Why do oscilations appear when reducing the time step?
 

Hi,

I am simulating a flow past a circular cylinder, and according to references, the fluid flow establishes a oscilating pattern.
Using a certain time step, there is a deviation (5%) in the frequency of my simulation and the claimed frequency in references. For this reason I have reduced the time step in order to obtain better accuracy.
But, when reducing the time step of the simulation, several small oscilations appear additionally to the main oscilation expected. Why are these small oscialtions appearing? Which is the physics behind these oscilations?
I was wondering if there could be an error in the implementation of the algorithm.

Best regards,
Hector.

an error in the implementation is always possible but it would imply that your time integration method is not consistent at all...
On the other hand, reducing the computational time step means an increasing in the Nyquist cut-off pi/dt, therefore you velocity field can show more frequencies. But this is relevant in DNS/LES formulation, what are you using?

Hi Filippo,
Thanks for your reply.

I do not use any turbulence model. The simulation is for laminar flow. No DNS or LES formulation is used.

Then, according to your statement, it could be an error in the integration method.
The algorithm contains a relaxation factor for the integration method.
Right now, I have set this relaxation factor to 0.6666, which means that 0.666 times of the velocity at time n is take into account and 0.333 times of the velocity at time n+1 is take into account.

Based on your suggestion, the problem could be in the value used for this relaxation factor.

Best regards,
Hector.

What is your Reynolds number?

Oh, and given your time step, what is your maximum CFL number?

well, he wrote that diminuishing the time step oscillations appear, that would exclude a numerical instability....

My thought was that he might be using an implicit method.

Edit: Or something with dual time stepping, in which case the max CFL for the outer loop is the number I'm interested in.

The Reynolds number is 100 (Which I consider is laminar).

The maximum time step for the algorithm that fulfills the CFL condition is 0.001 (both convective and diffusive limitation), and initially I am using 0.0005 as time step for the simulation. With this value, no small oscilations happens. When using 0.0001 (even more reduced value) as time step for the simulation is when the small osicilations appear.

I am using an implicit method in the equation of the pressure. The value of the relaxation factor for the pressure equation I am using is 0.666.
The type of algortithm I am using is the so called Characteristics Based Split algorithm (CBS), that uses a split scheme with a correction step once the pressure is calculated.
So, both relaxation factors I am using:
One for the velocity (explicit equation): 0.6666
Another for the pressure (implicit equation): 0.6666

could you post some results showing the comparison for both time step?

A further issue to check is the threshold for the iterative solvers, it could be useful to diminuish it according to the time step

What time stepping scheme you are using.

Also is it a collocated solver? Because pressure velocity may decouple at small time steps and could give you oscillations or checkerboarding.

I am attaching the results I am getting:
- VelocityYDirectionTimeStep1 When using a time step of 0.0005
- VelocityYDirectionTimeStep2 When using a time step of 0.0002

As you can see, when reducing the time step, some oscilations appear in between the main oscilations of the pattern flow.

Try reducing all thresholds in the iterative solvers.

My area of knowledge is centered around implicit compressible time marching methods. So I'm not sure if that carries over to what you're doing. However, a CFL of 0.5 may be too large to insure accurate time marching for a method with an explicit component. It may be stable but possibly not accurate. One may need to go for dual time stepping, fully implicit, higher order time discretization, or lower CFL to achieve higher time accuracy.

That being said, an Re of 100 is low, so unless your grid is really coarse, I don't see what what the problem is. Hopefully one of the other posts above helps you out.

Good luck,

BTW, I am assuming that the boundary conditions are implemented correctly and that grid is not being subdivided. If the grid is being subdivided and distributed to more than one processor then the B.C.s at the grid edges may be lagged. In which case dual time stepping might be required. But, I'm not sure if that applies to your algorithm.

the shape of oscillations makes me suppose that you should try to work on the residuals, try two order of magnitude lower.

Do you check similar problem by refining the spatial grid?

This problem does not appear in a coarse grid.
It has appeared when I have used a finer grid.

I understand that your statement "to work on the residuals," refers to the tolerance (threshold) of the iterative solver, doesn't it?

but you have simultaneously decreased both the time step and the grid sizes?

Yes I have drecreased both time step and grid size simultaneously, since the shorter the grid the more reduced the time step should be used. Otherwise the solution does not converge.

and what about the ratio dt/h, it results increased on the refined grid?

I have kept constant the dt/h ratio between grids.