Phonon hydrodynamics in porous graphene from direct solution of the Boltzmann equation

We present a theoretical investigation of hydrodynamic phonon transport in porous monolayer graphene by solving the phonon Boltzmann transport equation with first-principles input, via a discrete unified gas kinetic scheme on unstructured meshes. This multiscale approach efficiently captures both momentum-conserving and -destroying phonon scattering mechanisms in complex geometries. Our simulations reveal distinct hydrodynamic features, including a parabolic heat flux profile along the neck cross-section and the super-linear dependence of effective thermal conductivity on pore diameter. Systematic examination shows hydrodynamic regime is highly sensitive to geometric confinement, with the critical pore diameter increasing by one order of magnitude as the porosity rises from 5 % to 50 %. Moreover, we demonstrate a negative nonlocal temperature response near pore boundaries at an optimal porosity (∼35 %), arising from the interplay between geometric confinement and collective phonon transport. These results establish a promising paradigm for engineering phonon hydrodynamics in porous materials through rational microstructure design.