Riemann invariant manifolds for performance evaluation of absorbing boundary conditions for an acoustic waveguide

Abstract

Riemann invariant manifolds (RIM) are used to evaluate the performance of absorbing boundary conditions (ABC) for numerical modeling of an unbounded acoustic waveguide. The evaluation is carried out by extracting, from the computed solution, spurious waves caused by the approximate nature of the ABC used. Unlike the traditional bicharacteristics method for multi-dimensional wave motion, use of RIMs leads to an equivalent one-dimensional problem involving invariants along characteristics. The clear physical meaning associated with the invariant allows for the estimation of the energy flux into the computational domain due to reflected waves from the ABC. Numerical examples demonstrate that the total energy carried by reflected waves that enter the computational domain becomes smaller as the unbounded domain is modeled more accurately, and thus can be used to evaluate the performance of the ABC.