[bouloumag]

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.