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

abstract

• 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. 2010 Elsevier Inc.

authors

• Morel, Jim

published proceedings

• JOURNAL OF COMPUTATIONAL PHYSICS

author list (cited authors)

• Edwards, J. D., Morel, J. E., & Knoll, D. A.

complete list of authors

• Edwards, Jarrod D||Morel, Jim E||Knoll, Dana A

publisher

• Elsevier  Publisher

published in

• Journal of Computational Physics  Journal

keywords

• Nonlinear Radiative Diffusion
• Trapezoidal Bdf-2

Digital Object Identifier (DOI)

• 10.1016/j.jcp.2010.10.035

start page

• 1198

end page

• 1214

volume

• 230

issue

• 4