What's the causes of numerical oscillation?
 

What's the causes of numerical oscillation?

By taking the Fourier transformation, I find an oscillation in my solution with scaled wavenumber 3.14.

How such things can happen? I am using centered difference and RK method.

Thank you in advance.

I am not sure about the scaled wave number. Is it with respect to the cell width?

Anyway, I will try to provide a few points for cause of oscillations.

1)
In CFD, oscillations mostly occur at discontinuities. While solving, the numerical schemes try to fit the solution with a function, the degree of which would determine the order of the underlying scheme. Now, in the presence of discontinuities, a function approximation near the discontinuous solution would result in the so called Gibbs phenomenon. This becomes much more serious with higher order schemes.

2)
Oscillations can also occur due to the flux approximations. A less diffusive HLLC scheme would have more oscillations than the diffusive Lax Friedrich flux.

3)
Depending on the stability of numerical scheme, the (unstable) schemes could support certain modes of oscillations which can grow in time. A weakly unstable scheme can provide a better CFL limit, but would need some way of dissipating the unstable waves. For a central difference scheme, this would not be the case.

What about mesh size?
 

Hi to everybody,
I just want to know that does mesh size also play role in numerical oscillations? I have used tetrahedral mesh of size 7mm with size function attached to the airfoil which i have to study was of size 5mm which gradually increases merges with tetrahedral grid which as i have aforesaid was of size 7mm. I have applied unsteady DES and Standard k-omega model both are showing oscillations in converging solution. Thus i want to ask whether mesh size affects the oscillations in solutions.