On deriving nonreflecting boundary conditions in generalized curvilinear coordinates

Abstract

In this work, nonreflecting boundary conditions in generalized three-dimensional curvilinear coordinates are derived, relying on the original analysis that was done in Cartesian two-dimensional coordinates by Giles (AIAA Journal, 28.12, 2050-2058, 1990). A thorough Fourier analysis of the linearized Euler equation is performed to determine the eigenvalues and the eigenvectors that are then used to derive the appropriate inflow and outflow boundary conditions. The analysis lacks rigorous proof of the well-posedness in the general case, which is open to investigation (a weak assumption is introduced here to complete the boundary conditions). The boundary conditions derived here are not tested on specific applications.