016)

    Article  Google Scholar 

  8. Rutland, C.: (2011) Large-eddy simulations for internal combustion engines–a review. Int. J. Engine Res. https://doi.org/10.11771/1468087411407248

  9. Schmitt, M., Frouzakis, C.E., Tomboulides, A.G., Wright, Y.M., Boulouchos, K.: Direct numerical simulation of multiple cycles in a valve/piston assembly. Phys. Fluid. 26(3), 035105 (2014)

    Article  Google Scholar 

  10. Schmitt, M., Frouzakis, C., Wright, Y., Tomboulides, A., Boulouchos, K.: Investigation of wall heat transfer and thermal stratification under engine-relevant conditions using DNS. Int. J. Engine Res. 17(1), 63 (2016)

    Article  Google Scholar 

  11. Patera, A.: A spectral element method for fluid dynamics: laminar flow in a channel expansion. J. Comput. Phys. 54, 468 (1984)

    Article  MATH  Google Scholar 

  12. Ho, L.: A Legendre spectral element method for simulation of incompressible unsteady viscous free-surface flows. Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA (1989)

  13. Ho, L., Maday, Y., Patera, A., Rønquist, E.: A high-order Lagrangian-decoupling method for the incompressible Navier–Stokes equations. Comput. Methods Appl. Mech. Eng. 80, 65 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ho, L., Patera, A.: A Legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows. Comput. Methods Appl. Mech. Eng. 80, 355 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  15. Fischer, P., Schmitt, M., Tomboulides, A.: Recent developments in spectral element simulations of moving-domain problems. Fields Institute Communications: Recent Progress and Modern Challenges in Applied Mathematics, Modelling and Computational Science, Springer/Fields Institute, Berlin (2016)

  16. Orszag, S., Israeli, M., Deville, M.: Boundary conditions for incompressible flows. J. Sci. Comput. 1, 75 (1986)

    Article  MATH  Google Scholar 

  17. Maday, Y., Patera, A., Rønquist, E.: An operator-integration-factor splitting method for time-dependent problems: application to incompressible fluid flow. J. Sci. Comput. 5, 263 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  18. Tomboulides, A., Israeli, M., Karniadakis, G.: Efficient removal of boundary-divergence errors in time-splitting methods. J. Sci. Comput. 4, 291 (1989)

    Article  MathSciNet  Google Scholar 

  19. Perot, J.: An analysis of the fractional step method. J. Comput. Phys. 108, 51 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  20. Couzy, W.: Spectral element discretization of the unsteady Navier–Stokes equations and its iterative solution on parallel computers. Ph.D. thesis, Swiss Federal Institute of Technology-Lausanne (1995). Thesis nr. 1380

  21. Fischer, P.: An overlapping Schwarz method for spectral element solution of the incompressible Navier–Stokes equations. J. Comput. Phys. 133, 84 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  22. Fischer, P., Lottes, J.: In: Kornhuber, R., Hoppe, R., Périaux, J., Pironneau, O., Widlund, O., Xu, J. (eds.) Domain Decomposition Methods in Science and Engineering Series, Springer, Berlin (2004)

  23. Lottes, J.W., Fischer, P.F.: Hybrid multigrid/Schwarz algorithms for the spectral element method. J. Sci. Comput. 24, 45 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  24. Tufo, H., Fischer, P.: Fast parallel direct solvers for coarse-grid problems. J. Parallel Distrib. Comput. 61, 151 (2001)

    Article  MATH  Google Scholar 

  25. Fischer, P., Lottes, J., Pointer, W., Siegel, A.: Petascale algorithms for reactor hydrodynamics. J. Phys. Conf. Ser. 125, 012076 (2008)

    Article  Google Scholar 

  26. Lottes, J.: Independent quality measures for symmetric AMG components. Tech. Rep. ANL/MCS-P1820-0111, Argonne National Laboratory, Argonne, IL (2011)

  27. Boyd, J.: Two comments on filtering for Chebyshev and Legendre spectral and spectral element methods. J. Comput. Phys. 143, 283 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  28. Fischer, P., Mullen, J.: Filter-based stabilization of spectral element methods, Comptes rendus de l’Académie des sciences, Série I- Analyse numérique 332, 265 (2001)

