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Volume 5, Issue 2-4
A Family of Relaxation Schemes for Nonlinear Convection Diffusion Problems

Fausto Cavalli, Giovanni Naldi, Gabriella Puppo & Matteo Semplice

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

Published online: 2009-02

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  • 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.

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@Article{CiCP-5-532, author = {Fausto Cavalli, Giovanni Naldi, Gabriella Puppo and Matteo Semplice}, title = {A Family of Relaxation Schemes for Nonlinear Convection Diffusion Problems}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {2-4}, pages = {532--545}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7748.html} }
TY - JOUR T1 - A Family of Relaxation Schemes for Nonlinear Convection Diffusion Problems AU - Fausto Cavalli, Giovanni Naldi, Gabriella Puppo & Matteo Semplice JO - Communications in Computational Physics VL - 2-4 SP - 532 EP - 545 PY - 2009 DA - 2009/02 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7748.html KW - AB -

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.

Fausto Cavalli, Giovanni Naldi, Gabriella Puppo and Matteo Semplice. (2009). A Family of Relaxation Schemes for Nonlinear Convection Diffusion Problems. Communications in Computational Physics. 5 (2-4). 532-545. doi:
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