Numerical Methods for Solving the Linear Boltzmann Equation

The UFTTG (University of Florida Transport Theory Group) has been investigating a large number of aspects related to the numerical solution of the Linear Boltzmann Equation. The objective of these studies has been to improve the accuracy and efficiency of the methologies to simulate radiation transport processes in large nuclear/medical systems. Up to now the following issues have been investigated:

• Demonstrated the cause of unphysical oscillations of the standard Sn formulation
• Developed of the Directional Theta-Weighted Formulation, which accurate, positive, and minimal unphysical oscillations
• Developed of adaptive differencing strategy •Developed the Exponential Directional Weighted formulation
• Developed Taylor Projection Mesh Coupling (TPMC) formulation
• Developed various (space, energy, angular, and their hybrids) parallel Sn algorithms
• Developed new quadrature sets which do not have limitations on the Sn order
• Developed biased quadrature sets for regional refinements
• Developed angular and spatial multigrid formulations for accelerating convergence rate of the Sn formulation

The current research topics are:

• Development of an acceleration technique based on the even-parity form of the Simplified Sn equations
• Developing approximate formulation for determination of approximate adjoint function for electron transport