Le mardi 17 juillet 2012 12:09:54 UTC-4, (inconnu) a écrit : > Le dimanche 15 juillet 2012 12:29:05 UTC-4, bouloumag a écrit : > > A class of TVD scheme was developed by Sweby where a flux limiter is added to the Second Order Upwind (SOU) schemes differencing scheme to prevent the formation of oscillations in the scalar field. > > > > I am interested by the CFL restriction of these scheme in the context of the explicit forward euler time integration. > > > > One important property of the SOU discussed by Leonard  is that even-order upwind schemes have a two times wider stability interval than odd-order ones. Thus, SOU is stable at the extended interval 0 &lt; CFL &lt; 2. > > > > Question : Are there any TVD scheme based on SOU that also preserve stability for CFL &lt; 2 or more ? > > > > Thanks for your help ! > > > > Christine > > > >  P. K. Sweby. High resolution schemes using flux limiters for hyperbolic conservation laws. > > SIAM Journal of Numerical Analysis, 21(5):995?1011, 1984. > > > >  Leonard, B. P. Stability of explicit advection schemes. The > > balance point location rule. > > Int. J. Numer. Meth. Fluids 38, 471 ?514, 2002. > > The minmod limiter is just a simple switch between the Beam-Warming and the Lax-Wendroff method. Both schemes are stable for clf < 2.
Thanks for your answer, but I am a little confused ...
Isn't this Lax-Wendroff equivalent to the central difference scheme (phi=1 in the Sewby diagram) ? It is only stable for clf<=1 as far as I know.
As the SOU (Beam-Warming ?) is given by phi=r in the diagram and is TVD up to phi=2, I think that a limiter of the form