Nonlinear convergence, accuracy, and time step control in nonequilibrium radiation diffusion

We study the interaction between converging the nonlinearities within a tim e step and time step control, on the accuracy of nonequilibrium radiation d iffusion calculations. Typically, this type of calculation is performed usi ng operator-splitting where the nonlinearities are lagged one time step. Th is method of integrating the nonlinear system results in an "effective" tim e-step constraint to obtain accuracy. A time-step control that limits the c hange in dependent variables (usually energy) per time step is used. We inv estigate the possibility that converging the nonlinearities within a time s tep may allow significantly larger time-step sizes and improved accuracy as well. The previously described Jacobian-free Newton-Krylov method (JQSRT 6 3 (1999) 15) is used to converge all nonlinearities within a time step. In addition, a new time-step control method, based on the hyperbolic model of a thermal wave (J. Comput. Phys. 152 (1999) 790), is employed. The benefits and cost of a second-order accurate time step are considered. It is demons trated that for a chosen accuracy, significant increases in solution effici ency can be obtained by converging nonlinearities within a time step. (C) 2 001 Elsevier Science Ltd. All rights reserved.