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Astrophysics

"Terascale Simulation Initiative" PI: Tony Messacappa

Project Status: Inactive

During SciDAC-1, ITAPS researchers at ORNL had collaborations with the astrophysics SciDAC-1 center: the Terascale Supernova Initiative (TSI) led by Mezzacappa. The primary focus was the exploration of alternative discretization strategies for various aspects of the solution process. In addition, they explored a 3D spatial caching strategy to reduce costly evaluations of the scattering kernels for Boltzman transport.

Discontinuous Galerkin Discretizations for Radiative Transfer

ITAPS Personnel: Valmor de Almeida (ORNL), Ed D'Azevedo (ORNL)

TSI Personnel: Tony Mezzacappa (ONRL), Bronson Messer (ORNL), Matthias Liebendoerfer (ORNL)

With the TSI team, ITAPS researchers at ORNL explored new schemes for solving models of radiative transfer in stellar atmospheres representative of supernova type 2 core collapse/explosions. The current solution method, namely, discrete ordinates, in conjunction with finite differences, may require petascale computing power when extended to three dimensions. The ITAPS/TSI interaction was aimed at exploring novel schemes that are able to keep computational requirements at the terascale level.

A series of radiative transfer prototype problems have been chosen by the TSI group. These problems are simplified forms of Boltzmann's integro-differential equation for radiative transfer and thus have features significant to supernova collapse/explosion modeling.

The first problem, Milne's axis-symmetric pure scattering of photons in extended stellar atmospheres, has been studied successfully. In this problem the dependent variable is the radiative intensity field (photon distribution function), and the independent variables are the radius of the spherical stellar atmosphere and the polar angle made by the radius and the photon velocity vector. The new method of analysis consists of a discontinuous Galerkin (DG) approach for the approximation of the radiative intensity field in phase space (the Cartesian product of the one-dimensional radius domain and the polar angle domain). The integro-differential equation is treated as a linear hyperbolic PDE at each step of an iterative scheme that corrects the value of the integral scattering kernel. Each iteration is accelerated by evaluating the kernel from the first and zeroth moments of the original problem. The DG method applied to the linear hyperbolic problem at each iteration was implemented explicitly in phase space since the characteristic curves are known a priori. This allows the resulting linear algebraic set of equations to be solved locally and progressively along wave fronts normal to the characteristics. The DG method developed for the Milne's problem was found to be memory efficient (requiring one order of magnitude less storage than the discrete ordinate method) and fast (one order of magnitude faster than DOM). In addition, in view of the adaptive mesh used, the results were significantly more accurate when capturing important features of the solution. For instance, the region of transition from diffusive radiation to streaming was correctly captured, and the outward peaking (a delta function like sharp increase) of the radiation field at the outer boundary of the extended atmosphere was correctly reproduced. The results were obtained for a range of atmosphere sizes including the range of interest to supernova applications. Although the results are exciting, supernova models are significantly more complex, involving the extended set of equations that couple neutrino radiation transfer to relativistic flow, that is radiative hydrodynamics.

Caching Strategies for Boltzman Transport

ITAPS Personnel: Ed D'Azevedo (ORNL)

TSI Personnel: Bronson Messer (ORNL)

Another interaction between ITAPS and TSI is the use of a 3D spatial cache for avoiding redundant and costly evaluations of scattering kernels for Boltzmann transport. The scattering kernel is a function of density, temperature and species fraction. We have generated trace data over a realistic TSI computation and visualized the trajectories of evaluation in 3D phase space (density, temperature, species fraction). Initial analysis shows 3D interpolation with a small global cache has good hit ratio of over 90%, or about 9 of 10 evaluations of scattering kernels can be computed by 3D interpolation instead of the actual costly computations.