FSLBM one-way coupling to Advection-Diffusion Equation

[Danial.Khazaeipoul]

Dear community,

I would like to know about the feasibility of directly integrating the FSLBM sub-model with the advection-diffusion equation.

While it appears relatively straightforward to link the LBM sub-model to the advection-diffusion equation through either NavierStokesAdvectionDiffusionCoupling or NavierStokesAdvectionDiffusionVelocityCoupling structs, based on whether the coupling is two-way or one-way, I’m uncertain how these methods apply to the FSLBM sub-model, particularly considering that the gas field is not solved within this model.

Regards,
Danial

[Adrian]

Coupling ADE to a free surface model for the fluid phase should be possible in the way you describe (there may be some modification required in the specific coupling operator you want to use). Of course transport within the gas phase won’t be covered by such a combined model by definition.

[Danial.Khazaeipoul]

Thank you for your assistance, Adrian.

I have tried to start with a much simpler problem involving Poiseuille flow within a 3d pipe. The following steps are taken in order to prepare the benchmark case for OpenLB:

1. For the Navier-Stokes submodel a D3Q19<> was used with BGKdynamics and following BCs and ICs:

(a) Pipe wall: setBounceBackBoundary (No-slip zero velocity)
(b) Pipe inlet: setInterpolatedVelocityBoundary (CirclePoiseuille3D)
(c) Pipe outlet: setInterpolatedPressureBoundary
(d) Initial condition: Pressure and velocity are initialized according to the analytical solution.

2. For the Advection-Diffusion submodel a D3Q7<VELOCITY> was used with AdvectionDiffusionBGKdynamics and following BCs and ICs:

(a) Pipe wall: setBounceBackBoundary (Fixed value concentration, i.e., 0.0)
(b) Pipe inlet: setAdvectionDiffusionTemperatureBoundary (Fixed value concentration, i.e., 1.0)
(c) Pipe outlet: setZeroGradientBoundary
(d) Initial condition: Concentration is initialized to zero throughout the domain.

The sub-model for the Navier-Stokes solves the flow problem correctly. However, I am facing a problem when solving for the concentration field as it seems that the pipe’s wall has no effect on concentration distribution within the pipe. According to the benchmark, one should expect parabolic concentration profile but in my case, the wall seems to have no effect and the average concentration approaches to 1.0 as the simulation evolves through time.

I have tried to further investigate this by examining the microMixer3d example and it seems to me that the same behavior is also occurring there. I am suspecting the bounceback boundary on the walls might be responsible for this behavior, but not sure why it works perfectly fine within the Navier-Stokes submodel. Is the fact that the advection-diffusion dynamics uses equilibria::FirstOrder relevant here?

[Danial.Khazaeipoul]

I am trying to post images to compare the concentration field distribution between benchmark, COMSOL, and OpenLB simulations to describe the problem more clearly but it seems that I can not include links into my post the in the forum.

[shota]

Please send us the pictures via mail or upload them and send us a link, then we can have more insight into your issue.

[Danial.Khazaeipoul]

Dear shota,

Since I was not able to post pictures here, I created an issue on OpenLB’s gitlab repository but I am not sure if it is getting monitored.

[shota]

Dear Danial,

thank you for your notice. We will have a look on your issue and reply on gitlab.

[Author]

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