Publications
Showing 60 results for Author: Cory D. Hauck
Jun, 2014
Journal
An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation
We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic tem- perature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both lo- cal and nonlocal paralle…
May, 2012
Conference Paper
Approximation and error estimation in high dimensional space for stochastic collocation methods on arbitrary sparse samples
We have develop a fast method that can capture piecewise smooth functions in high dimensions with high order and low computational cost. This method can be used for both approximation and error estimation of stochastic simulations where the computations can either be guided or come from a legacy database.
Sep, 2010
Journal
High-Order Entropy-Based Closures for Linear Transport in Slab Geometries
We compute, for the first time, high-order entropy-based ($M_N$) models for a linear transport equation on a one-dimensional, slab geometry. We simulate two test problems from the literature: the two-beam instability and the plane-source problem. In the former case we compute solutions for systems up to order $N=5$ ; in the latter, up to $N=15$. The most notable outcome of…
Jun, 2010
Journal
Robust and Accurate Filtered Spherical Harmonics Expansions for Radiative Transfer
We present a novel application of filters to the spherical harmonics (PN) expansion for radiative transfer problems in the high energy density regime. The filter we use is based on non-oscillatory spherical splines and a filter strength chosen to (i) preserve the equilibrium diffusion limit and (ii) vanish as the expansion order tends to infinity. Our implementation is based on…
May, 2010
Journal
Simulating Radiative Transfer with Filtered Spherical Harmonics
This letter presents a novel application of filters to the spherical harmonics ($P_N$) expansion for radiative transfer problems in the high-energy-density regime. The filter, which is based on non-oscillatory spherical splines, preserves both the equilibrium diffusion limit and formal converges properties of the unfiltered expansion. Results demonstrate that solutions to…