To simulate the flow around a free oscillating cylinder in Re=200, you will need to use a dynamic mesh approach to account for the motion of the cylinder. The following changes may need to be made to the dynamic mesh settings to complete the solution:

Mesh deformation: You will need to define the deformation of the mesh in response to the motion of the cylinder. This can be done by specifying the motion of the cylinder as a function of time, and using an appropriate mesh deformation method such as the Arbitrary Lagrangian-Eulerian (ALE) method or the immersed boundary method.

Time step: The time step used in the simulation should be small enough to accurately capture the motion of the cylinder. The time step should be smaller than the characteristic time scale of the cylinder motion, which can be estimated using the natural frequency of the cylinder.

Solver settings: The solver settings may need to be adjusted to account for the dynamic mesh. For example, you may need to use a solver that is capable of handling moving meshes, such as the sliding mesh or overset mesh method.

Turbulence modeling: The choice of turbulence model can have a significant impact on the accuracy of the simulation. In the case of flow around a free oscillating cylinder, a turbulence model that is capable of capturing unsteady and separated flows may be required. The choice of turbulence model should be based on a validation study and/or prior experience.

Boundary conditions: The boundary conditions used in the simulation should be appropriate for the problem being solved. For example, the inflow and outflow boundaries should be far enough from the cylinder to avoid interference with the flow around the cylinder. The boundary conditions for the cylinder surface may also need to be adjusted to account for the motion of the cylinder.

Thank you for the answer sir, I feel like there's an issue with my mesh deformation because the boundary conditions, Turbulence modelling, solver settings are based on various research articles, for time step I had calculated the time step previously as per the method you mentioned and put the value as 0.001 but I'm unable to solve that also my knowledge is very limited on the ALE and Immersed Boundary Method. How should I proceed next sir?

In general, the Eulerian mesh is typically structured, meaning that it consists of regular shapes such as squares or triangles, and is fixed in space. The Lagrangian mesh, on the other hand, is typically unstructured, meaning that it consists of irregular shapes such as tetrahedra or hexahedra, and is allowed to deform and move with the object or boundary being simulated.

The shape and density of the Lagrangian mesh can be adjusted to optimize the accuracy and efficiency of the simulation. For example, in regions where the fluid flow is expected to be complex or highly localized, the Lagrangian mesh may be refined to capture the detailed flow features. Conversely, in regions where the fluid flow is expected to be relatively simple or uniform, the Lagrangian mesh may be coarsened to reduce computational cost.

Sir below I have attached the snippets of my updated mesh. Is this correct with what you have mentioned above?

Sir!??

I'm still unable to simulate the free oscillation without the negative volume error

To complete the solution for this problem, you may need to make certain changes to the dynamic mesh settings. Dynamic mesh refers to the ability to model fluid-structure interactions where the shape or position of the mesh changes during the simulation. Since the cylinder is oscillating, the mesh needs to deform accordingly to accurately capture the flow behavior. The specific changes required will depend on the software you are using for the simulation. Generally, you'll need to enable dynamic mesh, set appropriate boundary conditions, and define the motion of the cylinder. Additionally, you may need to adjust time-step size and other parameters to ensure stability and accuracy in the simulation.

I would recommend, if you have not already done it, letting the flowfield somewhat converge before allowing the cylinder motion. In other words, simulate some time steps without any cylinder motion, and then activate the possibility of the cylinder moving. I say this because typically in the fluid simulation you have a small transient at the beginning where forces can be quite high, and this may induce large non-physical motions of your cylinder.

It might be informative if you take a look at how much motion the cylinder is undergoing when you get these negative volumes, e.g. in terms of cylinder diameters. This can help you discern whether the problem is the mesh deformation (if the motion is small, less than 0.1 diameters I would say) or something else (if the motion is large).

Also, I would be wary of the previous answers here, as they seem to be generated with some kind of artificial intelligence tool. There are online tools to help you detect this. It might be fruitless to engage in conversation with people who only answer what chatGPT says...

specific changes that you can make to your dynamic mesh settings:

• Increase the mesh size. This will help to reduce the amount of distortion in the mesh.
• Increase the frequency of the dynamic mesh updates. This will ensure that the mesh is updated more frequently, which will help to prevent it from becoming too distorted.
• Adjust the remeshing parameters. This will help to ensure that the mesh is updated in a way that minimizes the negative cell volume errors.@Muthiah CT