Impedance boundary condition for truncated open spaces

The propagation of waves governed by hyperbolic systems at a surface is in general reflective. The numerical solution of many problems in mechanics necessitates the truncation of an open space to a finite domain. The reflectivity of the boundary of a truncated domain can be effectively characterized by a few parameters and implemented as a time-domain impedance boundary condition. It is shown that the concept of a time-domain impedance boundary condition affords a simple and effective treatment of waves, allowing them to exit the surfaces of a truncated domain as a causal, local, space-time continuation rather than a global boundary confinement. We present and discuss the open-space impedances of radiative and convective fields, their modeling, analytic structures, implementation, and solution effectiveness as an open-space impedance boundary condition. We further propose a general methodology for numerical definition of open-space impedance and its application within existing schemes to reduce truncated domains and computational resources.