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

• Autorzy: Després B. , Lagoutiere F.
• 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 (Lagoutiere, 2005; Lagoutiere, 2006).

Słowa kluczowe

EN

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

PL

transport wielowymiarowy; schemat objętości skończonych; siatka trójkątów

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2007
• Tom: Vol. 17, no 3
• Strony: 321--328
• Opis fizyczny: Bibliogr. 9 poz., rys., wykr.

Twórcy

autor

Després B.

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

autor

Lagoutiere F.

• Université Paris-VII and Laboratoire Jacques-Louis, Lions, UMR 7598, 175, rue du Chevaleret, 75013 Paris, France

Bibliografia

• [1] Després B. and Lagoutière F. (2001): Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids. ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 35, No. 6, pp. 1159-1183.
• [2] Després B. and Lagoutière F. (2001): Contact discontinuity capturing schemes for linear advection and compressible gas dynamics. Journal of Scientific Computing. Vol. 16, No. 4, pp. 479-524.
• [3] Després B. and Lagoutière F. (2007): Numerical resolution of a two-component compressible fluid model with interfaces. Progress in Computational Fluid Dynamics, (to appear).
• [4] Lagoutière F. (2005): Stability of reconstruction schemes for scalar hyperbolic conservation laws. 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 athttp://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.
• [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.