  Many fundamental problems in fluid dynamics are related to the effects of
solid boundaries. In general, they install sharp gradients and contribute to
the developement of small-scale structures, which are computationally expensive
to resolve with numerical simulations. A way to access extremely fine scales
with a reduced number of degrees of freedom is to consider the equations on
logarithmic lattices in Fourier space. Here we introduce new toy models for
flows with walls, by showing how to add boundaries to the logarithmic lattice
framework. The resulting equations retain many important properties of the
original systems, such as the conserved quantities, the symmetries and the
boundary effects. We apply this technique to many flows, with emphasis on the
inviscid limit of the Navier-Stokes equations. For this setup, simulations
reach impressively large Reynolds numbers and disclose interesting insights
about the original problem.
