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This paper introduces and evaluates the Adding and Doubling Method (ADM) for solving the Bateman equations for depletion systems with varying numbers of nuclides and compares it to the Chebyshev Rational Approximation Method (CRAM), both implemented in the reactor physics analysis application Griffin. ADM, when applied to the Crank-Nicolson Finite Difference method, can produce results comparable in accuracy and precision to CRAM with comparable run times for systems with 35 or 297 nuclides. For systems with more than 300 nuclides, the matrix-matrix operations required by ADM are significantly more costly than the matrix-vector operations required by CRAM, making CRAM the more efficient method for systems with large numbers of nuclides. ADM is an accurate method that maintains other advantages over CRAM in that it does not depend on pre-generated coefficients or require complex number operations. ADM also manages to outperform CRAM by a factor of more than 250 in terms of run time for depletion systems that require multiple Bateman solves while the depletion matrix and time step size remain constant over all depletion intervals. [ABSTRACT FROM AUTHOR]

In the beautifully situated tenth-century castle, about 75 participants from all over the world presented and attended seven sessions during five days concerning such topics as radionuclide production, equations of state of a Fermi gas, the advection-diffusion equation, the Fokker-Planck equation, neutron multiplicity and branching, transport in a moving mesh, pressurized water reactor control rod motion, waves in gas bubbles, the Vlasov-Poisson-Landau kinetic equation, plasma transport, Monte Carlo, stochastic COVID-19 modeling, the BGK equation, charged particle transport, and more specialized topics in particle transport theory. Every odd year from 1969 through 2019 - and then in 2022 on account of the COVID-19 pandemic - a select group of mathematicians, physicists, engineers, and computational scientists calling themselves transport theorists gathered for one week at what was originally called the Blacksburg Conference (now known as the International Conference on Transport Theory [ICTT]). Originated by Paul F. Zweifel (deceased), Bob Erdman, and Chuck Siewert, the conference was intended to bring together theorists the world over to discuss common methods to solve the neutron transport equation with application to nuclear energy. [Extracted from the article]

Computing in the energy dimension is one of the greatest challenges confronting present-day deterministic neutron transport solvers. Accurately resolving the neutron flux as neutrons downscatter across resonances in the nuclear cross sections currently requires considerable computing power and suffers from approximation errors. Flux uncertainty resulting from the uncertainty of the resonance structure is the single-largest cause of reactivity uncertainty. Any additional reference solution for the critical neutron downscattering problem with resonance phenomena would be a boon to verification and validation of neutronics codes. This paper establishes a benchmark to verify the accuracy of neutron transport criticality solvers along the energy dimension. For the first time, the analytic solution of the flux amplitude is derived in the particular case of an infinite homogeneous medium with isotropic scattering in the center of mass and an arbitrary number of no-threshold, neutral particle reaction resonances (e.g., radiative capture, fission, and resonance scattering). Original analytic expressions are established to quantify the discrepancy between the ψ k (E) and ψ α (E) flux amplitudes, respective solutions of the multiplication factor k , or the exponential time-evolution frequency α eigenproblems. The physical study of these relations led to analysis of their first-order relative difference near the criticality condition α = 0. Finally, numerical solutions are provided to a benchmark problem constituted of the first resonance of 239Pu, the 6.67-eV resonance of 238U, and a scattering isotope with a flat cross section, allowing for the computational verification of the energy resolution of current neutron transport criticality codes. Through these novel results, this analytic benchmark can serve as a reference to verify the energy resolution and sensitivity analysis of neutron transport criticality calculations. [ABSTRACT FROM AUTHOR]