A deterministic photon free method to solve radiation transfer equations

A new method to solve radiation transfer equations is presented. In the absence of scattering, material motion, and heat conduction, the photon variables can be eliminated from the fully implicit, multi-group, discrete-ordinate, finite difference (finite element) equations of continuum radiation transfer to yield a smaller set of equations which depends only on temperature. The solution to this smaller set of equations is used to generate the solution to the original set of equations from which the reduced set is derived. The reduced system simplifies to a nonlinear heat equation in the regime of strong absorption and strong emission. We solve the reduced set of equations by the Newton-GMRES method in which the Jacobian update is preconditioned by a linearization of this nonlinear heat equation. The performances of this new method and of the semi-implicit linear method, which is preconditioned by grey transport acceleration combined with diffusion synthetic acceleration, are compared on two test problems. The test results indicate that the new method can take larger time steps, requires less memory, is more accurate, and is competitive in speed with the semi-implicit linear method.