Graduate Thesis Or Dissertation
 

Evaluating preconditioning options for the Jacobian-Free Newton Krylov Method applied to radiative transfer with matter coupling

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  • The objective of this thesis was to investigate the use of the Jacobian Free Newton Krylov Method (JFNK) with physics based preconditioning for solving coupled radiative transport and material energy balance. Modeling of these physics is important in inertial confinement fusion and other high energy density systems. In this thesis, the non-linear equations for radiative transfer and matter balance are converged within the JFNK framework. Coupling of the transport problem to the material energy balance is attempted in a manner unlike Britton Chang's Photon Free Method [5]. The effects of various physics-based preconditioners are compared. The proposed method with the various formulated preconditioners accurately solve the Su and Olson benchmark problem but difficulty is encountered when Chang's test problem is attempted. Analysis is performed to determine the limits of the proposed method. It is concluded that the most efficient physics-based preconditioning in the Su and Olson problem is found by taking the derivative with respect to temperature for the material energy balance equation. Because of the difficulties experienced when attempting to solve Chang's problem it is concluded that the proposed method in this thesis fails for tightly coupled problems. This is due to overloading the inner GMRES iterative solver for the full problem.
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