Parallel Computations of Radiative Heat Transfer Using the Discrete Ordinates Method

Krishnamoorthy, Gautham; Rawat, Rajesh; Smith, Phillip J.

doi:10.1080/10407790490487451

Cited by 33 publications

(8 citation statements)

References 16 publications

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“…The ARCHES code is massively parallel and highly scalable through its integration in the Uintah framework [27], and also through use of parallel solvers like Hypre [9] and PETSc [2]. As part of the ARCHES development, substantial research has been done on radiative heat transfer using the parallel Discrete Ordinates Method and the P1 approximation to the radiative transport equation [17]. In reacting flow simulations, the main computational cost is the solution of the large number of systems of linear equations required by the Discrete Ordinates Method.…”

Section: The Arches Combustion Simulation Componentmentioning

confidence: 99%

Radiation modeling using the Uintah heterogeneous CPU/GPU runtime system

Humphrey

Meng

Berzins

et al. 2012

Proceedings of the 1st Conference of the Extreme Science and Engineering Discovery Environment: Bridging From the eXtreme to Th

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The Uintah Computational Framework was developed to provide an environment for solving fluid-structure interaction problems on structured adaptive grids on large-scale, long-running, data-intensive problems. Uintah uses a combination of fluid-flow solvers and particle-based methods for solids, together with a novel asynchronous task-based approach with fully automated load balancing. Uintah demonstrates excellent weak and strong scalability at full machine capacity on XSEDE resources such as Ranger and Kraken, and through the use of a hybrid memory approach based on a combination of MPI and Pthreads, Uintah now runs on up to 262k cores on the DOE Jaguar system. In order to extend Uintah to heterogeneous systems, with ever-increasing CPU core counts and additional onnode GPUs, a new dynamic CPU-GPU task scheduler is designed and evaluated in this study. This new scheduler enables Uintah to fully exploit these architectures with support for asynchronous, outof-order scheduling of both CPU and GPU computational tasks. A new runtime system has also been implemented with an added multi-stage queuing architecture for efficient scheduling of CPU and GPU tasks. This new runtime system automatically handles the details of asynchronous memory copies to and from the GPU and introduces a novel method of pre-fetching and preparing GPU memory prior to GPU task execution. In this study this new design is examined in the context of a developing, hierarchical GPUbased ray tracing radiation transport model that provides Uintah with additional capabilities for heat transfer and electromagnetic wave propagation. The capabilities of this new scheduler design are tested by running at large scale on the modern heterogeneous systems, Keeneland and TitanDev, with up to 360 and 960 GPUs respectively. On these systems, we demonstrate significant speedups per GPU against a standard CPU core for our radiation problem.

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Section: The Arches Combustion Simulation Componentmentioning

confidence: 99%

Radiation modeling using the Uintah heterogeneous CPU/GPU runtime system

Humphrey

Meng

Berzins

et al. 2012

Proceedings of the 1st Conference of the Extreme Science and Engineering Discovery Environment: Bridging From the eXtreme to Th

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“…Recently, many numerical methods have been developed to solve the problems of radiative heat transfer in semitransparent media. The solution methods may mainly be classified into two classes: (1) the methods based on ray tracing, such as the zonal method [1] and the Monte Carlo method [2,3]; and (2) the methods based on the discretization of a standard form or variation of the radiative transfer equation (RTE), such as the discrete-ordinates method (DOM) [3][4][5][6][7][8][9][10][11][12][13][14][15], the finite-volume method (FVM) [16][17][18][19][20][21][22][23], and the finite-element method (FEM) [24][25][26][27][28][29]. The ray-tracing-based methods do not rely explicitly on the RTE.…”

Section: Introductionmentioning

confidence: 99%

Second-Order Radiative Transfer Equation and Its Properties of Numerical Solution Using the Finite-Element Method

Zhao

Liu

2007

Numerical Heat Transfer, Part B: Fundamentals

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The original radiative transfer equation is a first-order integrodifferential equation, which can be taken as a convection-dominated equation. The presence of the convection term may cause nonphysical oscillation of solutions. This type of instability can occur in many numerical methods, including the finite-difference method and the finite-element method, if no special stability treatment is used. To overcome this problem, a second-order radiative transfer equation is derived, which is a diffusion-type equation similar to the heat conduction equation for an anisotropic medium. The consistency of the second-order radiative transfer equation with the original radiative transfer equation is demonstrated. The perturbation characteristics of error are analyzed and compared for both the first-and second-order equations. Good numerical properties are found for the second-order radiative transfer equation. To show the properties of the numerical solution, the standard Galerkin finite-element method is employed to solve the second-order radiative transfer equation. Four test problems are taken as examples to check the numerical properties of the second-order radiative transfer equation. The results show that the standard Galerkin finite-element solution of the second-order radiative transfer equation is numerically stable, efficient, and accurate.

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“…This provides the developers and users with an easy access to a suite of direct and iterative solvers and preconditioners that can be suitably selected depending on the problem being solved. Employing the solvers and preconditioners in PETSc to solve the system of linear equations arising from a finite volume discretization of the discrete ordinates method has been described previously in Krishnamoorthy et al [42,43]. Further, scaling of the radiation solver to 1000 processors was demonstrated.…”

Section: Interfacing Petsc With the P 1 Radiation Modelmentioning

confidence: 99%

“…distributed on the upper and lower triangular portion of the matrix. The number of diagonals on either side of the main diagonal depends on the direction of the DO sweep [42,43]. Due to this difference in matrix type (non-symmetry), the GMRES solver (as opposed to CG for the P 1 16 radiation model) has previously been determined to be the optimum solver choice for the DO model [42,43].…”

Section: Comparisons Of Iterative Solver Performancementioning

confidence: 99%

A computationally efficient P1 radiation model for modern combustion systems utilizing pre-conditioned conjugate gradient methods

Krishnamoorthy

2017

Applied Thermal Engineering

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The iterative convergence of the P 1 radiation model can be slow in optically thin scenarios when employing classical iterative methods. In order to remedy this shortcoming, an inhouse P 1 radiation model was interfaced with high performance, scalable, linear solver libraries. Next, the accuracies of P 1 radiation model calculations was assessed by comparing its predictions against discrete ordinates (DO) model calculations for prototypical problems representative of modern combustion systems. Corresponding benchmark results were also included for comparison. Utilizing Pre-Conditioners (PC) to the Conjugate Gradients (CG) method, the convergence time of the P 1 radiation model reduced by a factor of 30 for modest problem sizes and a factor of 70 for larger sized problems when compared against classical Gauss Seidel sweeps. Further, PC provided 50% computational savings compared to employing CG in a standalone mode. The P 1 model calculation times were about 25-30% of the DO model calculation time. The time to solution also scaled linearly with an increase in problem size. The weighted sum of gray gases model employed in this study in conjunction with the P 1 model provided good agreement against benchmark data with L 2 error norms (defined relative to corresponding DO calculations) improving when isotropic intensities were prevalent.

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Parallel Computations of Radiative Heat Transfer Using the Discrete Ordinates Method

Cited by 33 publications

References 16 publications

Radiation modeling using the Uintah heterogeneous CPU/GPU runtime system

Radiation modeling using the Uintah heterogeneous CPU/GPU runtime system

Second-Order Radiative Transfer Equation and Its Properties of Numerical Solution Using the Finite-Element Method

A computationally efficient P1 radiation model for modern combustion systems utilizing pre-conditioned conjugate gradient methods

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