GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Optimum positive linear schemes for advection in two and three dimensions
SIAM Journal on Numerical Analysis
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Bounded skew high-order resolution schemes for the discrete ordinates method
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method
Journal of Computational Physics
Journal of Computational Physics
Device level communication libraries for high-performance computing in Java
Concurrency and Computation: Practice & Experience
Parallel algorithms for Sn transport sweeps on unstructured meshes
Journal of Computational Physics
Hi-index | 31.47 |
The application of flux limiters to the discrete ordinates method (DOM), S"N, for radiative transfer calculations is discussed and analyzed for 3D enclosures for cases in which the intensities are strongly coupled to each other such as: radiative equilibrium and scattering media. A Newton-Krylov iterative method (GMRES) solves the final systems of linear equations along with a domain decomposition strategy for parallel computation using message passing libraries in a distributed memory system. Ray effects due to angular discretization and errors due to domain decomposition are minimized until small variations are introduced by these effects in order to focus on the influence of flux limiters on errors due to spatial discretization, known as numerical diffusion, smearing or false scattering. Results are presented for the DOM-integrated quantities such as heat flux, irradiation and emission. A variety of flux limiters are compared to ''exact'' solutions available in the literature, such as the integral solution of the RTE for pure absorbing-emitting media and isotropic scattering cases and a Monte Carlo solution for a forward scattering case. Additionally, a non-homogeneous 3D enclosure is included to extend the use of flux limiters to more practical cases. The overall balance of convergence, accuracy, speed and stability using flux limiters is shown to be superior compared to step schemes for any test case.