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Re: Flux limiter and explicit method CFL restriction
Posted:
Jul 17, 2012 2:01 PM


Le mardi 17 juillet 2012 12:09:54 UTC4, (inconnu) a écrit : > Le dimanche 15 juillet 2012 12:29:05 UTC4, bouloumag a écrit : > > A class of TVD scheme was developed by Sweby[1] 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 [2] is that evenorder upwind schemes have a two times wider stability interval than oddorder 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 > > > > [1] P. K. Sweby. High resolution schemes using flux limiters for hyperbolic conservation laws. > > SIAM Journal of Numerical Analysis, 21(5):995?1011, 1984. > > > > [2] 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 BeamWarming and the LaxWendroff method. Both schemes are stable for clf < 2.
Thanks for your answer, but I am a little confused ...
Isn't this LaxWendroff 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 (BeamWarming ?) is given by phi=r in the diagram and is TVD up to phi=2, I think that a limiter of the form
min(r, something smaller or equal to 2)
should be a good candidate.



