A Linear Prolongation Approach to Stabilizing CMFD

Wang, Dean; Xiao, Sicong

doi:10.1080/00295639.2017.1417347

Cited by 45 publications

(9 citation statements)

References 3 publications

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“…The update scheme is implementation-dependent, so in this example, the transport sweep is assumed to take place before the acceleration step. We note that other prolongation operators have been developed that are linear [15], but a multiplicative update is generally used. φ ( +1/2) is the scalar flux obtained from the transport sweep, Φ ( +1/2) is the homogenized scalar flux from the transport sweep, Φ ( +1) is the solution from the acceleration step, and φ ( +1) is the scalar flux to be used in the source for the transport sweep in the next iteration.…”

Section: Prolongation Of the Scalar Fluxmentioning

confidence: 99%

The Stability of Linear Diffusion Acceleration Relative to CMFD

Dodson

Kochunas

Larsen

2021

JNE

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Coarse Mesh Finite Difference (CMFD) is a widely-used iterative acceleration method for neutron transport problems in which nonlinear terms are introduced in the derivation of the low-order CMFD diffusion equation. These terms, including the homogenized diffusion coefficient, the current coupling coefficients, and the multiplicative prolongation constant, are subject to numerical instability when a scalar flux estimate becomes sufficiently small or negative. In this paper, we use a suite of contrived problems to demonstrate the susceptibility of CMFD to failure for each of the vulnerable quantities of interest. Our results show that if a scalar flux estimate becomes negative in any portion of phase space, for any iterate, numerical instability can occur. Specifically, the number of outer iterations required for convergence of the CMFD-accelerated transport problem can increase dramatically, or worse, the iteration scheme can diverge. An alternative Linear Diffusion Acceleration (LDA) scheme addresses these issues by explicitly avoiding local nonlinearities. Our numerical results show that the rapid convergence of LDA is unaffected by the very small or negative scalar flux estimates that can adversely affect the performance of CMFD. Therefore, our results demonstrate that LDA is a robust alternative to CMFD for certain sensitive problems in which CMFD can exhibit reduced effectiveness or failure.

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Section: Prolongation Of the Scalar Fluxmentioning

confidence: 99%

The Stability of Linear Diffusion Acceleration Relative to CMFD

Dodson

Kochunas

Larsen

2021

JNE

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“…Another CMFD variant is the linear prolongation CMFD (lp-CMFD) scheme, which is a method first proposed by Wang and Xiao (2018). Where regular CMFD updates the fine mesh flux in a coarse mesh basis after the diffusion step, lp-CMFD uses a linear additive approach from bilinear interpolation of the coarse mesh flux to update the fine mesh scalar flux, thereby resulting in a smoother transport flux update.…”

Section: Introductionmentioning

confidence: 99%

lp-CMFD acceleration schemes in multi-energy group 2D Monte Carlo transport

Than

Xiao

2022

Front. Energy Res.

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The linear prolongation flux update scheme is extended to both regular CMFD acceleration, as well as partial CMFD acceleration in 2D multi energy group Monte Carlo k-eigenvalue neutron transport problems. The acceleration performance of these CMFD variants were investigated in simple 2D slab geometries, first with a monoenergetic case and then with a three group problem on the same geometry based on the monoenergetic cross sections. Flux convergence was determined via an on-the-fly convergence diagnostics developed by Ueki and Brown. It is found that on top of providing better acceleration in general, the linear prolongation scheme is also able to correct for instabilities in the CMFD scheme. Overall, the lp-pCMFD scheme employing a maximum history length is found to have the best performance across the cases presented.

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“…But it can degrade and even fail when the optical EPJ Web of Conferences 247, 03006 (2021) PHYSOR2020 https://doi.org/10.1051/epjconf/202124703006 thickness of the mesh becomes large. Therefore several methods, including partial current-based CMFD (pCMFD) [2], optimally diffusive CMFD (odCMFD) [3] and linear prolongation CMFD (lpCMFD) [4] [5], has been proposed to stabilize the conventional CMFD method.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, a category of CMFD methods , regarded as "higher-order" prolongation methods (hpCMFD) [9], was proposed to use both the local and neighboring coarse mesh fluxes to update the fine cell flux. One of the hpCMFD methods, refered to lpCMFD, was proposed by Wang and Xiao [4] to use a linear prolongation to update the fine cell scalar fluxes, which will be discussed in the next section. It showed that lpCMFD is more stable than conventional CMFD methods and is effective for a wide range of optical thicknesses.…”

Section: Introductionmentioning

confidence: 99%

Demonstration of a Linear Prolongation CMFD Method on Moc

Wang

et al. 2021

EPJ Web Conf.

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Coarse Mesh Finite Difference (CMFD) method is a very effective method to accelerate the iterations for neutron transport calculation. But it can degrade and even fail when the optical thickness of the mesh becomes large. Therefore several methods, including partial current-based CMFD (pCMFD) and optimally diffusive CMFD (odCMFD), have been proposed to stabilize the conventional CMFD method. Recently, a category of “higherorder” prolongation CMFD (hpCMFD) methods was proposed to use both the local and neighboring coarse mesh fluxes to update the fine cell flux, which can solve the fine cell scalar flux discontinuity problem between the fine cells at the bounary of the coarse mesh. One of the hpCMFD methods, refered as lpCMFD, was proposed to use a linear prolongation to update the fine cell scalar fluxes. Method of Characteristics (MOC) is a very popular method to solve neutron transport equations. In this paper, lpCMFD is applied on the MOC code MPACT for a variety of fine meshes. A track-based centroids calculation method is introduced to find the centroids coordinates for random shapes of fine cells. And the numerical results of a 2D C5G7 problem are provided to demonstrate the stability and efficiency of lpCMFD method on MOC. It shows that lpCMFD can stabilize the CMFD iterations in MOC method effectively and lpCMFD method performs better than odCMFD on reducing the outer MOC iterations.

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A Linear Prolongation Approach to Stabilizing CMFD

Cited by 45 publications

References 3 publications

The Stability of Linear Diffusion Acceleration Relative to CMFD

The Stability of Linear Diffusion Acceleration Relative to CMFD

lp-CMFD acceleration schemes in multi-energy group 2D Monte Carlo transport

Demonstration of a Linear Prolongation CMFD Method on Moc

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