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Capabilities for nuclear data sensitivity and uncertainty analysis have been recently implemented in numerous continuous-energy Monte Carlo codes, including the Reactor Monte Carlo (RMC) code. Previous work developed the capability for RMC of computing sensitivity coefficients of the effective multiplication factor and related uncertainties, due to nuclear data. In this work, such capability was extended to generalized responses in the form of ratios of linear response functions of the forward flux based on the collision history-based approach as implemented in SERPENT2. The superhistory algorithm was also adopted in RMC to reduce memory consumption for generalized sensitivity calculations. These new capabilities of RMC were verified by comparing results of TSUNAMI-1D in SCALE6.1 code package, and SERPENT2 through Jezebel, Flattop and the UAM TMI PWR pin cell benchmark problems.

A new Monte Carlo transport code RMC has been being developed by Department of Engineering Physics, Tsinghua University, Beijing as a tool for reactor core analysis on high-performance computing platforms. To meet the requirements of reactor analysis, RMC now has such functions as criticality calculation, fixed-source calculation, burnup calculation and kinetics simulations. Some techniques for geometry treatment, new burnup algorithm, source convergence acceleration, massive tally and parallel calculation, and temperature dependent cross sections processing are researched and implemented in RMC to improve the efficiency. Validation results of criticality calculation, burnup calculation, source convergence acceleration, tallies performance and parallel performance shown in this paper prove the capabilities of RMC in dealing with reactor analysis problems with good performances. [ABSTRACT FROM AUTHOR]

Criticality search is a very important aspect in reactor physics analysis. Due to the advantages of Monte Carlo method and the development of computer technologies, Monte Carlo criticality search is becoming more and more necessary and feasible. Existing Monte Carlo criticality search methods need large amount of individual criticality runs and may have unstable results because of the uncertainties of criticality results. In this paper, a new perturbation based Monte Carlo criticality search method is proposed and discussed. This method only needs one individual criticality calculation with perturbation tallies to estimate k eff changing function using initial k eff and differential coefficients results, and solves polynomial equations to get the criticality search results. The new perturbation based Monte Carlo criticality search method is implemented in the Monte Carlo code RMC, and criticality search problems in density, enrichment and concentration are taken out. Results show that this method is quite inspiring in accuracy and efficiency, and has advantages compared with other criticality search methods. [ABSTRACT FROM AUTHOR]

With the increasing demands of high fidelity neutronics analysis and the development of computer technology, Monte Carlo method is becoming more and more attractive in accurate simulation of pebble bed High Temperature gas-cooled Reactor (HTR), owing to its advantages of the flexible geometry modeling and the use of continuous-energy nuclear cross sections. For the double-heterogeneous geometry of pebble bed, traditional Monte Carlo codes can treat it by explicit geometry description. However, packing methods such as Random Sequential Addition (RSA) can only produce a sphere packing up to 38% volume packing fraction, while Discrete Element Method (DEM) is troublesome and also time consuming. Moreover, traditional Monte Carlo codes are difficult and inconvenient to simulate the mixed and polytype particles or pebbles. A new random geometry method was developed in Monte Carlo code RMC to simulate the particle transport in polytype particle/pebble in double heterogeneous geometry systems. This method was verified by some test cases, and applied to the full core calculations of HTR-10 benchmark. The reactivity, temperature coefficient and control rod worth of HTR-10 were compared for full core and initial core in helium and air atmosphere respectively, and the results agree well with the benchmark results and experimental results. This work would provide an efficient tool for the innovative design of pebble bed, prism HTRs and molten salt reactors with polytype particles or pebbles using Monte Carlo method. [ABSTRACT FROM AUTHOR]

Variance reduction methods in Monte Carlo calculations are essential especially for the design and analysis of some real-world nuclear applications with complex and large geometry. As the most popular variance reduction method, weight window technique has demonstrated its great capability and been implemented in most Monte Carlo particle transport codes. In this work, we propose two new variance reduction methods based on weight window. One is automatic inner iterative fixed source calculation method, which makes it more convenient and efficient to use weight window technique. The other is called adaptive weight window method, which solves one of the most common frustrations when using weight window that the output of zero weight windows and difficulties to obtain a set of variance reduction parameters in some deep penetration problems. These two new methods are verified and compared. The efficiency of newly proposed adaptive weight window method and automatic inner iterative fixed source calculation method was found to be 32,966 and 25,793 times higher than that of an analogue run. [ABSTRACT FROM AUTHOR]

