Impedance of open spaces

The propagation of waves governed by hyperbolic systems is in general reflective. The numerical solution of many problems in mechanics necessitates the truncation of an open space to a finite domain. The reflective boundaries of this domain can be effectively characterized by a few parameters and implemented as Time-domain Impedance Boundary Condition (TDIBC). It will be shown that the concept of TDIBC affords a simple, effective, proper, broadband treatment of the wave at a truncated boundary as a causal space-time continuation rather than a local or global confinement. We will present and discuss the open-space impedances of radiative and convective fields, their modeling, analytic structure, implementation, and efficacy as open-space TDIBC. We will also propose a general methodology for defining numerically the open-space impedance and implementing it with existing schemes for solution of problems formulated on open spaces but numerically computed on truncated domains.