Skip to main content

Weno Scheme for Transport Equation on Unstructured Grids with a DDFV Approach

  • Conference paper
  • First Online:
Book cover Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems (FVCA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 200))

Included in the following conference series:

  • 1322 Accesses

Abstract

In this paper we develop a DDFV approach for WENO scheme on unstructred grids for 2D transport equations. An order 2 scheme is presented using the DDFV diamond structure to define the different stencils. Numerical tests illustrate the accuracy and robustness of the method.

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

Access this chapter

Institutional subscriptions

References

  1. Abgrall, R.: On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation. J. Comput. Phys. 114(1), 45–58 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. Clain, S., Diot, S., Loubère, R.: A high-order finite volume method for hyperbolic systems: Multi-dimensional Optimal Order Detection (MOOD). J. Comput. Phys. pp. 0–0 (2011)

    Google Scholar 

  3. Domelevo, Komla, Omnes, Pascal: A finite volume method for the laplace equation on almost arbitrary two-dimensional grids. ESAIM: Math. Model. Numer. Anal. (Modlisation Mathmatique et Analyse Numrique) 39(6), 1203–1249 (2005)

    Google Scholar 

  4. Eymard, R., Gallout, T., Herbin, R.: Finite volume methods. In: Solution of Equation in n (Part 3), Techniques of Scientific Computing (Part 3), Handbook of Numerical Analysis, vol. 7, pp. 713–1018. Elsevier (2000). http://dx.doi.org/10.1016/S1570-8659(00)07005-8. http://www.sciencedirect.com/science/article/pii/S1570865900070058

  5. Friedrich, O.: Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids. J. Comput. Phys. 144(1), 194–212 (1998)

    Article  MathSciNet  Google Scholar 

  6. Harten, A., Engquist, B., Osher, S., Chakravarthy, S.R.: Uniformly high order accurate essentially non-oscillatory schemes, iii. J. Comput. Phys. 131(1), 3–47 (1997)

    Article  MATH  Google Scholar 

  7. Harten, A., Osher, S.: Uniformly high-order accurate nonoscillatory schemes. I. SIAM J. Numer. Anal. 24(2), 279–309 (1987). doi:10.1137/0724022

    Article  MathSciNet  MATH  Google Scholar 

  8. Harten, A., Osher, S., Engquist, B., Chakravarthy, S.R.: Some results on uniformly high-order accurate essentially nonoscillatory schemes. Appl. Numer. Math. 2(3), 347–377 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hermeline, F.: A finite volume method for the approximation of diffusion operators on distorted meshes. J. Comput. Phys. 160(2), 481–499 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hu, C., Shu, C.W.: Weighted essentially non-oscillatory schemes on triangular meshes. J. Comput. Phys. 150(1), 97–127 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  11. Krell, S.: Schémas volumes finis en mécanique des fluides complexes. Ph.D. thesis, Aix-Marseille Université (2010)

    Google Scholar 

  12. LeVeque, R.J.: High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 33(2), 627–665 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  13. Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77(2), 439–471 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zalesak, S.T.: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys. 31(3), 335–362 (1979)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Florence Hubert or Rémi Tesson .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Hubert, F., Tesson, R. (2017). Weno Scheme for Transport Equation on Unstructured Grids with a DDFV Approach. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_2

Download citation

Publish with us

Policies and ethics