Numerical simulations for radiation hydrodynamics - II. Transport limit

A finite difference scheme is proposed for two-dimensional radiation hydrod ynamical equations in the transport limit. The scheme is of Godunov-type, i n which the set of time-averaged flux needed in the scheme is calculated th rough Riemann problems solved. In the scheme, flow signals are explicitly t reated, while radiation signals are implicitly treated. Flow fields and rad iation fields are updated simultaneously. An iterative approach is proposed to solve the set of nonlinear algebraic equations arising from the implici tness of the scheme. The sweeping method used in the scheme significantly r educes the number of iterations or computer CPU time needed. A new approach to further accelerate the convergence is proposed, which further reduces t he number of iterations needed by more than one order. No matter how many c ells radiation signals propagate in one time step, only an extremely small number of iterations are needed in the scheme, and each iteration costs onl y about 0.8 percent of computer CPU time which is needed for one time step of a second order accurate and fully explicit scheme. Two-dimensional probl ems are treated through a dimensionally split technique. Therefore, iterati ons for solving the set of algebraic equations are carried out only in each one-dimensional sweep. Through numerical examples it is shown that the sch eme keeps the principle advantages of Godunov schemes for flow motion. In t he time scale of flow motion numerical results are the same as those obtain ed from a second order accurate and fully explicit scheme. The acceleration of the convergence proposed in this paper may be directly applied to other hyperbolic systems. (C) 2000 Academic Press.