Uneven-order decentered Shapiro filters for boundary filtering

This paper addresses the use of Shapiro filters for boundary filtering. A new class of uneven-order decentered Shapiro filters is proposed and compared to classical Shapiro filters and even-order decentered Shapiro filters. The theoretical analysis shows that the proposed boundary filters are more accurate than the centered Shapiro filters and more robust than the even-order decentered boundary filters usable at the same distance to the boundary. The benefit of the new boundary filters is assessed for computations using the compressible Euler equations.