Goal-Oriented Regional Angular Adaptive Algorithm for the <i>S<sub>N</sub></i> Equations

Zhang, Bin; Zhang, Liang; Liu, Cong; Chen, Yixue

doi:10.1080/00295639.2017.1394085

Cited by 20 publications

(7 citation statements)

References 12 publications

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“…Outside of these smooth regions, they employ an optimisation scheme to try and "fix-up" the interpolation to preserve 0th order moments. Finally [21] also divide their spatial domain into regions and perform goal-based angular adaptivity based on a nested quadrature. They perform interpolation by fitting high-order spherical harmonics to portions of each octant and show results up to 6 levels of refinement.…”

Section: Adaptive S Nmentioning

confidence: 99%

“…A number of authors have investigated using angular adaptivity in Boltzmann transport applications. We loosely classify these into four main categories: sparse-grid methods [15,15]; adaptive S n quadratures [16,17,18,19,20,21]; h adaptive FEMs [22,23] and adaptive wavelet methods [24,2,4,8,9,11,10,12]. We do not discuss p adaptive FEMs here, as we are focused on problems with discontinuities in the angular domain.…”

Section: Introductionmentioning

confidence: 99%

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Scalable angular adaptivity for Boltzmann transport

Dargaville

Buchan

Smedley-Stevenson

et al. 2020

Journal of Computational Physics

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This paper describes an angular adaptivity algorithm for Boltzmann transport applications which for the first time shows evidence of O(n) scaling in both runtime and memory usage, where n is the number of adapted angles. This adaptivity uses Haar wavelets, which perform structured h-adaptivity built on top of a hierarchical P 0 FEM discretisation of a 2D angular domain, allowing different anisotropic angular resolution to be applied across space/energy. Fixed angular refinement, along with regular and goal-based error metrics are shown in three example problems taken from neutronics/radiative transfer applications. We use a spatial discretisation designed to use less memory than competing alternatives in general applications and gives us the flexibility to use a matrix-free multgrid method as our iterative method. This relies on scalable matrix-vector products using Fast Wavelet Transforms and allows the use of traditional sweep algorithms if desired.

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Section: Adaptive S Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scalable angular adaptivity for Boltzmann transport

Dargaville

Buchan

Smedley-Stevenson

et al. 2020

Journal of Computational Physics

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“…Several methods have been proposed to simultaneously satisfy conservation of energy and maintain the shape of the phase function [58], [59]. Modifications of the angular discretization procedure have been used to reduce the ray effects, namely by averaging the computed solution for several reference frame orientations [60], by employing a goal-based angular adaptivity method [61] or a goal-oriented regional angular adaptive algorithm [62]. The application to problems with specular reflection was addressed in Refs.…”

Section: Discrete Ordinates and Finite Volume Methodsmentioning

confidence: 99%

The impact of radiative heat transfer in combustion processes and its modeling – with a focus on turbulent flames

Liu

Consalvi

Coelho

et al. 2020

Fuel

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Radiative heat transfer (RHT) is often the dominant mode of heat transfer in flames, fires, and combustion systems and affects significantly temperature distributions directly and kinetically controlled chemical processes indirectly. Modeling RHT accurately in multidimensional flames and combustion systems is challenging mainly due to the highly spectral dependence of radiative properties of combustion products, the high computational cost of solving the radiative transfer equation (RTE), and the strong turbulence and radiation interactions (TRI). Significant progress has been made in all the three aspects in the last three decades and the state-of-the-art models and methods have been incorporated into CFD practice for modeling fires, turbulent jet flames, and turbulent combustion in combustion systems. In this article, we first discuss the coupling between RHT and combustion and the important role played by RHT in some fundamental flame phenomena. Then we discuss the state-of-the-art radiation models with a focus on RTE solvers, radiative property models and TRI. Next, we review the recent simulations of turbulent combustion systems involving these state-of-the-art radiation models. Finally, we provide concluding remarks and some potential research areas to advance RHT modeling in multiphase reacting flows. Nomenclature, , area normal to directions x, y and z [m 2 ] non-grey stretching factor for WSGG, SLW, and FSK methods absorption cross-section of a soot primary particle [m 2 ] absorption cross-section of a soot aggregate [m 2 ] diameter [m] , , integral over a control angle of the direction cosines relative to x, y and z-axis particle size parameter [-] radiant fraction [-] array of variables defining the absorption coefficient, = { , , , } Ω solid angle [sr] Subscript Fuel direction j spectral line S soot at a given wavenumber Superscript aggregate lth direction (DOM) or lth control angle (FVM) mth direction (DOM) or mth control angle (FVM) primary particle Operators 〈 〉 Reynolds averaged quantity ′ Reynolds fluctuating quantity ̅ filtered (or resolved) quantity ′′ subgrid-scale (or residual) fluctuation Recently, quasi-MC methods [43], [44] were employed to solve RHT problems in 3D participating media, aimed at the improvement of the convergence rate, and therefore the computational efficiency. In these methods, the random numbers are replaced by low-

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“…In terms of ray effects, in addition to increase discrete directions, to modify direction layout is another common remedy [11][12][13][14][15]. Numerical experiments have been conducted by Li et al [11] showing that ray effects can be reduced by modifying direction layouts, and three corresponding countermeasures were proposed in their paper.…”

Section: Introductionmentioning

confidence: 99%

“…Quadrature rotation was also applied to solve time-dependent transport and results showed that ray effects were reduced significantly, including for small numbers of quadrature points [13]. Recently, goal-oriented angular adaptive algorithm was also utilized to mitigate ray effects [14,15]. However, neither increasing discrete directions nor modifying direction layout is a partially effective remedy for ray effects [16,17].…”

Section: Introductionmentioning

confidence: 99%

Ray Effects and False Scattering in Improved Discrete Ordinates Method

Cheng¹,

Yang²,

Huang³

2021

Energies

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The improved discrete ordinates method (IDOM) developed in our previous paper is extended to solve radiative transfer in three-dimensional radiative systems with anisotropic scattering medium. In IDOM, radiative intensities in a large number of new discrete directions are calculated by direct integration of the conventional discrete ordinates method (DOM) results, and radiative heat flux is obtained by integrating radiative intensities in these new discrete directions. Ray effects and false scattering, which tend to compensate each other, are investigated together in IDOM. Results show that IDOM can mitigate both of them effectively with high computation efficiency. Finally, the effect of scattering phase function on radiative transfer is studied. Results of radiative heat flux at boundaries containing media with different scattering phase functions are compared and analyzed. This paper indicates that the IDOM can overcome the shortages of the conventional DOM well while inheriting its advantages such as high computation efficiency and easy implementation.

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Goal-Oriented Regional Angular Adaptive Algorithm for the S_N Equations

Cited by 20 publications

References 12 publications

Scalable angular adaptivity for Boltzmann transport

Scalable angular adaptivity for Boltzmann transport

The impact of radiative heat transfer in combustion processes and its modeling – with a focus on turbulent flames

Ray Effects and False Scattering in Improved Discrete Ordinates Method

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Goal-Oriented Regional Angular Adaptive Algorithm for the SN Equations

Cited by 20 publications

References 12 publications

Scalable angular adaptivity for Boltzmann transport

Scalable angular adaptivity for Boltzmann transport

The impact of radiative heat transfer in combustion processes and its modeling – with a focus on turbulent flames

Ray Effects and False Scattering in Improved Discrete Ordinates Method

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Product

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Goal-Oriented Regional Angular Adaptive Algorithm for the S_N Equations