High-Order Higdon Non-Reflecting Boundary Conditions for the Linearized Euler Equations

Abstract

Abstract : We wish to solve fluid flow problems in only a portion of a large or infinite domain. By restricting our area of interest, we effectively create a boundary where none exists physically dividing our computational domain from the rest of the physical domain. The challenge we must overcome, then, is defining this boundary in such a way that it behaves computationally as if there were no physical boundary. Such a boundary definition is often called a non-reflecting boundary, as its primary function is to permit wave phenomena to pass through the open boundary without reflection. In this dissertation we develop several non-reflecting boundary conditions for the linearized Euler equations of inviscid gas dynamics. These boundary conditions are derived from the Higdon, Givoli-Neta, and Hagstrom-Warburton boundary schemes for scalar equations and they are adapted here for a system of first-order partial differential equations. Using finite difference methods, we apply the various boundary schemes to the gas dynamic equations in two dimensions, in an open domain with and without the influence of gravity or Coriolis forces. These new methods provide significantly greater accuracy than the classic Sommerfeld radiation condition with only a modest increase to the computation time.