Analysis of the convected Helmholtz equation with a uniform mean flow in a waveguide with complete radiation boundary conditions

作者：Kim Seungil^*

来源：Journal of Mathematical Analysis and Applications, 2014, 410(1): 275-291.

DOI：10.1016/j.jmaa.2013.08.018

• Waveguide
• Helmholtz equation
• Convected Helmholtz equation
• Complete radiation boundary conditions
• Prandtl-Glauert transformation

In this paper, we propose complete radiation boundary conditions (CRBCs) for solutions of the convected Helmholtz equation with a uniform mean flow in a waveguide. We first study CRBCs for the Helmholtz equation in a waveguide. Noting that the convected Helmholtz equation is associated with the Helmholtz equation via the Prandtl-Glauert transformation, CRBCs for the convected Helmholtz equation is derived from CRBCs for the Helmholtz equation. We analyse well-posedness and convergence of approximate solutions satisfying CRBCs for the convected Helmholtz equation. In addition, simple numerical experiments will be presented to confirm the theoretical results.

• 出版日期2014-2-1