  29. Malm, J., Schlatter, P., Fischer, P., Henningson, D.: Stabilization of the spectral-element method in convection dominated flows by recovery of skew symmetry. J. Sci. Comput. 57, 254 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  30. Tufo, H., Fischer, P.: In: Proceedigs of the ACM/IEEE SC99 Conference on High Performance Networking and Computing, Gordon Bell Prize, IEEE Computer Soc., CDROM (1999)

  31. Deville, M., Fischer, P., Mund, E.: High-Order Methods for Incompressible Fluid Flow. Cambridge University Press, Cambridge (2002)

    Book  MATH  Google Scholar 

  32. Pironneau, O.: On the transport-diffusion algorithm and its applications to the Navier–Stokes equations. Numer. Math. 38, 309 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  33. Tomboulides, A., Lee, J., Orszag, S.: Numerical simulation of low Mach number reactive flows. J. Sci. Comput. 12, 139 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  34. Fischer, P.: Projection techniques for iterative solution of \({A}{\underline{ x}} ={\underline{ b}} \) with successive right-hand sides. Comput. Methods Appl. Mech. Eng. 163, 193 (1998)

    Article  MATH  Google Scholar 

  35. Fischer, P.: In: 22nd AIAA Computational Fluid Dynamics Conference, AIAA Aviation, AIAA 2015-3049 (2015)

  36. Walsh, O.: In: Heywood, J., Masuda, K., Rautmann, R., Solonikkov, V. (eds.) The NSE II-Theory and Numerical Methods, pp. 306–309. Springer, Berlin (1992)

  37. Pedley, T., Stephanoff, K.: Flow along a channel with a time-dependent indentation in one wall: the generation of vorticity waves. J. Fluid Mech. 160, 337 (1985)

    Article  Google Scholar 

  38. Ralph, M., Pedley, T.: Flow in a channel with a moving indentation. J. Fluid Mech. 190, 87 (1988)

    Article  Google Scholar 

  39. Udaykumar, H., Mittal, R., Rampunggoon, P., Khanna, A.: A sharp interface cartesian grid method for simulating flows with complex moving boundaries. J. Comput. Phys. 174(1), 345 (2001)

    Article  MATH  Google Scholar 

  40. Ho, L., Patera, A.: A legendre spectral element method for simulation of unsteady incompressible viscous free-surface flows. Comput. Methods Appl. Mech. Eng. 80, 355 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  41. Sick, V., Reuss, D., Yang, X., Kuo, T.W.: TCC-III CFD Input Dataset. https://deepblue.lib.umich.edu/handle/2027.42/108382

  42. Masud, A., Hughes, T.J.R.: A space-time Galerkin/least-squares finite element formulation of the Navier–Stokes equations for moving domain problems. Comput. Methods Appl. Mech. Eng. 146, 91 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  43. Kanchi, H., Masud, A.: A 3d adaptive mesh moving scheme. Int. J. Numer. Methods Fluids 54, 923 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  44. Bello-Maldonado, P., Fischer, P.: Scalable low-order finite element preconditioners for high-order spectral element poisson solvers. (2018). Submitted

Download references

Acknowledgements

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under Contract DE-AC02-06CH11357. The research also used resources of the Argonne Leadership Computing Facility, which is supported by the U.S. Department iof Energy, Office of Science, under Contract DE-AC02-06CH11357.

Author information

Authors and Affiliations

  1. Leadership Computing Facility at Argonne National Laboratory, Lemont, IL, USA

    Saumil Patel

  2. Argonne National Laboratory and University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Paul Fischer

  3. Mathematics and Computer Science Division at Argonne National Laboratory, Lemont, IL, USA

    Misun Min

  4. Argonne National Laboratory and Aristotle University of Thessaloniki, Thessaloniki, Greece

    Ananias Tomboulides

Authors
  1. Saumil Patel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paul Fischer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Misun Min
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ananias Tomboulides
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saumil Patel.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Patel, S., Fischer, P., Min, M. et al. A Characteristic-Based Spectral Element Method for Moving-Domain Problems. J Sci Comput 79, 564–592 (2019). https://doi.org/10.1007/s10915-018-0876-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-018-0876-6

Keywords

Search

Navigation