Accelerated convergence to steady state by gradual far-field damping

Abstract

Reflections from artificial boundaries inhibit convergence of transient solutions to their steady limit. Far-field damping operators to suppress such reflections are presented for general first order hyperbolic systems, and particular reference is made to the compressible Euler equations. The damping operator has the following properties: (a) No reflections are generated due to the introduction of the clamping terms and (b) Different wave systems may be damped at different rates. Feature (a) enables the attenuation of waves over relatively short length scales, while feature (b) enables the damping operator to act selectively on the outgoing waves alone, leaving the incoming waves unharmed. This property is desirable in genuine timedependent problems where consistent information should be allowed to propagate from the artificial boundaries. Results for compressible Euler flows past aerofoils show the potential of far-field damping in substantially accelerating, particularly in fully subsonic problems.