arXiv:2610.13680v1 Announce Type: cross Abstract: We consider the Helmholtz equation in a Dirichlet angular sector (which may be locally perturbed) covered on one side by a thin homogeneous layer. First, we propose an asymptotic expansion of the solution at any order and for any angle when the thickness of the layer tends to 0, using a matched asymptotic expansion. This consists in introducing different asymptotic expansions in three subdomains -- the vicinity of the corner, the layer and the rest of the domain -- that are linked through matching conditions. The presence of the corner makes these matching conditions delicate to derive because the fields have complex singular behaviors. We overcome this difficulty using a novel system of algebraic tools, including formal series and operators on these series. Moreover, we justify the asymptotic expansion with error estimates and provide details on the form of the expansion depending on the angle. We numerically validate this expansion up to order 5. This requires computing the behavior at infinity of some corner profiles. To do this, we introduce a Galerkin-type method enriched by complements at infinity. These complements are known functions that appear in the behavior at infinity of the corner profiles with coefficients that become unknowns of the system. Finally, we propose effective models of order 3, resp. 5 where, far from the corner, the layer is replaced with an effective Robin, resp. Ventcel, boundary condition and, near the corner, an artificial boundary is introduced and a Dirichlet-to-Neumann (DtN) type condition is imposed. The DtN map relies on a modal decomposition of the truncated asymptotic expansion at order 3, resp. 5. The modes take into account the singular behavior of the expansion terms, the corner profiles and some algebraic matching coefficients. We prove the well-posedness of our effective models, as well as error estimates, and provide numerical results.