VETTAM: A scheme for radiation hydrodynamics with adaptive mesh
  refinement using the variable Eddington tensor method
  We present Variable Eddington Tensor-closed Transport on Adaptive Meshes
(\texttt{VETTAM}), a new algorithm to solve the equations of radiation
hydrodynamics (RHD) with support for adaptive mesh refinement (AMR) in a
frequency-integrated, two-moment formulation. The method is based on a
non-local Variable Eddington Tensor (VET) closure computed with a hybrid
characteristics scheme for ray tracing. We use a Godunov method for the
hyperbolic transport of radiation with an implicit backwards-Euler temporal
update to avoid the explicit timestep constraint imposed by the light-crossing
time, and a fixed-point Picard iteration scheme to handle the nonlinear
gas-radiation exchange term, with the two implicit update stages jointly
iterated to convergence. We also develop a modified wave-speed correction
method for AMR, which we find to be crucial for obtaining accurate results in
the diffusion regime. We demonstrate the robustness of our scheme with a suite
of pure radiation and RHD tests, and show that it successfully captures the
streaming, static diffusion, and dynamic diffusion regimes and the spatial
transitions between them, casts sharp shadows, and yields accurate results for
rates of momentum and energy exchange between radiation and gas. A comparison
between different closures for the radiation moment equations, with the
Eddington approximation (0th-moment closure) and the $M_1$ approximation
(1st-moment closure), demonstrates the advantages of the VET method (2nd-moment
closure) over the simpler closure schemes. \texttt{VETTAM} has been coupled to
the AMR \texttt{FLASH} (magneto-)hydrodynamics code and we summarize by
reporting performance features and bottlenecks of our implementation.
