Artificial Boundary Conditions for High-Accuracy Aeroacoustic Algorithms

Abstract

This article deals with high-accuracy finite-difference schemes for hyperbolic equations, namely, dispersion-relation-preserving (DRP) scheme by Tam and Webb [J. Comput. Phys., 107 (1993), pp. 262-281] and its modifications by Bogey and Bailly [J. Comput. Phys., 194 (2004), pp. 194-214]. The technique of dispersion relation optimization is extended to equations at nearboundary nodes. The latter equations must approximate the dispersion of a governing scheme. Outflow and inflow artificial boundary conditions are constructed for the approximations to the transport equation and the Euler equations in both one and two dimensions. The stability analysis and test computations demonstrate the robustness of the algorithms proposed.

Development of Non-Reflecting Boundary Condition for Application in 3D Computational Fluid Dynamics Codes

“…The literature on the implementation of NRBCs usually groups the boundary conditions into three categories. The first one comprises the methods based on a decomposition into Fourier modes (Atassi, 2004;Hagstrom and Hariharan, 1988;Dorodnicyn, 2010). In the second category the conservation equations are extrapolated in order to obtain asymptotic solutions (Tam, 1995;Bogey and Bailly, 2002;Dea et al, 2009).…”

Numerical Boundary Conditions for Schemes with Centered and Biased Differences in Subsonic Gas Dynamics

“…The disadvantage is the neglecting a possibility to improve boundary conditions by introducing appropriate tangential derivatives-see Ref. [4,11,12]. In this way one obtains local boundary conditions nonreflecting for vorticity waves in the Euler equations.…”

“…Polynomial (12) has the two roots q 1 and q 2 , and the general normal-mode solution has the approximate (leading-term) form…”