A Simple Boundary Condition for Unbounded Hyperbolic Flows

A Sommerfeld radiation condition (2.2) is proposed for problems requiring a prescribed open boundary. The equations must be hyperbolic in nature (although the author believes that they may also be good for some elliptic and parabolic problems). It is proven that the proposed condition was shown to be free of reflection for single wave propagation. Two severe tests were used to demonstrate the applicability of the open boundary condition: (i) the collapsing bubble, a dynamic event which excites many different internal gravity waves. The results show minimum distortion. (ii) The spatially growing K-H instability. This test differs from the previous one in that the only waves excited are those corresponding to the maximum unstable wavelengths. In this case, the maximum amplitude is reached at the open boundary. As it has been shown, the open boundary condition (2.2) produces minimum distortion.