The iterated fission probability (IFP) method has been demonstrated to be an accurate alternative for estimating the adjoint-weighted parameters in continuous-energy Monte Carlo forward calculations. However, the memory requirements of this method are huge especially when a large number of sensitivity coefficients are desired. Therefore, data decomposition techniques are proposed in this work. Two parallel strategies based on the neutron production rate (NPR) estimator and the fission neutron population (FNP) estimator for adjoint fluxes, as well as a more efficient algorithm which has multiple overlapping blocks (MOB) in a cycle, are investigated and implemented in the continuous-energy Reactor Monte Carlo code RMC for sensitivity analysis. Furthermore, a region-specific sensitivity analysis capability is developed in RMC. These new strategies, algorithms and capabilities are verified against analytic solutions of a multi-group infinite-medium problem and against results from other software packages including MCNP6, TSUANAMI-1D and multi-group TSUNAMI-3D. While the results generated by the NPR and FNP strategies agree within 0.1% of the analytic sensitivity coefficients, the MOB strategy surprisingly produces sensitivity coefficients exactly equal to the analytic ones. Meanwhile, the results generated by the three strategies in RMC are in agreement with those produced by other codes within a few percent. Moreover, the MOB strategy performs the most efficient sensitivity coefficient calculations (offering as much as an order of magnitude gain in FoMs over MCNP6), followed by the NPR and FNP strategies, and then MCNP6. The results also reveal that these three strategies employed by RMC maintain high parallel efficiency of approximately 96–98% within the observed 600 processors, and the memory requirements per processor decrease almost linearly as the number of processors increases from 120 to 600. To conclude, RMC is capable of performing sensitivity analysis with sufficient accuracy and high efficiency. [ABSTRACT FROM AUTHOR]

Highlights: [•] A 2D PWR core pin-by-pin depletion is carried out with the RMC code. [•] Memory requirements are effectively reduced by using data decompositions. [•] Results demonstrate the feasibility of MC burnup analysis for large cores. [•] RMC is proved to be suitable for large-scale MC burnup calculations. [ABSTRACT FROM AUTHOR]

• The connection calculation between the weak neutron field and the strong neutron field is implemented in the RMC code. • A connection calculation method between the three-dimensional Direct Kinetics Simulation method and the Predictor-Corrector Quasi-Static method is proposed. • The connection calculation method is about 3 times faster than the pure Direct Kinetics Simulation method. In the future, it will be used in simulation calculations of reactor start-up without external neutron source. Reactor startup without external neutron source is beneficial to improve the economics of nuclear energy, especially in a more and more competitive energy market with the rapid development and deployment of renewable energy. This paper conducts the research on the connection calculation of Monte Carlo Direct Kinetics Simulation (DKS) method and Predictor-Corrector Quasi-Static (PCQS) method during the weak source start-up process of the reactor based on the Monte Carlo code RMC, addressing the calculation methods for time absorption source, delayed neutron source, reactivity, effective delayed neutron fraction and neutron generation time. It achieves advantages in the calculation efficiency in three-dimensional simulations of the connection calculation between DKS in weak neutron field based on stochastic neutron transport equation and PCQS in strong neutron field based on time-dependent Boltzmann neutron transport equation. [ABSTRACT FROM AUTHOR]

Highlights: [•] Fission matrix method is used for undersampling diagnostics in MC calculations. [•] Two criterions are proposed to diagnose keff and local tallies. [•] The diagnostic method has been implemented in the RMC Monte Carlo code. [•] The mesh effect on the fission matrix method is investigated. [Copyright &y& Elsevier]

Abstract: The Monte Carlo burnup calculation has always been a challenging problem because of its large time consumption when applied to full-scale assembly or core calculations, and thus its application in routine analysis is limited. Most existing MC burnup codes are usually external wrappers between a MC code, e.g. MCNP, and a depletion code, e.g. ORIGEN. The code RMC is a newly developed MC code with an embedded depletion module aimed at performing burnup calculations of large-scale problems with high efficiency. Several measures have been taken to strengthen the burnup capabilities of RMC. Firstly, an accurate and efficient depletion module called DEPTH has been developed and built in, which employs the rational approximation and polynomial approximation methods. Secondly, the Energy-Bin method and the Cell-Mapping method are implemented to speed up the transport calculations with large numbers of nuclides and tally cells. Thirdly, the batch tally method and the parallelized depletion module have been utilized to better handle cases with massive amounts of burnup regions in parallel calculations. Burnup cases including a PWR pin and a 5×5 assembly group are calculated, thereby demonstrating the burnup capabilities of the RMC code. In addition, the computational time and memory requirements of RMC are compared with other MC burnup codes. [Copyright &y& Elsevier]

