Title: Operator Splitting Techniques for Radiation-Hydrodynamics
Author: Jim E. Morel, Professor of Nuclear Engineering, TAMU.
Dr. Morel is an expert in the area of numerical methods for radiation diffusion, transport, and associated multi-physics calculations such as radiation-hydrodynamics. Prior to accepting his position at Texas A&M University, he was a scientific advisor at Los Alamos National Laboratory from 2001 to 2005, group leader of the Transport Methods Group from 1997 to 2001, and a staff scientist from 1984 to 1997. Before coming to Los Alamos National Laboratory, he was a staff scientist at Sandia National Laboratory from 1976 to 1984, and before coming to Sandia was a nuclear research officer at the Air Force Weapons Laboratory at Kirtland Air Force Base from 1974 to 1976. He received a B.S. in mathematics from Louisiana State University in 1972, an M.S. in nuclear engineering from Louisiana State University in 1974, and a Ph.D. in nuclear engineering from the University of New Mexico in 1979. He has held the position of adjunct professor and directed the thesis and dissertation research of students at the University of New Mexico, Louisiana State University, Pennsylvania State University, and Rensselear Polytechnic Institute. He held the position of National Laboratory Professor at the University of New Mexico from 2004 to 2005. Dr. Morel has published over 140 refereed articles in journals and conference proceedings in the areas of neutron transport, coupled electron-photon transport, thermal radiation transport, and radiation-hydrodynamics.
The cutting-edge of high-performance scientific computing currently lies in the domain of multiphysics computation. Computational physicists have traditionally relied upon operator splitting to make the solution of multiphysics systems tenable. Such splitting enables each component of the physics to be solved in an essentially independent manner using standard solution techniques for each component. This practice has been called into question in recent years through demonstrations that operator splitting can lead to unreliable convergence and a loss of asymptotic preservation. We first give an overview of modern solution techniques for the radiative transfer equation based upon preconditioned Krylov methods. Then we describe new operator splitting techniques that are expected to yield reliable first-order accurate solutions of the radiation-hydrodynamics equations. Finally, we discuss possible approaches for second-order accurate operator splitting.the algorithm and illustrate through various examples the pertinency of the approach to get at least impressive speed up in the restitution time and most often full efficiency of the parallel method. We shall present new realizations and provide some open problems and ways to may be overcome them.