Convergence of Implicit Difference Scheme for 1D Lagrangian   Hydrodynamics coupled to Radiation Transport Equation
  A fully implicit finite difference scheme has been developed to solve the hydrodynamic equations coupled with radiation transport. Solution of the time dependent radiation transport equation is obtained using the discrete ordinates method and the energy flow into the Lagrangian meshes as a result of radiation interaction is fully accounted for. A tridiagonal matrix system is solved at each time step to determine the hydrodynamic variables implicitly. The results obtained from this fully implicit radiation hydrodynamics code in the planar geometry agrees well with the scaling law for radiation driven strong shock propagation in aluminium. For the point explosion problem the self similar solutions are compared with results for pure hydrodynamic case in spherical geometry and the effect of radiation energy transfer is determined. Having, thus, benchmarked the code, convergence of the method w.r.t. time step is studied in detail and compared with the results of commonly used semi-implicit method. It is shown that significant error reduction is feasible in the implicit method in comparison to the semi-implicit method, though at the cost of slightly more CPU time. 
Karabi Ghosh and S.V.G.Menon