Multiblock Adaptive Mesh Refinement for the SN Transport Equation Based on Lattice Boltzmann Method

Abstract Computational accuracy and resource consumption are two sides of the mesh-based neutron transport calculation, whose balance is a common concern in engineering application. To overcome the inflexibility of the multiblock (MB) refinement technique and the complexity of the adaptive-mesh-refinement (AMR) technique, this paper presents a MB-AMR–based neutron transport lattice Boltzmann method (LBM) for the first time, which is a development and in-depth study for the current nonuniform mesh technique. The neutron transport problems are solved using the LBM with finite Boltzmann scheme, and the mesh configuration is adaptively adjusted using the MB-AMR technique. The MB-AMR technique combines the simplicity of the MB technique and the flexibility of the AMR technique and overcomes their shortcomings. By using invariant blocks, the complicated tree structure used in the traditional AMR technique is eliminated. By adjusting the mesh configuration according to the calculation results adaptively, the inflexible of the MB technique is overcome. By using the finite Boltzmann scheme instead of the traditional LBM, the implementation is further simplified and the interface treatment between different blocks can be solved as inner nodes using streaming process. Based on the above advantages and the simplicity of the LBM, the difficulty of the AMR technique in neutron transport calculation has been greatly reduced. To verify the accuracy and flexibility of the proposed MB-AMR–based neutron transport LBM, five benchmark problems are simulated. Results show that the proposed neutron transport LBM can simulate the multigroup transient and steady-state neutron transport problems accurately and that the MB-AMR technique can adaptively adjust the mesh configuration flexibly and simply. This paper may provide some alternative perspectives to realize the nonuniform mesh–based neutron transport solution and a powerful technique for large-scale engineering.

[1]  A. Zolfaghari,et al.  Adaptive refinement for P N neutron transport equation based on conjoint variational formulation and discontinuous finite element method , 2017 .

[2]  Kan Wang,et al.  Coupled neutronics/thermal-hydraulics analysis of a full PWR core using RMC and CTF , 2017 .

[3]  Ya-Ling He,et al.  Lattice Boltzmann simulations of convection heat transfer in porous media , 2017 .

[4]  C.R.E. de Oliveira,et al.  An arbitrary geometry finite element method for multigroup neutron transport with anisotropic scattering , 1986 .

[5]  X. Shan,et al.  Mass Transport/Diffusion and Surface Reaction Process with Lattice Boltzmann , 2011 .

[6]  Benoit Forget,et al.  Preliminary Coupling of the Monte Carlo Code OpenMC and the Multiphysics Object-Oriented Simulation Environment for Analyzing Doppler Feedback in Monte Carlo Simulations , 2017 .

[7]  Liangzhi Cao,et al.  Auto MOC—A 2D neutron transport code for arbitrary geometry based on the method of characteristics and customization of AutoCAD , 2008 .

[8]  Hitesh Bindra,et al.  Lattice Boltzmann method for solving non-equilibrium radiative transport problems , 2017 .

[9]  R. Sman.  Finite Boltzmann schemes , 2006 .

[10]  R. Furfaro,et al.  A hybrid method for the solution of linear Boltzmann equation , 2014 .

[11]  Phillip Colella,et al.  Interpolation methods and the accuracy of lattice-Boltzmann mesh refinement , 2014, J. Comput. Phys..

[12]  Double multiple-relaxation-time lattice Boltzmann model for solid–liquid phase change with natural convection in porous media , 2015, 1503.08406.

[13]  Hua Li,et al.  Lattice Boltzmann model for combustion and detonation , 2013, 1304.7421.

[14]  G. E. Hansen,et al.  Multitable Treatments of Anisotropic Scattering in SN Multigroup Transport Calculations , 1967 .

[15]  C. J. Everett,et al.  A practical manual on the Monte Carlo method for random walk problems , 1960 .

[16]  G. Rimpault,et al.  APOLLO3 homogenization techniques for transport core calculations—application to the ASTRID CFV core , 2017 .

[17]  R. P. Smedley-Stevenson,et al.  Linear and quadratic octahedral wavelets on the sphere for angular discretisations of the Boltzmann transport equation , 2005 .

[18]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[19]  Y L He,et al.  Improved axisymmetric lattice Boltzmann scheme. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  D. Fournier,et al.  Reactivity Perturbation Formulation for a Discontinuous Galerkin–Based Transport Solver and Its Use with Adaptive Mesh Refinement , 2011 .

[21]  R. Baker.  A Block Adaptive Mesh Refinement Algorithm for the Neutral Particle Transport Equation , 2002 .

[22]  Liangzhi Cao,et al.  An acceleration technique for 2D MOC based on Krylov subspace and domain decomposition methods , 2011 .

