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 < 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 > >  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.