Can anyone explain when do we apply Zou/He boundary conditions?

I just couldn’t understand when exactly do we apply Zou/He boundary conditions. It seems that it should be applied in every problem at the inlet and outlet to insure mass conservation or something like that, but i’m not sure.

Is the dirichlet and neumann boundary conditions the same as Zou/He??


Hi there,

Zou/He boundary conditions are applied to give constant values for either flow velocity or fluid density. Which of these conditions are required depends on the system in question: you might need a constant velocity condition if you wish to apply shear or constant density conditions for pressure-based boundaries.

They are not necessarily required for every problem, however: some problems may not need anything other than periodic boundary conditions, plus there are alternatives to Zou/He for constant velocity or density conditions that may be more appropriate (e.g. regularised LB conditions might be more numerically stable at extremes of viscosity).

In mathematical terms, Zou/He boundary conditions are Dirichlet conditions, as they fix the property (density or velocity) to a set value. A Neumann boundary condition fixes the gradient of the property to a particular value: this can be implemented in LB with Zou/He boundary conditions by calculating the property required at the boundary to satisfy the value of the gradient. (I believe there is a report somewhere on the Palabos website that gives more detail.)

I hope this is helpful.



Hello Mike,

I am new to LBM. Although I have some experience with CFD, I am not comfortable with boundary conditions. You said we use constant velocity for shear based and density for pressure based conditions. Can you explain that or direct me to an article/book which gives ,in detail, how/why we should choose only certain type of boundary conditions?