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DOE awards $59.7 million for university nuclear R&D in 2024; $1 billion in 15 years
The Office of Nuclear Energy is awarding $59.7 million to 25 U.S. colleges and universities, two national laboratories, and one industry organization to support nuclear energy research and development and provide access to world-class research facilities, the Department of Energy announced on April 15.
Peter G. Maginot, Jean C. Ragusa, Jim E. Morel
Nuclear Science and Engineering | Volume 179 | Number 2 | February 2015 | Pages 148-163
Technical Paper | doi.org/10.13182/NSE13-65
Articles are hosted by Taylor and Francis Online.
We examine several mass matrix lumping techniques for the discrete ordinates (SN) particle transport equations spatially discretized with arbitrary order discontinuous finite elements in one-dimensional (1-D) slab geometry. Though positive outflow angular flux is guaranteed with traditional mass matrix lumping for linear solution representations in source-free, purely absorbing 1-D slab geometry, we show that when used with higher-degree polynomial trial spaces, traditional lumping does not yield strictly positive outflows and does not increase the solution accuracy with increase in the polynomial degree of the trial space. As an alternative, we examine quadrature-based lumping strategies, which we term “self-lumping” (SL). Self-lumping creates diagonal mass matrices by using a numerical quadrature restricted to the Lagrange interpolatory points. When choosing equally spaced interpolatory points, SL is achieved through the use of closed Newton-Cotes formulas, resulting in strictly positive outflows for odd degree polynomial trial spaces in 1-D slab geometry. When selecting the interpolatory points to be the abscissas of a Gauss-Legendre or a Lobatto-Gauss-Legendre quadrature, it is possible to obtain solution representations with a strictly positive outflow in source-free pure absorber problems for any degree polynomial trial space in 1-D slab geometry. Furthermore, there is no inherent limit to local truncation error order of accuracy when using interpolatory points that correspond to Gauss-Legendre or Lobatto-Gauss-Legendre quadrature points. A single-cell analysis is performed to investigate outflow positivity and truncation error as a function of the trial space polynomial degree, the choice of interpolatory points, and the numerical integration strategy. We also verify that the single-cell local truncation error analysis translates into the expected global spatial convergence rates in multiple-cell problems.