This study deals with the development of boundary conditions (BC) to take into account sound absorbing materials in CAA codes. Time-marching approach is necessary to reproduce wideband noise propagation with a single run. Time-domain translation of the impedance relation is done by a costly discrete Fourier transform. Impedance tube simulations show that the velocity profile of shear flows is to be count with depending on the Mach number. Data storage is then reduced using the z-transform properties. For generalization sake, impedance relation is made 1D along the surface normal at each mesh node. This curvilinear treatment based on the solver metric routines allows a spurious frequencies free local application. Simulation of sound diffraction and propagation near liners then requires little storage and a CPU run time similar to hard wall treatment. Acoustic absorption in resonators is then studied looking forward to extending such BC to higher acoustic levels.