Can Zou/He boundary conditions be applied in the thermal case study?

Hi everyone,
Zou/He boundary conditions (for velocity and pressure) are widely used in the resolution of momentum LBM equation. The question is , if i’m dealing with a coupled problem (mass+ heat), can i apply those boundary conditions to the thermal field also? (i’m using the double distribution functions thermal model : “f” for momentum and “g” for energy )
Please help me even with a simple point of vue or hint …

Hi there,

You can use Zou/He boundaries (bounce-back of non-equilibrium distribution functions) for energy as well as momentum fields, but there is a twist: you have to use the resulting fluid velocity for the energy distribution functions. That means you have to apply the Zou/He condition to the momentum distribution function first, which then gives a velocity to plug in for the energy distribution function. Along with the desired temperature, you can then use the bounce-back of non-equilibrium distribution functions to solve for all unknown distribution functions apart from the one orthogonal to the boundary, which can then be calculated from the temperature itself and the sum of all other distribution functions.