why tvd limiter can lead to oscillation
 

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

Re: why tvd limiter can lead to oscillation
 

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.

Re: why tvd limiter can lead to oscillation
 

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

Re: why tvd limiter can lead to oscillation
 

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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