Commun. Comput. Phys., 5 (2009), pp. 532-545.


A Family of Relaxation Schemes for Nonlinear Convection Diffusion Problems

Fausto Cavalli 1, Giovanni Naldi 2, Gabriella Puppo 3*, Matteo Semplice 2

1 Universita degli Studi di Brescia, Dipartimento di Matematica, Via Valotti, 9-25133 Brescia, Italy.
2 Universita degli Studi di Milano, Dipartimento di Matematica, Via Saldini 50, 20133 Milano, Italy.
3 Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

Received 28 September 2007; Accepted (in revised version) 1 March 2008
Available online 1 August 2008

Abstract

In this work we present a family of relaxation schemes for nonlinear convection diffusion problems, which can tackle also the cases of degenerate diffusion and of convection dominated regimes. The schemes proposed can achieve any order of accuracy, give non-oscillatory solutions even in the presence of singularities and their structure depends only weakly on the particular PDE being integrated. One and two dimensional results are shown, and a nonlinear stability estimate is given.

AMS subject classifications: 65M20, 65M12, 35K65

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Key words: Convection-diffusion, relaxation schemes, degenerate parabolic problems.

*Corresponding author.
Email: fausto.cavalli@ing.unibs.it (F. Cavalli), naldi@mat.unimi.it (G. Naldi), gabriella.puppo@polito.it (G. Puppo), semplice@mat.unimi.it (M. Semplice)
 

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