Skip to main content

A High-Order Discontinuous Galerkin Chimera Method for the Euler and Navier-Stokes Equations

  • Chapter
IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 128))

Abstract

In this article a non-conservative Chimera method for the Euler and Navier-Stokes equations is introduced. The CFD solver for the Chimera method is based on a high-order Discontinuous Galerkin formulation and employs modal basis functions. As the method features at least two different grids, interpolation operators have to be defined between the two grids which is achieved by a discrete projection. A detailed description of the adaption of the temporal integration schemes is given and their implementation is validated for the explicit and implicit schemes against results using only a single grid.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benek, J., Steger, J., Dougherty, F.: A flexible grid embedding technique with application to the Euler equations. In: Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics and Astronautics (July 1983)

    Google Scholar 

  2. Reed, W., Hill, T.: Triangular mesh methods for the neutron transport equation. Technical report, Los Alamos Scientific Laboratory (1973)

    Google Scholar 

  3. Cockburn, B., Shu, C.: TVB Runge-Kutta local projection Discontinuous Galerkin finite element method for conservation law II: General framework. Mathematics of Computation 52(186), 411–435 (1989)

    MathSciNet  MATH  Google Scholar 

  4. Bassi, F., Rebay, S.: A high-order accurate Discontinuous Finite Element Method for the numerical solution of the compressible Navier-Stokes equations. Journal of Computational Physics 131, 267–279 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bassi, F., Crivellini, A., Rebay, S., Savini, M.: Discontinuous Galerkin solution of the Reynolds-averaged Navier-Stokes and k − ω turbulence model equations. Computers & Fluids 34, 507–540 (2005)

    Article  MATH  Google Scholar 

  6. Galbraith, M., Orkwis, P., Benek, J.: Extending the Discontinuous Galerkin scheme to the chimera overset method. In: Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics and Astronautics (June 2011)

    Google Scholar 

  7. Galbraith, M., Orkwis, P., Benek, J.: Discontinuous Galerkin scheme applied to chimera overset viscous meshes on curved geometries. In: Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics and Astronautics (June 2012)

    Google Scholar 

  8. Harten, A., Lax, P., Leer, B.: On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review 25(1), 35–61 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  9. Roe, P.: Approximate Riemann solvers, parameter vectors, and difference schemes. Journal of Computational Physics 43(2), 357–372 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bassi, F., Rebay, S., Mariotti, G., Pedinotti, S., Savini, M.: A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows. In: Decuypere, R., Dibelius, G. (eds.) 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, pp. 99–108. Technologisch Instituut, Antwerpen (1997)

    Google Scholar 

  11. Landmann, B., Keßler, M., Wagner, S., Krämer, E.: A parallel, high-order Discontinuous Galerkin code for laminar and turbulent flows. Computers & Fluids 37(4), 427–438 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Sen, S., Mittal, S., Biswas, G.: Steady separated flow past a circular cylinder at low Reynolds numbers. Journal of Fluid Mechanics 620, 89–119 (2009)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Wurst .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Wurst, M., Kessler, M., Krämer, E. (2015). A High-Order Discontinuous Galerkin Chimera Method for the Euler and Navier-Stokes Equations. In: Kroll, N., Hirsch, C., Bassi, F., Johnston, C., Hillewaert, K. (eds) IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 128. Springer, Cham. https://doi.org/10.1007/978-3-319-12886-3_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-12886-3_19

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12885-6

  • Online ISBN: 978-3-319-12886-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics