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

Bruno Després; Frédéric Lagoutière

doi:10.2478/v10006-007-0026-z

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

International Journal of Applied Mathematics and Computer Science

Volume 17 (2007): Issue 3 (September 2007)

By: Bruno Després and Frédéric Lagoutière

Open Access

|Oct 2007

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).

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