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Topic: Flux limiter and explicit method CFL restriction
Replies: 2   Last Post: Jul 17, 2012 2:01 PM

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bouloumag@gmail.com

Posts: 10
Registered: 7/31/08
Re: Flux limiter and explicit method CFL restriction
Posted: Jul 17, 2012 2:01 PM
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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[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 even-order upwind schemes have a two times wider stability interval than odd-order ones. Thus, SOU is stable at the extended interval 0 < CFL < 2.
> >
> > Question : Are there any TVD scheme based on SOU that also preserve stability for CFL < 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 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

min(r, something smaller or equal to 2)

should be a good candidate.



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