1. Thermal Radiation Solver
PDT Thermal Radiation Transport Package Marvin L. Adams, Wm. Daryl Hawkins, Ryan G. McClarren, Jim E. Morel Dept. of Nuclear Engineering, Texas A&M University
PDT Introduction
Solves the time-dependent linear Boltzmann and thermal radiation equations
3D (XYZ) or 2D (XY)
Multigroup in energy
Discrete ordinates (quadrature set can vary by energy group)
Finite-volume and finite-element methods on arbitrary polyhedral/polygonal cells
Various time discretization methods (Fully Implicit, Crank-Nicolson, Trapezoidal BDF2)
Various partitioning algorithms (KBA, Volumetric, Hybrid, METIS)
Various iterative schemes obtained via scheduling choices (Sweeps, Block-Jacobi, Hybrid)
Supports various Krylov methods (GMRES, BiCGSTAB, CG, CGS)
Massively parallel with the parallelism obtained via the underlying PTTL parallel
components library
Written entirely in C++
PDT/BATSRUS Coupling
PDT can successfully run radiation transport problems from within BATSRUS
PDT exposes to BATSRUS two core interfaces functions
pdt_initialize() is called once during BATSRUS setup to initialize PDT data structures and ensure consistency between BATSRUS and PDT inputs. Receives from BATSRUS geometry, grid, material, and cell identification information.
pdt_execute() is called by each BATSRUS process and passes to PDT material densities, material average velocities, and electron energy densities for cells owned by the BATSRUS calling process.
pdt_execute() communicates the information passed to it by BATSRUS to the appropriate PDT processes so that PDT can use its own domain decomposition (such as KBA)
pdt_execute() returns to each BATSRUS process the radiation/matter momentum exchange rate density vector, the radiation /matter energy exchange rate density, and the electron energy density for the appropriate BATSRUS cells belonging to the BATSRUS calling process.
Complexity is mostly on PDT side. Coding complete except for redistribution.
Initial debugging and verification will be helped by a simplified radiation model (cell-
wise infinite-medium), which should give the same solution from PDT as from the
embedded BATSRUS diffusion solver
PDT Data Structures
Elements contain fundamental spatial unknowns and volumetric sources
Supports multiple element types
Whole-cell elements Corner elements
for finite-volume for finite-element
discretizations discretizations
Cells contain elements and encapsulate material information
Cells are stored in a grid
Grid is stored as a graph
Vertices of the graph correspond to cells
Edges of the graph correspond to cell faces
Contains methods to store and read angular intensities
Graph is a templated C++ class that handles various cell, element, and edge types
Cell
Cell
Test Problems
Approximately 50 test problems in the PDT radiation transport test suite
Testing various combinations of discretizations, iterative solvers, etc.
Includes simple semi-analytic one-cell heat-up problem and light-front propagation problem
Adding many more as time goes on
Su-Olsen boundary problem detailed in LA-UR
Equilibrium Marshak wave problem (Ryan McClarren)
ρ = 1.0 g/cm3
κ = 1.0 cm2/g
Te = 100 K (0.008 eV)
α = 4a, Cv = αTe3
200 spatial cells, S2 quadrature order
LPWLD discretization, GMRES, TBDF2
Δt = 1.0×10-13 s
X = 0 cm X = 20cm
Tr = 1 keV
Thermal Radiation Solver
PDT solves equations for radiation intensity and electron temperature
Much code is shared by the linear Boltzmann solver and the radiation transport solver
Group-summed absorption-rate density is the solver unknown
Can converge A.R.D. pointwise in addition to norm of the residual
Many changes have been made to the solver to improve its robustness and handling
of negative energy densities and temperatures
Can use opacity data from tables, fits, and simple analytic functions
TOPS data
Interpolated TOPS data
Κ = A+BTC
Can use simple analytic functions of temperature for specific heats
Cv = A+BTC
Several options for time-centering opacities and specific heats:
Beginning of time-step Te
Extrapolated Te
Converged Te
Time-step control includes a simple and effective adaptive time-step capability
Many performance and memory usage improvements
ρ = 3.0 g/cm3
κ = ×1023 cm2/g
Te = 0.01 eV
Cv = ×1019eV/g-K
1000 spatial cells, S2 quadrature order
LPWLD discretization, GMRES, Fully-Implicit
Δt = 1.0×10-13 s
X = 0 cm X = 0.5cm
Tr = 1 keV