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

• Autorzy: Bruno Després , Frédéric Lagoutière
• Języki publikacji: EN

Abstrakty

EN

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)

Słowa kluczowe

EN

anti-dissipative schemes; multidimensional transport; finite-volume schemes; triangular grids

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2007
• Tom: 17
• Numer: 3
• Strony: 321-328

Daty

wydano

2007

Twórcy

autor

Bruno Després

• Commissariat à l'Énergie Atomique, DIF/DSSI, 91680 Bruyères-le-Châtel, France

autor

Frédéric Lagoutière

• Université Paris-VII and Laboratoire Jacques-Louis Lions, UMR 7598, rue du Chevaleret, 75013 Paris, France

Bibliografia

• 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.
• 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.
• Després B. and Lagoutière F. (2007): Numerical resolution of a two-componentcompressible fluid model with interfaces. Progress in Computational Fluid Dynamics, (to appear).
• Lagoutière F. (2005): Stability of reconstruction schemes for scalar hyperbolic conservationlaws. Preprint available at http://www.ann.jussieu.fr/publications/2005/R05004.html.
• Lagoutière F. (2006): Non-dissipative reconstruction schemes satisfying entropy inequalities. Preprint available at tt http://www.ann.jussieu.fr/publications/2006/R06017.html.
• 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.
• Noh W.F. and Woodward P.R. (1976): SLIC (Simple Line Interface Calculation). Lecture Notes in Physics, Vol.25, Berlin: Springer, pp.330-339.
• 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.
• Zalesak S.T. (1979): Fully multidimensional flux-corrected transport algorithms for fluids. Journal of Computational Physics, Vol.31, No.3, pp.335-362