Skip to main content
SpringerLink
Log in
Book cover

Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects pp 169–176Cite as

Conservative Finite Differences as an Alternative to Finite Volume for Compressible Flows

  • Conference paper
  • First Online:

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 77))

Abstract

Finite Volume schemes are the natural choice when simulating flows with shocks, since conservation is essential in the physics and as such in the simulation of this phenomenon. But finite difference schemes can be conservative as well. Conservation requires in such schemes a high internal consistency of the spatial and the temporal discretization. We present a skew-symmetric finite difference scheme, which is fully conservative due to its consistency, still easy to implement and numerically efficient. A variety of different flow configurations containing shocks and turbulence are presented.

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

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 EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
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

Learn about institutional subscriptions

References

  1. Bogey, C., De Cacqueray, N., Bailly, C.: A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations. JCP 228(5), 1447–1465 (2009)

    Article  MATH  Google Scholar 

  2. Brouwer, J., Reiss, J., Sesterhenn, J.: Fully conservative finite-difference schemes of arbitrary order for compressible flow. AIP Conf. Proc. 1479(1), 2290–2293 (2012)

    Article  Google Scholar 

  3. Brouwer, J., Reiss, J., Sesterhenn, J.: Conservative time integrators of arbitrary order for finite-difference discretization of compressible flow (2013). Submitted to Computers & Fluids

    Google Scholar 

  4. Kok, J.: A high-order low-dispersion symmetry-preserving finite-volume method for compressible flow on curvilinear grids. JCP 228(18), 6811 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Lee, B.: Self-sustained shock oscillations on airfoils at transonic speeds. Prog. Aerosp. Sci. 37(2), 147–196 (2001)

    Article  Google Scholar 

  6. Lund, T.: Generation of turbulent inflow data for spatially-developing boundary layer simulations. JCP 140, 233–258 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Morinishi, Y.: Forms of convecction and quadratic conservative finite difference schemes for low mach number compressible flow simulations. Trans. Jap. Soc. Mech. Eng. B (2007)

    Google Scholar 

  8. Pirozzoli, S., Bernardini, M.: Turbulence in supersonic boundary layers at moderate reynolds number. J. Fluid Mech. 688, 120 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pirozzoli, S., Bernardini, M., Grasso, F.: Direct numerical simulation of transonic shock/ boundary layer interaction under conditions of incipient separation. JFM 657, 361 (2010)

    Article  MATH  Google Scholar 

  10. Reiss, J., Sesterhenn, J.: A conservative, skew-symmetric finite difference scheme for the compressible navier-stokes equations. Accepted by Computers and Fluids

    Google Scholar 

  11. Strand, B.: Summation by parts for finite difference approximations for d/dx. JCP 110, 47 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  12. Verstappen, R., Veldman, A.: Symmetry-preserving discretization of turbulent flow. JCP 187(1), 343 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. TU Berlin, ISTA, Mueller-Breslau Str. 8, 10623, Berlin, Germany

    Jens Brouwer, Julius Reiss & Jörn Sesterhenn

Authors
  1. Jens Brouwer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Julius Reiss
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jörn Sesterhenn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jens Brouwer .

Editor information

Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

  2. Institute Comp. Applied Mathematics, University of Münster Center for Nonlinear Sciences (CeNoS ), Münster, Germany

    Mario Ohlberger

  3. Inst. Appl. Analysis and Num. Simulation, University of Stuttgart, Stuttgart, Germany

    Christian Rohde

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Brouwer, J., Reiss, J., Sesterhenn, J. (2014). Conservative Finite Differences as an Alternative to Finite Volume for Compressible Flows. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_15

Download citation

Publish with us

Policies and ethics

Search

Navigation