Genuinely multi-dimensional non-dissipative finite-volume schemes for transport

Bruno Després; Frédéric Lagoutière

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 3, page 321-328
  • ISSN: 1641-876X

Abstract

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We develop a new multidimensional finite-volume algorithm for transport equations. This algorithm is both stable and non-dissipative. It is based on a reconstruction of the discrete solution inside each cell at every time step. The proposed reconstruction, which is genuinely multidimensional, allows recovering sharp profiles in both the direction of the transport velocity and the transverse direction. It constitutes an extension of the one-dimensional reconstructions analyzed in (Lagoutière, 2005; Lagoutière 2006)

How to cite

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Després, Bruno, and Lagoutière, Frédéric. "Genuinely multi-dimensional non-dissipative finite-volume schemes for transport." International Journal of Applied Mathematics and Computer Science 17.3 (2007): 321-328. <http://eudml.org/doc/207839>.

@article{Després2007,
abstract = {We develop a new multidimensional finite-volume algorithm for transport equations. This algorithm is both stable and non-dissipative. It is based on a reconstruction of the discrete solution inside each cell at every time step. The proposed reconstruction, which is genuinely multidimensional, allows recovering sharp profiles in both the direction of the transport velocity and the transverse direction. It constitutes an extension of the one-dimensional reconstructions analyzed in (Lagoutière, 2005; Lagoutière 2006)},
author = {Després, Bruno, Lagoutière, Frédéric},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {anti-dissipative schemes; multidimensional transport; finite-volume schemes; triangular grids; numerical examples; transport equations; algorithm; reconstruction},
language = {eng},
number = {3},
pages = {321-328},
title = {Genuinely multi-dimensional non-dissipative finite-volume schemes for transport},
url = {http://eudml.org/doc/207839},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Després, Bruno
AU - Lagoutière, Frédéric
TI - Genuinely multi-dimensional non-dissipative finite-volume schemes for transport
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 3
SP - 321
EP - 328
AB - We develop a new multidimensional finite-volume algorithm for transport equations. This algorithm is both stable and non-dissipative. It is based on a reconstruction of the discrete solution inside each cell at every time step. The proposed reconstruction, which is genuinely multidimensional, allows recovering sharp profiles in both the direction of the transport velocity and the transverse direction. It constitutes an extension of the one-dimensional reconstructions analyzed in (Lagoutière, 2005; Lagoutière 2006)
LA - eng
KW - anti-dissipative schemes; multidimensional transport; finite-volume schemes; triangular grids; numerical examples; transport equations; algorithm; reconstruction
UR - http://eudml.org/doc/207839
ER -

References

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  1. Després B. and Lagoutière F. (2001): Generalized Harten formalism and longudinal variation diminishing schemes for linear advection on arbitrary grids. ESAIM: Mathematical Modelling and Numerical Analysis, Vol.35, No.6, pp.1159-1183. Zbl1005.76063
  2. Després B. and Lagoutière F. (2001): Contact discontinuity capturing schemes for linear advection and compressible gasdynamics. Journal of Scientific Computing. Vol.16, No.4, pp.479-524. Zbl0999.76091
  3. Després B. and Lagoutière F. (2007): Numerical resolution of a two-componentcompressible fluid model with interfaces. Progress in Computational Fluid Dynamics, (to appear). Zbl1152.76443
  4. Lagoutière F. (2005): Stability of reconstruction schemes for scalar hyperbolic conservationlaws. Preprint available at http://www.ann.jussieu.fr/publications/2005/R05004.html. 
  5. Lagoutière F. (2006): Non-dissipative reconstruction schemes satisfying entropy inequalities. Preprint available at tt http://www.ann.jussieu.fr/publications/2006/R06017.html. 
  6. Mosso S. and Cleancy S. (1995): A geometrical derived priority system for Young's interface reconstruction. Technical Report No.LA-CP-95-0081, Los Alamos National Laboratory. 
  7. Noh W.F. and Woodward P.R. (1976): SLIC (Simple Line Interface Calculation). Lecture Notes in Physics, Vol.25, Berlin: Springer, pp.330-339. Zbl0382.76084
  8. Youngs D.L. (1984): An interface tracking method for a 3D eulerian hydrodynamics code. Technical Report No.44/92/35, A.W.R.E. Aldermaston. 
  9. Zalesak S.T. (1979): Fully multidimensional flux-corrected transport algorithms for fluids. Journal of Computational Physics, Vol.31, No.3, pp.335-362 Zbl0416.76002

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