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Paper details
Number 3 - September 2007
Volume 17 - 2007
Genuinely multi-dimensional non-dissipative finite-volume schemes for transport
Bruno Després, Frédéric Lagoutière
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).
Keywords
multidimensional transport, finite-volume schemes, anti-dissipative schemes, triangular grids