Dear all

When checking the sample codes of the 2D flow past a cylinder I noticed that the velocity (u and v components) on the wall nodes are not zero. (I checked both Matlab and Fortran versions). If I understood correctly, the boundary conditions used at the walls are full-way bounce-back BC, according to this website nomenclature, or also named as on-grid bounce-back according to Succi’s book nomenclature. Fist question: Although with different names these boundary conditions are the same, aren´t they?

In my opinion the fact that the no-slip velocity at the wall is not attained is because a periodic BC is imposed along the domain edges when performing the streaming step. When I remove these periodic conditions I get the expected zero velocity.

Moreover, If I displace the wall node velocity to a location 1/2 inside the fluid domain I also get the correct shear stress.

Second question: Is my reasoning correct? I read somewhere in this forum that someone (I believe it was Tim, if not I apologize) used periodic bc conditions in all boundaries and after that, over them, superimposed the right boundary conditions, i.e. the ones that he wanted to have in his flow. I am not sure but I think that by doing this, in this specific order, one might end up having incorrect results.

My final question has nothing to do with boundary conditions.

As much debated in this forum when one has a constant force acting in the flow it is unanimous that the following simple expression for the body force term can be used: Fi=wi*ei*F/cs^2.

Now my question is how fluid velocity is defined.

Everyone defines the fluid velocity as being equal to the “equilibrium” velocity (i.e. the velocity used in the equilibrium distribution computation).

But in Buick and Greated article “Gravity in a lattice Boltzmann model” it is said that the fluid velocity is different from the equilbrium one in 1/2*F. I think that in Ladd’s paper “Lattice Boltzmann Simulations of Particle-Fluid Suspensions” the same is said.

I performed computations using both velocity definitions and found out that, for instance, keeping all parameters constant except tau, the Buick’s definition is better for small tau’s, i.e. below 1, while the traditional definition is better for tau>=1.

I also substituted both definitions of the fluid velocity in the mass and momentum conservation equations, which resulted from the Chapman-Enskog procedure applied to the LB equations with this particular forcing term, and found out that Buick’s definition yields the exact continuity equation but also more extra artificial terms in the momentum equations than with the traditional velocity definition. However, this traditional velocity definition does not yield a correct continuity equation if div(F) is different from zero.

Does anyone have already achieved the same conclusions? Or can explain me more about the advantages/disadvantages of both definitions?

Thanks in advance for the help.

Goncalo