Robust and simple non-reflecting boundary conditions for the space-time conservation element and solution element method

Abstract

This paper reports on a significant advance in the area of non-reflecting boundary conditions for unsteady flow computations. Sets of new non-reflecting boundary conditions for ID Euler problems are developed without using any characteristics-based techniques. These conditions are much simpler than those commonly reported in the CFD literature, yet so robust that they are applicable to subsonic, transonic and supersonic flows even in the presence of discontinuities. The paper details the theoretical underpinning of the boundary conditions, and explains their unique robustness and accuracy, in terms of the conservation of space-time fluxes. Some numerical results for an extended Sod's shock-tube problem, illustrating the effectiveness of the boundary condi* Senior Research Scientist, e-mail: [e-mail] ^Member, AIAA; e-mail: [e-mail] ^Member, AIAA; e-mail: [e-mail] § Member, AIAA, and Research Associate, e-mail: [e-mail] ^Member, AIAA, and Senior Engineer, e-mail: [e-mail] II Member, AIAA, and Aerospace Engineer, e-mail: [e-mail] Copyright ©1997 American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental Purposes. All other rights are reserved by the copyright owner. tions, are included, together with the simple Fortran computer program with which they were obtained. Since the properties of the numerical boundary conditions are closely linked to the previously developed interior schemes, a summary of the interior schemes is also provided.