Spatial domain decomposition for Neutron transport problems

Yavuz, M.; Larsen, Edward W.

doi:10.1080/00411458908204321

Cited by 12 publications

(2 citation statements)

References 5 publications

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“…Source Iteration (SI) is the simplest transport iterative method based on sweeping [2,6,24,62,63,122]. In the literature, SI may alternatively be called "Richardson iteration" or "iteration on the scattering source", among other aliases.…”

Section: Transport Iterative Methods (Single-physics)mentioning

confidence: 99%

The NILO-CMFD Method for Iteratively Solving Coupled Neutron Transport–Thermal Hydraulics Problems

Adamowicz

Manera

Larsen

2022

Nuclear Science and Engineering

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The interactions between neutron radiation and matter are nonlinear. Specifically, certain neutron nuclear reactions (e.g., fission events) generate heat, which modifies the temperature and density of the surrounding material, which in turn modify the neutron interaction probabilities (through the macroscopic cross sections). This nonlinear process is referred to as neutron transport with thermal hydraulics feedback.Linear transport problems (without feedback) are accurately described by the Neutron Transport Equation (NTE). Discretized forms of the NTE are routinely solved using iterative transport acceleration schemes, for example, the standard Coarse Mesh Finite Difference (CMFD) method. CMFD and related acceleration schemes for linear transport problems are reliable and well-understood. However, when these same iterative methods are applied to nonlinear (i.e. multiphysics) problems, significant performance and stability issues often occur.In this thesis, we propose modifications to the CMFD procedure, so that it can more robustly and efficiently solve loosely-coupled neutron transport -thermal hydraulics multiphysics problems. We refer to the new method as Nonlinearly Implicit Low-Order CMFD (NILO-CMFD). In this method, the transport-corrected diffusion equationa foundational component of the CMFD method -is modifed to include approximate thermal hydraulics and nuclear data update physics.To begin, we provide a general derivation of the 3-D NILO-CMFD method. Then, to initially analyze and test the method, we develop an approximate 1-D multiphysics model of a 3-D nuclear reactor fuel pin. The 1-D model consists of: (i) a 1-D neutron transport equation describing neutron transport, (ii) a 1-D advection-diffusion equation describing fluid temperature variation, (iii) a fuel temperature that depends on the 1-D fission heat source, and (iv) model equations that define the neutron cross sections and related nuclear data in terms of the fluid and fuel temperatures. The implementation of this model in a 1-D test code shows that the NILO-CMFD method overcomes the instabilities that occur in the standard Relaxed-CMFD (R-CMFD) method.x To test the new NILO-CMFD method on realistic 3-D problems, we implemented an incomplete version of the method, NILO-A, in the 3-D neutron transport code MPACT. For multiphysics problems, MPACT is loosely coupled to the 3-D COBRA-TF (CTF) code, which performs subchannel thermal hydraulics calculations. In every 3-D problem that we ran, NILO-CMFD successfully reduced the number of outer iterations to the low number required by CMFD for single-physics calculations. Unfortunately, due to lack of time, we could not implement the full NILO-CMFD method, which would have significantly reduced the wall clock time of the simulations. Consequently, some of our 3-D simulations required more wall clock time to converge than R-CMFD.Nonetheless, our results show that the NILO-CMFD method is a legitimate generalization of single-physics CMFD to multiphysics problems. The number of outer iterations requi...

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Section: Transport Iterative Methods (Single-physics)mentioning

confidence: 99%

The NILO-CMFD Method for Iteratively Solving Coupled Neutron Transport–Thermal Hydraulics Problems

Adamowicz

Manera

Larsen

2022

Nuclear Science and Engineering

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“…To solve this type of numerical problems one relies on massively parallel computations using high-performance computers. Parallel methodologies for transport problems are based on various transport sweeping algorithms and domain decomposition methods [3][4][5][6][7][8][9][10]. Let us consider that the spatial domain D of the transport problem (1) is divided into a number of subdomains D l (D = l D l ).…”

Section: Introductionmentioning

confidence: 99%

Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Anistratov

Azmy

2015

Journal of Computational Physics

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We study convergence of the integral transport matrix method (ITMM) based on a parallel block Jacobi (PBJ) iterative strategy for solving particle transport problems. The ITMM is a spatial domain decomposition method proposed for massively parallel computations. A Fourier analysis of the PBJ-based iterations applied to S N diamond-difference equations in 1D slab and 2D Cartesian geometries is performed. It is carried out for infinite-medium problems with homogeneous material properties. To analyze the performance of the ITMM with the PBJ algorithm and evaluate its potential in scalability we consider a limiting case of one spatial cell per subdomain. The analysis shows that in such limit the spectral radius of the iteration method is one without regard to values of the scattering ratio and optical thickness of the spatial cells. This implies lack of convergence in infinite medium. Numerical results of finite-medium problems are presented. They demonstrate effects of finite size of spatial domain on the performance of the iteration algorithm as well as its asymptotic behavior when the extent of the spatial domain increases. These numerical experiments also show that for finite domains iterative convergence to a finite criterion is achievable in a multiple of the sum of number of cells in each dimension.

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Practical considerations for the adoption of Anderson acceleration in nonlinear diffusion accelerated transport

Shen,

Kochunas

2024

Annals of Nuclear Energy

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Spatial domain decomposition for Neutron transport problems

Cited by 12 publications

References 5 publications

The NILO-CMFD Method for Iteratively Solving Coupled Neutron Transport–Thermal Hydraulics Problems

The NILO-CMFD Method for Iteratively Solving Coupled Neutron Transport–Thermal Hydraulics Problems

Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Practical considerations for the adoption of Anderson acceleration in nonlinear diffusion accelerated transport

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