I am a professor of nuclear engineering whose research interests include the development of numerical methods to solve the equations describing steady-state and transient behavior of nuclear reactors including neutron transport, gamma transport, and multiphysics phenomena.
The Implicit Monte Carlo (IMC) method has been used for over 30 years to analyze radiative transf... more The Implicit Monte Carlo (IMC) method has been used for over 30 years to analyze radiative transfer problems, such as those encountered in stellar atmospheres or inertial confinement fusion. Reference [2] provided an exact error analysis of IMC for 0-D problems and demonstrated that IMC can exhibit substantial errors when timesteps are large. These temporal errors are inherent in the method and are in addition to spatial discretization errors and approximations that address nonlinearities (due to variation of physical constants). In Reference [3], IMC and four other methods were analyzed in detail and compared on both theoretical grounds and the accuracy of numerical tests. As discussed in, two alternative schemes for solving the radiative transfer equations, the Carter-Forest (C-F) method and the Ahrens-Larsen (A-L) method, do not exhibit the errors found in IMC; for 0-D, both of these methods are exact for all time, while for 3-D, A-L is exact for all time and C-F is exact within ...
The default energy deposition model in the CASL neutronics code MPACT assumes all fission energy ... more The default energy deposition model in the CASL neutronics code MPACT assumes all fission energy is deposited locally in fuel rods. Furthermore, equilibrium delayed energy release is assumed for both steady-state and transient calculations. These approximations limit the accurate representation of the heat generation distribution in space and its variations over time, which are essential for power distribution and thermal-hydraulic coupling calculations. In this paper, an improved energy deposition model is presented in both the spatial and time domains. Spatially, the energy deposition through fission, neutron capture, and slowing-down reactions are explicitly modeled to account for the heat generation from all regions of a reactor core, and a gamma smearing scheme is developed that utilizes the gamma sources from neutron fission and capture. In the time domain, the delayed energy release is modeled by solving an additional equation of delayed heat emitters, similar to the equation...
This paper presents the most recent progress on the development of gamma transport capability for... more This paper presents the most recent progress on the development of gamma transport capability for the CASL neutronics code MPACT: (1) 3D gamma transport and (2) explicit gamma heating capabilities. The 3D gamma calculation capability was implemented by leveraging the 2D/1D solver originally developed for neutron calculations. The results were verified by MCNP6 on a small assembly with 5 × 5 pins. Generally, errors were lower than 0.5% on each axial mesh as long as MPACT was running with enough axial meshes. The gamma heating calculation considered the energy deposition from photoelectric absorption, Compton scattering, and pair production. Verification with MCNP6 for both 2D and 3D benchmarks showed that the errors of energy depositions are comparable with those of gamma fluxes, proving the proper implementation of the energy deposition.
The Implicit Monte Carlo (IMC) method has been used for over 30 years to analyze radiative transf... more The Implicit Monte Carlo (IMC) method has been used for over 30 years to analyze radiative transfer problems, such as those encountered in stellar atmospheres or inertial confinement fusion. Reference [2] provided an exact error analysis of IMC for 0-D problems and demonstrated that IMC can exhibit substantial errors when timesteps are large. These temporal errors are inherent in the method and are in addition to spatial discretization errors and approximations that address nonlinearities (due to variation of physical constants). In Reference [3], IMC and four other methods were analyzed in detail and compared on both theoretical grounds and the accuracy of numerical tests. As discussed in, two alternative schemes for solving the radiative transfer equations, the Carter-Forest (C-F) method and the Ahrens-Larsen (A-L) method, do not exhibit the errors found in IMC; for 0-D, both of these methods are exact for all time, while for 3-D, A-L is exact for all time and C-F is exact within ...
The default energy deposition model in the CASL neutronics code MPACT assumes all fission energy ... more The default energy deposition model in the CASL neutronics code MPACT assumes all fission energy is deposited locally in fuel rods. Furthermore, equilibrium delayed energy release is assumed for both steady-state and transient calculations. These approximations limit the accurate representation of the heat generation distribution in space and its variations over time, which are essential for power distribution and thermal-hydraulic coupling calculations. In this paper, an improved energy deposition model is presented in both the spatial and time domains. Spatially, the energy deposition through fission, neutron capture, and slowing-down reactions are explicitly modeled to account for the heat generation from all regions of a reactor core, and a gamma smearing scheme is developed that utilizes the gamma sources from neutron fission and capture. In the time domain, the delayed energy release is modeled by solving an additional equation of delayed heat emitters, similar to the equation...
This paper presents the most recent progress on the development of gamma transport capability for... more This paper presents the most recent progress on the development of gamma transport capability for the CASL neutronics code MPACT: (1) 3D gamma transport and (2) explicit gamma heating capabilities. The 3D gamma calculation capability was implemented by leveraging the 2D/1D solver originally developed for neutron calculations. The results were verified by MCNP6 on a small assembly with 5 × 5 pins. Generally, errors were lower than 0.5% on each axial mesh as long as MPACT was running with enough axial meshes. The gamma heating calculation considered the energy deposition from photoelectric absorption, Compton scattering, and pair production. Verification with MCNP6 for both 2D and 3D benchmarks showed that the errors of energy depositions are comparable with those of gamma fluxes, proving the proper implementation of the energy deposition.
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Papers by William R Martin