I use TVD limiters to calculate the linear pure convective equation to find that the limiters such as superbee, minmod, can still lead to a solution with unphysical oscillation, when The C.F.L. number is less than one. When i reduce the CFL number, the things became much better. I want to know the relation between CFL number and TVD property.(For my problem, it seems that CFL of one is a little larger for the superbee and minmod, etc.) Is there some mathematic explaination? Thanks in advance!

PS: The time adopts 1-order explicit scheme

These are very math-related issue. You can find many book mentioning about the stability and the TVD properties. In my case, I used the minmod limiter to reduce the oscillation at the discontinuities. It worked well.

In my solutions, there were no oscillations.

Thanks, if your CFL number is larger than 1(for example), can the minmod limiter cause osillations in your code?

In my code, cfl number is about 0.5. As far as I know, the CFL number should be less than 1.0 for stability. And if I used cfl=1.0, my code would also show the oscillation.

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