The Response Matrix Discrete Ordinates, Solution to the 1D Radiative Transfer Equation
The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and computational techniques have become more powerful and efficient. In this seminar, we again consider the analytical solution to the radiative transfer equation in a homogeneous medium by proposing a new, and consistent, form of solution improving upon previous solutions. Aided by a Wynn-epsilon convergence acceleration, its numerical evaluation achieves extreme accuracy as demonstrated by comparison with published benchmarks. Finally, one readily extends the solution to a heterogeneous medium producing a novel benchmark for a closed form Henyey-Greenstein scattering phase function.
Barry D. Ganapol is currently Professor in the Department of Aerospace and Mechanical Engineering (AME) at the University of Arizona and a Research Professor in the Department of Nuclear Engineering at the University of Tennessee. He received his PhD from the University of California, Berkeley in 1971 followed by two years at the Swiss Federal Institute for Reactor Research and one year at the Center for Nuclear Studies at Saclay in France. After three years at Argonne National Laboratory, he joined the Department of Nuclear Engineering (NE) faculty at the University of Arizona in 1976. Professor Ganapol has served as Chair of the NE Department and Acting and Associate Chair of the AME Department. His research interests include developing analytical and numerical methods to solve the neutron Boltzmann equation in the pursuit of high quality benchmark solutions. This activity has lead to his broader interest of verification and validation strategies applied to modeling and simulation of nuclear systems. In addition, Professor Ganapol has investigated the health of vegetation canopies from first principles of radiative transfer with application to satellite remote sensing. During his 45-year career, Professor Ganapol has held appointments at eleven DoE, NASA and military research laboratories and has nearly 300 publications. He is Fellow of the American Nuclear Society and recipient of the Gerald C. Pomraning Award from the Mathematics and Computation Division of the American Nuclear Society for his outstanding contributions to transport theory. In 2006, Professor Ganapol received the Da Vinci Award for excellence in overall scholarship, teaching and service from the College of Engineering at the University of Arizona.