Interesting equation- follow

It's Normal, the physical equation is converted into a numerical equation and in the digital domain the mass that leaves and enters is not the same. that's why we set the convergence conditions

Hi Narendra,

As you mentioned the discontinuity problem is usually due to mesh size. However, the number of iterations can be the reason.

About the Cr (Courant nu.):

It is not a general rule to determine the value of Cr for all of the problems. However, for most of incompressible fluid flow casee, the Cr < 1 is an appropriate choice. I faced with problems that converged with higher Cr numbers, and some problems with very lower Cr (such as Cr < 0.1 ).

Hi Ali Minaeian , As I refine the mesh, I was expecting better convergence and mass balance but continuity residual stopped dropping below 1.4e-4 and mass imbalance is around 4%. For coarser mesh, mass imbalance was less than 0.5%.

As I am using implicit scheme, I can use Courant number more than 1. on the other side, reducing Courant number (

Yes. As I mentioned in my first comment, the problem should be solved in another way. The Cr was because of your question about that.

Theory Guide is quite open to misinterpretation. Paragraph 16.3.7 clearly declares that for unsteady simulations, the VOF equation, and I quote: is solved using an explicit time-marching scheme. So my suggestion is to try a very low Courant (best-practices about VOF suggest CFL

Hello Narendra Patel

Your explanation was a little ambiguous for me,

is it a transient or steady simulation?

Did you do mesh independence study?

Marco Fontana and Mahdi Rezaei Adariani it's a steady state flow simulation. I am using implicit scheme so Cr can be greater than 1. I am not sure if we select courant number based on steady/unsteady type of problem. @Mahdi, it's part of my mesh independent study.

Narendra Patel

But if it is steady-state, why you need CFL? I mean CFL is a relation between velocity, mesh size and time step. Also coupled solver is a combination of Piso and simple algorithms, which is not designed for steady-state simulations.

Mahdi Rezaei Adariani Ansys requires Courant number , not necessary to satisfy CFL condition. I am not sure about that Coupled algo can not be used for steady state.

Narendra Patel

Here are some hints may help you to complete your simulation:

1) Try to have a logic mesh. I mean redo your mesh to have fine mesh in the regions that you will have a high gradient, boundary layer mesh and so on. you can read my answer regarding meshing rules here :

https://www.researchgate.net/post/How_can_I_understand_mesh_quality_and_simulation_results_in_CFD

2) Select a correct solver depends on your flow behaviour. If you want to do steady-state simulation, select simple solver and then you have to pay attention to relaxation factors instead of CFL. In fact, Fluent required CFL because you have selected a transient solver(coupled solver).

3) You can follow this procedure (https://www.computationalfluiddynamics.com.au/convergence-and-mesh-independent-study/) for mesh independence study and mass balance.

4) Residual less than 10-4 could be acceptable in your case, I think.

Let me know if you have further question.

Good luck

Mahdi Rezaei Adariani Thanks for useful info.

Dear Narendra,

In my experience and based upon the foundations, the procedure you dealt with is wrong. The courant number condition is designed to guarantee companion of time scale and length scale, so using 10 for courant number is that like the time scale is ten times of length scale, or in other words, the equations solve once for ten-time scales. That is a mistake as far as I know and result in divergent and diffusion. In this regard, I agree with @ Marco Fontana and your courant number must be not more than 1.

regards

Dear Hamed Majidian

Coupled solver is designed for courant number bigger than 1. In fact, it is a combination of piso solver(transient) and simple solver (steady). To my knowledge, It works exactly as same as pimple solver in OpenFoam.

So based on what you are looking for in the simulation, this solver can accept CFL even around 20.

Dear @Mahdi Rezaei Adariani

Thanks for your clarification, so what is the point of using large courant number?

Dear Hamed Majidian

If you look at the courant number definition, you will see that the only parameter to change with larger courant number is time step while normally, the velocity and mesh size are constant.

In other words, the main advantage of using large Courant numbers is that the time step can be increased drastically. That means solver will increase the time step to satisfy this Courant number and therefore the simulation will be faster.

Here is the explanation of how this algorithm works:

Within a one-time step, we do a steady-state simulation with under-relaxation factors until predefined convergence criteria (In Ansys Fluent under Run Calculation section, you can define the number of iteration for this loop on Max Iteration/Timestep).

After that, we leave steady-state simulation and move on in time.

This is done until we reach the end time of the simulation.

Dear @Mahdi Rezaei Adariani

Yet the case is vague to me, since reducing time will be penaltilized by divergence and diffusion. Practically, it could work but not equally for all part of the body or domain, so is it possible in Fluent to set courant number regionally? For certainly only far fields do not require accurate solution, but when it comes to bluff body, reduction of courant number even less than 1 would be advantagous in accuracy wise.

Dear Hamed Majidian

Its all depends on what you are looking for in the simulation. Of course, this solver is not suitable for all the CFD cases. for example in combustion simulations or calculation of drag and lift on a body, this methodology does not work well. You must keep courant number even around 0.3 to have an accurate solution.

This kind of solvers is really useful when you are looking for a general solution of flow filed without specific details in some regions. mostly industrial cases.

To clarify that, it is exactly as same as using wall functions or resolve the boundary layer in turbulence cases. I hope you get the point now.

Thanks a bunch dear @Mahdi Rezaei Adariani However, based on the model of case here, I am not sure if high courant number works well, since K-epsilon RNG is a high reynolds number turbulence model, and thus may raise issue in capturing of whole behavior of fluid field in channel. By the way, what you are saying is totally right.

Hamed Majidian K-E RNG can simulate both high and low Renolds number flows. You have to activate Differential term in the model to account low Renolds number effects.

Dear @Narendra Patel

Certainly it does, even simpler models could, however, it does not primarily suit for low Reynolds number purpose, while k-omega exists. K-epsilon models employ some kind of treatments for low Reynolds number, because in low Reynolds regions term k^2/epsilon yeilds to zero or undefined value so that turns turbulence viscosity to zero or undefined value which results in diffusion. To this end, RNG and other k-epsilon models have been developed for dealing with this issue. Nontheless, k-omega is particularly recommended for low Reynolds number regions.