Anomalous behavior of Newtonian hydrodynamics coupled with radiation transport

Abstract

This study shows that Newtonian hydrodynamics coupled with radiation transport, using a wide range of methods for treating the material-motion corrections, results in anomalous behavior. In particular, the flow of infinite-medium equilibration will accelerate whenever viewed moving past an observer in the laboratory frame. The acceleration may cause the velocity to increase exponentially in time. An exact fully-relativistic solution is derived to show that there is no acceleration, independent of the reference frame. This solution is analytic and may be used as a validation problem for the simulation of fully-relativistic radiation hydrodynamics.Current O(β)-accurate radiation treatments, where β is the velocity magnitude divided by the speed of light, also predict acceleration. But we show that the anomalous acceleration is not due to the radiation approximations, but rather from assuming that the hydrodynamics evolves on the fluid time scale, which leads to dropping terms from fully-relativistic hydrodynamics to give the Newtonian approximation. The addition of radiation energy and momentum sources to hydrodynamics introduces fast time scales, such as radiation equilibration. These fast time scales invalidate the use of Newtonian hydrodynamics for certain problems, even when β is small. Alternative formulations are discussed, but we find that removing the anomalous behavior comes at a cost, either by sacrificing conservation or accuracy.