Accurate modeling of neutral particle transport behavior is of great importance in many science and engineering applications. Many numerical transport algorithms suffer from slow convergence in optically thick regions, where particles undergo a large number of scattering and/or absorption re-emission events. We are developing a moment-based, scale-bridging algorithm that can mitigate slow convergence of transport algorithms. Our algorithm utilizes the low-order (LO) continuum equations that are consistently derived from the high-order (HO) transport equation. Due to discrete consistency, the LO system can be used not only for accelerating the HO solution, but also coupling to other physics.
In this talk, we present physics-based preconditioning strategy that utilizes the nonlinear elimination technique for the solution of the LO problem. The nonlinear elimination technique can reduce coupled PDEs/ODE to a scalar parabolic PDE via block Gauss elimination. This technique allows one to eliminate stiff nonlinear coupling from the system and hence reduces the number of required Newton iterations, with a trade-off of more complex Jacobian and nonlinear residual evaluations. We can then solve the LO system efficiently via multigrid preconditioned Newton-Krylov method with physics-based preconditioning. We discuss computational efficiency with different preconditioning operators.
We also discuss time stepping strategy of our moment-based scale-bridging algorithm for time-dependent thermal radiative transfer problems. Our goal is to obtain (asymptotically) second-order time accurate and consistent solutions without nonlinear iterations between the HO and LO systems within a time step. We compare the accuracy and efficiency of a predictor-corrector algorithm with the nonlinearly consistent algorithm.