  The wave property of phonons is employed to explore the thermal transport
across a finite periodic array of nano-scatterers such as circular and
triangular holes. As thermal phonons are generated in all directions, we study
their transmission through a single array for both normal and oblique
incidences, using a linear dispersionless time-dependent acoustic frame in a
two-dimensional system. Roughness effects can be directly considered within the
computations without relying on approximate analytical formulae. Analysis by
spatio-temporal Fourier transform allows us to observe the diffraction effects
and the conversion of polarization. Frequency-dependent energy transmission
coefficients are computed for symmetric and asymmetric objects. We demonstrate
that the phononic array acts as an efficient thermal barrier by applying the
theory of thermal boundary (Kapitza) resistances to arrays of smooth scattering
holes in silicon for an exemplifying periodicity of 10 nm in the [5-100 K]
temperature range. It is observed that the associated thermal conductance has
the same temperature dependence than that without phononic filtering.
