<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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).</p></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).

Genuinely Multi-Dimensional Non-Dissipative Finite-Volume Schemes for Transport

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

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

International Journal of Applied Mathematics and Computer Science

{"article-title":"Genuinely Multi-Dimensional Non-Dissipative Finite-Volume Schemes for Transport"}

We develop a new multidimensional finite-volume algorithm for transport equations. This algorithm is both stable and non-dissipative. It is based on a...

Genuinely Multi-Dimensional Non-Dissipative Finite-Volume Schemes for Transport

Published Online: Oct 11, 2007

Page range: 321 - 328

DOI: https://doi.org/10.2478/v10006-007-0026-z

Keywords
multidimensional transport, finite-volume schemes, anti-dissipative schemes, triangular grids

This content is open access.

Genuinely Multi-Dimensional Non-Dissipative Finite-Volume Schemes for Transport

Published Online: Oct 11, 2007

Page range: 321 - 328

DOI: https://doi.org/10.2478/v10006-007-0026-z

Keywordsmultidimensional transport, finite-volume schemes, anti-dissipative schemes, triangular grids

This content is open access.

Keywords
multidimensional transport, finite-volume schemes, anti-dissipative schemes, triangular grids