Numerical Simulation of Comoving Frame Transport Equation

Astronomy and Astrophysics – Astronomy

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According to the fireball model, Gamma-ray Bursts (GRBs) and their afterglows are thought to be radiated from the relativistically moving fluid with Lorentz factor of tens to hundreds. To simulate these relativistic radiation phenomena, we have been developing a relativistic radiation hydrodynamics code. In our code, the radiation transport equation is solved in the comoving frame which moves with the fluid. The advantage of using the comoving frame equation is that the fundamental properties of radiation such as emissivity, absorption and scattering can be treated in the same way as when the fluid is at rest. Starting from the lab frame transport equation, we have derived the comoving frame transport equation in 2-D Cartesian coordinates. The structure of the comoving frame transport equation is similar to that of the lab frame equation except that the comoving frame equation has additional terms of radiation intensity variation over angle and energy. We numerically solve this comoving frame transport equation using an implicit method based upon the sparse linear solver which has been used to solve the lab frame transport equation. Our transport code is implemented in an AMR capable fashion using PARAMESH, a parallel adaptive mesh refinement library. We exhibit the results of some verification tests in this presentation. The comoving frame transport code will be combined with the relativistic hydrodynamics code to build up the relativistic radiation hydrodynamics code. For our radiation hydrodynamics code, we have already developed a 2-D Cartesian relativistic hydrodynamics code using the Flux Corrected Transport (FCT) algorithm with Zalesak's multi-dimensional limiter.

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