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Diffusion Accelerated Implicit Monte Carlo via Nonlinear Elimination for Thermal Radiative Transfer
In this dissertation, we derive and implement a new transport-diffusion hybrid algorithm for solving thermal radiative transfer (TRT) problems. Using the method of nonlinear elimination (NLEM), the TRT system of equations can be written in terms of a transport equation with the absence of scattering and a diffusion equation. The transport solution is obtained using a Monte Carlo (MC) method with implicit capture and the diffusion solution is used to accelerate the transport convergence. We name this method Diffusion Accelerated Implicit Monte Carlo (DAIMC).
A series of tests are used to verify the proposed algorithm and its associated solvers.
After the verification of DAIMC, we investigate its performance by comparing DAIMC results to those obtained from the traditional Implicit Monte Carlo (IMC) method. In 1D slab geometry calculations, we show that DAIMC yields a more accurate solution than IMC when compared to the analytic solution. The increased accuracy of the DAIMC solution comes at the cost of an increased computational time when compared to IMC. We have also employed Quasi-Monte Carlo (QMC) in the DAIMC algorithm for 1D calculations. QMC retains the same accuracy as the MC implementation of DAIMC while decreasing the required computing time.
We also implemented DAIMC in 2D-XY geometry using a piecewise constant representation of temperatures for the Monte Carlo transport solver and a linear-continuous discretization for the diffusion equation. For problems in which the opacity is constant or has a T^{-1} temperature dependence, the implementation choice for DAIMC converges to the correct equilibrium solution and provides more accurate results than the IMC method. We observed that small time steps are required for DAIMC to produce the analytic equilibrium solution when the opacity has a temperature dependence of T^{-2}.
DAIMC results for a crooked pipe problem are compared with results obtained from the IMC method. We observed nonphysical overheating at the interface of the thick and thin material region for both our DAIMC method and the IMC method. The nonphysical overheating of the interface improves with refinement of the mesh for both methods