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.
A Family of Relaxation Schemes for Nonlinear Convection Diffusion Problems / F. Cavalli, G. Naldi, G. Puppo, M. Semplice. - In: COMMUNICATIONS IN COMPUTATIONAL PHYSICS. - ISSN 1815-2406. - 5:2-4(2009 Feb), pp. 532-545.
A Family of Relaxation Schemes for Nonlinear Convection Diffusion Problems
G. NaldiSecondo
;M. SempliceUltimo
2009
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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