Simulation of Radiation Transport in a Channel Based on the Quasi-Diffusion Method

Aristova, E. N.

doi:10.1080/00411450802522912

Cited by 26 publications

(18 citation statements)

References 6 publications

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“…However, the resulting discretized diffusion equation has the diffusion coefficient 38) and hence in general it is not a correct one. In case of the weight w(…”

Section: Nwf Methods In Discretized Formmentioning

confidence: 99%

“…Another half-cell FV discretization [47,38] uses the same half cells but expresses the integration of φ over adjacent faces ω − 1 and ω + 1 as the integration of a linear function based on φ iω and φ i (instead of just using φ ω−1 , φ ω+1 as in the GGK method). Hereafter, we refer to this discretization as AK method.…”

Section: Ak Methods For Discretization Of the Loqd Equationsmentioning

confidence: 99%

“…The low-order QD equations (LOQD) (5.3)-(5.5) are discretized with a finite volume method [39,38] and have the following form:…”

Section: Linearization Of the Discretized Qd Equationsmentioning

confidence: 99%

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Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

Anistratov¹,

Constantinescu²,

Roberts³

et al. 2007

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“…However, the resulting discretized diffusion equation has the diffusion coefficient 38) and hence in general it is not a correct one. In case of the weight w(…”

Section: Nwf Methods In Discretized Formmentioning

confidence: 99%

Section: Ak Methods For Discretization Of the Loqd Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

Anistratov¹,

Constantinescu²,

Roberts³

et al. 2007

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“…Для ускорения сходимости итераций по рассеянию, делению, а также для организации эффективной связи решения уравнения переноса с параметрами среды, используются так называемые HOLO алгоритмы решения уравнения переноса, в которых наряду с уравнением переноса (1) высокой размерности (HO -High Order) решаются уравнения более низкой размерности (LO -Low Order) [1][2][3][4][5][6][7]. Из семейства HOLO алгоритмов одним из самых успешных является метод квазидиффузии В.Я.Гольдина [4][5][6][7].…”

Section: Introductionunclassified

Bicompact high order schemes for quasi-diffusion equations

Aristova

Karavaeva

2018

KIAM Prepr.

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О р д е н а Л е н и н а ИНСТИТУТ ПРИКЛАДНОЙ МАТЕМАТИКИ имени М.В.Келдыша Р о с с и й с к о й а к а д е м и и н а у к Е.Н.Аристова, Н.И.Караваева Бикомпактные схемы высокого порядка аппроксимации для уравнений квазидиффузии Москва -2018Аристова Е.Н., Караваева Н.И. Бикомпактные схемы высокого порядка аппроксимации для уравнений квазидиффузии В работе рассмотрено построение бикомпактных схем для нестационарных уравнений квазидиффузии, используемых при решении уравнения переноса для ускорения сходимости итераций по рассеянию и делению. Дифференциальноразностная система уравнений бикомпактной схемы строится методом прямых на двухточечном пространственном шаблоне. Достигается четвертый порядок аппроксимации по пространству благодаря включению в список неизвестных не только узловых значений функций, но и интегральных средних. Полученная система дифференциально-разностных уравнений интегрируется по времени Lустойчивым диагонально-неявным методом Рунге-Кутты третьего порядка аппроксимации. Каждая стадия метода сводится к неявному методу Эйлера, реализованному для краевой задачи методом потоковой прогонки. Предложен итерационный алгоритм для сохранения высокого порядка аппроксимации при нелинейности, показано, что одной дополнительной итерации по нелинейности достаточно для восстановления четвертого порядка сходимости по пространственным переменным.Ключевые слова: уравнение переноса, метод квазидиффузии, HOLO алгоритмы решения уравнения переноса, потоковая прогонка, диагональнонеявные методы Рунге-Кутты Elena Nikolaevna Aristova, Nataliia Igorevna Karavaeva Bicompact High Order Schemes for Quasi-Diffusion EquationsThe construction of bicompact schemes for nonsteady quasi-diffusion equations used for acceleration of iterations over scattering and fission terms in a transport equation is considered. Differential-difference system of bicompact scheme equations is constructed by the method of lines on two points space stencil. The fourth order of approximation on space variable is achieved by calculating not only nodal values but integral averaged values of unknown function. This system is integrated over time by L-stable Runge-Kutta method of third order of approximation. Each stage of the method is equivalent to implicit Euler method which is realized by efficient method for boundary value problem. An iteration algorithm is proposed to save high order of approximation in presence of nonlinearity. It is shown that one additional iteration is sufficient for saving fourth order of convergence on space variable. Key words: transport equation, quasi-diffusion method, HOLO algorithms for transport equation solving, diagonally implicit Runge-Kutta method Работа выполнена при поддержке Российского фонда фундаментальных исследований, проект 18-01-00857-а.

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“…One popular approach is the quasi-diffusion (QD) method [3,11], where the S19 angularly integrated balance equation is nonlinearly closed by the second moment of the radiation field via the Eddington tensor. Often, the QD method is derived from the spatially continuous transport equation.…”

mentioning

confidence: 99%

An Efficient and Time Accurate, Moment-Based Scale-Bridging Algorithm for Thermal Radiative Transfer Problems

Park¹,

Knoll²,

Rauenzahn³

et al. 2013

SIAM J. Sci. Comput.

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We present physics-based preconditioning and a time-stepping strategy for a momentbased scale-bridging algorithm applied to the thermal radiative transfer equation. Our goal is to obtain (asymptotically) second-order time accurate and consistent solutions without nonlinear iterations between the high-order (HO) transport equation and the low-order (LO) continuum system within a time step. Modified equation analysis shows that this can be achieved via a simple predictor-corrector time stepping that requires one inversion of the transport operator per time step. We propose a physics-based preconditioning based on a combination of the nonlinear elimination technique and Fleck-Cummings linearization. As a result, the LO system can be solved efficiently via a multigrid preconditioned Jacobian-free Newton-Krylov method. For a set of numerical test problems, the physics-based preconditioner reduces the number of GMRES iterations by a factor of 3∼4 as compared to a standard preconditioner for advection-diffusion. Furthermore, the performance of the proposed physics-based preconditioner is insensitive to the time-step size.1. Introduction. Accurate modeling of neutral particle transport behavior is of great importance in many science and engineering applications [8,22]. Many numerical transport algorithms suffer from slow convergence in optically thick regions where particles undergo a large number of scattering and/or absorption and re-emission events. A moment-based scale-bridging algorithm for thermal radiative transfer (TRT) problems has shown great potential for accelerating the solution of the Boltzmann transport equation by bridging the diffusion and transport scales [21]. The algorithm utilizes low-order (LO) continuum equations that are consistently derived from the high-order (HO) transport equation. Due to discrete consistency, the LO system can be used not only for accelerating the HO solution but also for coupling to other physics.Moment-based acceleration has been very successful in the field of nuclear reactor physics. One popular approach is the quasi-diffusion (QD) method [3,11], where the

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Simulation of Radiation Transport in a Channel Based on the Quasi-Diffusion Method

Cited by 26 publications

References 6 publications

Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

Bicompact high order schemes for quasi-diffusion equations

An Efficient and Time Accurate, Moment-Based Scale-Bridging Algorithm for Thermal Radiative Transfer Problems

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