# Imposition of Dirichlet BC for Fourier pseudospectral in this paper

I was trying to implement the algorithm from the paper "Adapting a Fourier pseudospectral method to Dirichlet boundary conditions for Rayleigh–Benard convection".

I am having a hard time to understand the way the boundary conditions are imposed.

The author rewrites the no-slip (on upper and lower boundaries) boundary conditions as

$$\sum_{q} \tilde f_{\bot,pq} = 0 \forall p$$

where $$p$$ and $$q$$ are horizontal and vertical wavenumbers.

How do we impose that?

• Thanks Mr. Gillis for answering. I am aware of those methods that you mentioned. But my question was specific to the paper that I mentioned. The author in the paper gave an algorithm for applying fourier method to RBC but the way he reformulated the no-slip boundary condition in fourier domain (i.e $\sum_{q} \tilde{f}_{\bot,pq} = 0 \forall p$ ) even though makes sense, but I could not understand how would it be imposed in the code. – user162281 Apr 15 '19 at 7:41