The Brinkman model is a model of a viscous fluid in a heterogeneous medium where fractures, bubbles or channels are present in a porous matrix. It is an intermediate between a Stokes (free) flow and a Darcy (porous) flow, which degenerates to either model when some parameter (viscosity or inverse permeability) tend to 0 - which could happen in only part of the domain, in which case the model consists in a free flow in part of the domain and a porous media flow in another part of the domain. The nature of the Brinkman model, and the various physical situations it can represent in limiting cases, calls for designing numerical methods that are robust in both regimes, pure Stokes and pure Darcy -- possibly locally inside the domain. In this talk I will explain how, by combining ideas of the Hybrid High-Order method and the Discrete De Rham method, we can design a numerical scheme for the Brinkman model that is (i) robust in limiting regimes, (ii) applicable on generic polyhedral meshes, and (iii) of arbitrary order of accuracy.