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Flux limiter and explicit method CFL restriction
Posted:
Jul 15, 2012 12:29 PM


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 < 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.



