Publications

Nov, 2023

Journal

Data-driven surrogate modeling of hPIC ion energy-angle distributions for high-dimensional sensitivity analysis of plasma parameters’ uncertainty

We present a data-driven strategy for effective construction of a surrogate model in high-dimensional parameter space for the ion energy-angle distribution (IEAD) output of hPIC simulations of plasma-surface interactions. The methodology is based on a bin-by-bin least-squares fitting of the IEAD in the parameter space. The fitting is performed in a transformed coordinate s…

Nov, 2023

Conference Paper

Artificial Intelligence Design of Nuclear Systems Empowered by Advanced Manufacturing

Nov, 2023

Conference Paper

thornado-transport: IMEX schemes for two-moment neutrino transport respecting Fermi-Dirac statistics

We develop implicit-explicit (IMEX) schemes for neutrino transport in a background material in the context of a two-moment model that evolves the angular moments of a neutrino phase-space distribution function. Considering the upper and lower bounds that are introduced by Pauli's exclusion principle on the moments, an algebraic moment closure based on Fermi-Dirac statistic…

Nov, 2023

ORNL Report

Bound-Preserving Discontinuous Galerkin Methods for Conservative Phase Space Advection in Curvilinear Coordinates

Nov, 2023

Journal

Convergence of filtered spherical harmonic equations for radiation transport

We analyze the global convergence properties of the filtered spherical harmonic (FPN) equations for radiation transport. The well-known spherical harmonic (PN) equations are a spectral method (in angle) for the radiation transport equation and are known to suffer from Gibbs phenomena around discontinuities. The filtered equations include additional terms to address this is…

Nov, 2023

Journal

A Regularized Entropy-Based Moment Method for Kinetic Equations

We present a new entropy-based moment method for the velocity discretization of kinetic equations. This method is based on a regularization of the optimization problem defining the original entropy-based moment method, and this gives the new method the advantage that the moment vectors of the solution do not have to take on realizable values. We show that this equation sti…

Nov, 2023

Journal

Positivity Limiters for Filtered Spectral Approximations of Linear Kinetic Transport Equations

We analyze the properties and compare the performance of several positivity limiters for spectral approximations with respect to the angular variable of linear transport equations. It is well-known that spectral methods suffer from the occurrence of (unphysical) negative spatial particle concentrations due to the fact that the underlying polynomial approximations are not a…

Nov, 2023

Journal

Realizability-preserving DG-IMEX method for the two-moment model of fermion transport

Building on the framework of Zhang & Shu [1], [2], we develop a realizability-preserving method to simulate the transport of particles (fermions) through a background material using a two-moment model that evolves the angular moments of a phase space distribution function f. The two-moment model is closed using algebraic moment closures; e.g., as proposed by Cernohorsky &…

Nov, 2023

ORNL Report

Artificial Intelligence Design of Nuclear Systems

Nov, 2023

Journal

A Positive Asymptotic-Preserving Scheme for Linear Kinetic Transport Equations

We present a positive- and asymptotic-preserving numerical scheme for solving linear kinetic transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard spectral angular discretization and a classical micro-macro decomposition. The three main ingredients are a semi-implicit temporal discretiz…

Sep, 2023

Conference Paper

Implicit Graph Neural Networks: A Monotone Operator Viewpoint

Sep, 2023

Journal

Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency

We consider a kinetic description of multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In this model, the Maxwellians typically used in standard BGK operators are replaced by a generalization of such target functions, which are de…