Temporal accuracy of the nonequilibrium radiation diffusion equations employing a Saha ionization model

This manuscript presents an analysis of the temporal accuracy of two first-order in time and two second-order in time integration methods as applied to a coupled radiation diffusion/reaction system of equations. These methods are categorized by their temporal order of accuracy, whether the algorithm includes operator splitting, and whether the algorithm includes linearizations. Accuracy of the different methods on three different test problems is discussed. These test problems are not new to the literature, but the purpose here is to demonstrate that it is possible to maintain second-order time accuracy on a nontrivial coupled system while employing an operator-split and linearized method.