[23]  B. Rokrok,et al.  Mesh-free method for numerical solution of the multi-group discrete ordinate neutron transport equation , 2017 .

[24]  Hans Jürgen Herrmann,et al.  Lattice Boltzmann model for resistive relativistic magnetohydrodynamics. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Qiong Zhang,et al.  Hybrid Monte Carlo-Deterministic Methods for Reactor Analysis , 2012 .

[26]  Manuele Aufiero,et al.  Development of sensitivity analysis capabilities of generalized responses to nuclear data in Monte Carlo code RMC , 2016 .

[27]  Yahui Wang,et al.  Neutron transport solution of lattice Boltzmann method and streaming-based block-structured adaptive mesh refinement , 2018, Annals of Nuclear Energy.

[28]  S. Succi,et al.  Lattice Boltzmann across scales: from turbulence to DNA translocation , 2008 .

[29]  Joel Rhodes,et al.  A Linear Source Approximation Scheme for the Method of Characteristics , 2016 .

[30]  Richard McCulloch,et al.  Coupled radiative and conjugate heat transfer in participating media using lattice Boltzmann methods , 2016 .

[31]  B. Ganapol.  A more efficient implementation of the discrete-ordinates method for an approximate model of particle transport in a duct , 2015 .

[32]  W. Shyy,et al.  A multi‐block lattice Boltzmann method for viscous fluid flows , 2002 .

[33]  Matthaeus,et al.  Lattice Boltzmann model for simulation of magnetohydrodynamics. , 1991, Physical review letters.

[34]  O. Widlund,et al.  Iterative solution of elliptic systems : and applications to the neutron diffusion equations of reactor physics , 1967 .

[35]  P. Zweifel,et al.  Multigroup neutron transport. I. Full range , 1976 .

[36]  Yahui Wang,et al.  Lattice Boltzmann method for simulation of time-dependent neutral particle transport , 2017 .

[37]  S. A. Hosseini.  Development of Galerkin Finite Element Method Three-dimensional Computational Code for the Multigroup Neutron Diffusion Equation with Unstructured Tetrahedron Elements , 2016 .

[38]  Baochang Shi,et al.  Lattice Boltzmann model for nonlinear convection-diffusion equations. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  A. Mohamad.  Lattice Boltzmann Method , 2011 .

[40]  O. Filippova,et al.  Grid Refinement for Lattice-BGK Models , 1998 .

[41]  Arup Kumar Das,et al.  Lattice Boltzmann Method Applied to Radiative Transport Analysis in a Planar Participating Medium , 2014 .

[42]  Zhenhua Chai,et al.  Study of electro-osmotic flows in microchannels packed with variable porosity media via lattice boltzmann method , 2007 .

[43]  Abbas Fakhari,et al.  Finite-difference lattice Boltzmann method with a block-structured adaptive-mesh-refinement technique. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Huaqing Zheng,et al.  CAD-based Monte Carlo Program for Integrated Simulation of Nuclear System SuperMC , 2014, ICS 2014.

[45]  Norman J. McCormick,et al.  A Review of Neutron Transport Approximations , 1982 .

[46]  Won Sik Yang,et al.  A Consistent CMFD Formulation for the Acceleration of Neutron Transport Calculations Based on the Finite Element Method , 2017 .

[47]  Huaqing Zheng,et al.  CAD-based Monte Carlo Program for Integrated Simulation of Nuclear System SuperMC , 2014, ICS 2014.

[48]  T. Downar,et al.  The Development and Implementation of a One-Dimensional Sn Method in the 2D-1D Integral Transport Solution , 2014 .

[49]  Paul K. Romano,et al.  OpenMC: A State-of-the-Art Monte Carlo Code for Research and Development , 2014, ICS 2014.

[50]  Orestis Malaspinas,et al.  Advances in multi-domain lattice Boltzmann grid refinement , 2012, J. Comput. Phys..

[51]  Chuguang Zheng,et al.  A coupled lattice BGK model for the Boussinesq equations , 2002 .

[52]  Subhash C. Mishra,et al.  Analysis of transport of short-pulse radiation in a participating medium using lattice Boltzmann method , 2014 .

[53]  Huaqing Zheng,et al.  Benchmarking of CAD-based SuperMC with ITER benchmark model , 2014 .

[54]  A. Mohamad.  Lattice Boltzmann method : fundamentals and engineering applications with computer codes / A. A. Mohamad , 2011 .

[55]  B. Shi,et al.  Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method , 2002 .

[56]  Yahui Wang,et al.  Lattice Boltzmann solution of the transient Boltzmann transport equation in radiative and neutron transport. , 2017, Physical review. E.