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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

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 :
> &gt; 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.
> &gt;
> &gt; I am interested by the CFL restriction of these scheme in the context of the explicit forward euler time integration.
> &gt;
> &gt; 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 &amp;lt; CFL &amp;lt; 2.
> &gt;
> &gt; Question : Are there any TVD scheme based on SOU that also preserve stability for CFL &amp;lt; 2 or more ?
> &gt;
> &gt; Thanks for your help !
> &gt;
> &gt; Christine
> &gt;
> &gt; [1] P. K. Sweby. High resolution schemes using flux limiters for hyperbolic conservation laws.
> &gt; SIAM Journal of Numerical Analysis, 21(5):995?1011, 1984.
> &gt;
> &gt; [2] Leonard, B. P. Stability of explicit advection schemes. The
> &gt; balance point location rule.
> &gt; 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 &lt; 2.

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.

Date Subject Author
7/15/12 bouloumag@gmail.com
7/17/12 bigorneault@gmail.com
7/17/12 bouloumag@gmail.com