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Knoll, Dana A

Publications and source records attributed to Knoll, Dana A.

6 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Nonlinear variants of the TR/BDF2 method for thermal radiative diffusion

We apply the Trapezoidal/BDF2 (TR/BDF2) temporal discretization scheme to nonlinear grey radiative diffusion. This is a scheme that is not well-known within the radiation transport community, but we show that it offers many desirable characteristics relative to other second-order schemes. Several nonlinear variants of the TR/BDF2 scheme are defined and computationally compared with the Crank-Nicholson scheme. It is found for our test problems that the most accurate TR/BDF2 schemes are those that are fully iterated to nonlinear convergence, but the most efficient TR/BDF2 scheme is one based upon a single Newton iteration. It is also shown that neglecting the contributions to the Jacobian matrix from the cross-sections, which is often done due to a lack of smooth interpolations for tabular cross-section data, has a significant impact upon efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Application of the Jacobian-Free Newton-Krylov Method to Nonlinear Acceleration of Transport Source Iteration in Slab Geometry

The use of the Jacobian-free Newton-Krylov (JFNK) method within the context of nonlinear diffusion acceleration (NDA) of source iteration is explored. The JFNK method is a synergistic combination of Newton's method as the nonlinear solver and Krylov methods as the linear solver. JFNK methods do not form or store the Jacobian matrix, and Newton's method is executed via probing the nonlinear discrete function to approximate the required matrix-vector products. Current application of NDA relies upon a fixed-point, or Picard, iteration to resolve the nonlinearity. We show that the JFNK method can be used to replace this Picard iteration with a Newton iteration. The Picard linearization is retained as a preconditioner. We show that the resulting JFNK-NDA capability provides benefit in some regimes. Furthermore, we study the effects of a two-grid approach, and the required intergrid transfers when the higher-order transport method is solved on a fine mesh compared to the low-order acceleration problem.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2010

A Second Order Self-Consistent IMEX Method for Radiation Hydrodynamics

We present a second order non-linearly consistent implicit/explicit (methods that use com- bination of implicit/explicit discretizations are often referred to as IMEX (IMplicit/EXplicit) methods [2,1,3]) time integration technique for solving radiation hydrodynamics problems. The idea is to hybridize an implicit and an explicit discretization in a nonlinearly consis- tent way in order to achieve second order time convergent calculations. In this scope, the hydrodynamics equations are discretized explicitly making use of the capability of well- understood explicit schemes. On the other hand , the radiation diffusion part is solved implicitly. In the view of the non-linearly consistent IMEX method, the hydrodynamics equations are solved as part of the non-linear function evaluation within the framework of the Jacobian-Free Newton Krylov (JFNK) method [16,14]. This is to avoid order reductions in time convergence due to the operator splitting. We present results from several test prob- lems in order to validate the numerical order of the scheme. For each test, we established second order time convergence.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