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In this paper, we present the formulation of a time-domain impedance boundary model based on a finite-point approximation. Firstly, the scalar wave equation is numerically treated studying either the stability or the dispersion error in the case of a Cartesian regular mesh with standard clouds and weighted functions. Then, we develop the formulation of a locally reacting impedance boundary model suitable for the whole acoustic impedance range, and we carried out several numerical experiments to confirm the accuracy and the performance of the full model. Lastly, some conclusions and remarks of the method are discussed.