Abstract: The Monte Carlo codes used for neutron transport calculations are always time consuming, a large proportion of which is possessed by the treatment of continuous-energy cross sections. In this paper, two companion methods are developed for the optimization treatment of point-wise nuclear data, the first of which is called Computational-Expense Oriented (CEO) method based on the unionized energy grid approach and reconstructs only the computationally expensive cross sections in neutron transport simulation, and the other of which is called energy bin (EB) method, a companion of CEO method when the reaction rate tallies for MC-coupling burnup calculation are performed. These two methods are implemented in the code RMC, a Monte Carlo (MC) code used for reactor analysis, and tested on fast reactor core and BWR assembly problems. The numerical results show that CEO method, in comparison with reconstructing all cross sections under the unionized grid, requires the sharply decreased computer memory while achieving almost the same computational efficiency, and EB method can optimize the processing of nuclide-specific energy grid search and thus effectively reduce the total search number while requiring very small computer memory. [Copyright &y& Elsevier]

• Four coupling schemes of Monte Carlo burnup calculation are implemented and compared in RMC considering the accuracy, efficiency and memory requirement. • It is proved that two types of predictor-corrector coupling schemes have identical effect on accuracy and efficiency. • Memory reqiurement of the four coupling schemes is analyzed, it is demonstrated that the high order predictor-corrector with sub-step method can be implemented in large-scale burnup problem. As wrapping tools for coupling Monte Carlo (MC) neutron transport code with depletion solver, four different coupling schemes are implemented in Reactor Monte Carlo Code (RMC) developed at Tsinghua University, and verified in two assembly testing cases derived from VERA international benchmark. In this paper, accuracy and time consumption are comparatively analyzed, as well as memory requirement which is significant in large-scale burnup calculation. Results illustrate that beginning of step approximation, as the basic and simplest coupling method, performed with relatively poor accuracy. With nearly the same efficiency, two predictor-corrector methods provide identical accuracy better than the beginning of step approximation, but require different computer memories. High order predictor-corrector combined with sub-step method (HSPC) has the best performance and requires the most memory. By means of hybrid parallelism, domain decomposition and parallel depletion solver in RMC, HSPC is able to be applied in large-scale burnup problem. [ABSTRACT FROM AUTHOR]

• The integrated parallelism strategy was proposed for full core depletion problem. • The integrated platform combines domain and data decomposition and hybrid parallel. • OpenMP with domain decomposition performed better than with data decomposition. • The batch method was adopted to reduce the time for collective communication. • The proposed strategy can handle ∼20 millions of burnup regions with high efficiency. The Monte Carlo (MC) method is becoming more and more attractive for high fidelity simulations in reactor physics. The huge memory consumption is the bottleneck in the three dimensional (3D) full core detailed depletion calculations. Three strategies were proposed to overcome the memory problem, including domain decomposition, data decomposition and hybrid parallelism. These methods can solve this problem in some extent, but each of them has its own limitation. In this paper, the integrated parallelism platform which combines these three strategies was proposed and developed in the Reactor Monte Carlo (RMC) code. Based on this platform, the performances of different combinations of these three strategies were investigated on PWR assembly and PWR full-core models on the Tianhe-2 supercomputer. The results show that "domain decomposition + hybrid parallelism" performed better than "tally data decomposition + hybrid parallelism" at the scale of above 0.6 million burnup regions. Moreover, the batch method was adopted to reduce the frequency of collective communications and thus save computational time. Finally, the strategy of "domain decomposition + burnup data decomposition + hybrid parallelism" with the batch method was proposed and tested on Tianhe-2 supercomputer compute nodes, equipped with 64 Gigabytes (GB) of memory. The proposed strategy can handle about twenty millions of burnup regions with high efficiency, which is the important foundation of full core detailed depletion calculation and high fidelity simulation. [ABSTRACT FROM AUTHOR]

Geometric sensitivity analyses of the k -eigenvalue have many applications in analyses of geometric uncertainty, calculations of differential control rod worth, and searches for critical geometry. The adjoint-weighted first-order geometric sensitivity theory is widely used and has continuously evolved with the Monte Carlo methods. However, the existing adjoint-weighted algorithm can do only uniform isotropic expansions or contractions of surfaces. The adjoint-weighted algorithm also requires computation of adjoint-weighted scattering and fission reaction rates exactly at material interfaces, which has an infinitesimal probability in reality. This paper presents an improved geometry adjoint-weighted perturbation algorithm that is incorporated into the continuous-energy Reactor Monte Carlo (RMC) code. The improvement of the adjoint-weighted algorithm is decomposed into three steps for constructing a cross-section function of geometric parameters using logical expressions, calculating the derivative of the cross-section function, and estimating the adjoint-weighted surface reaction rates. The improved algorithm can accommodate common one-parameter geometric perturbations of internal interfaces or boundary surfaces as well as those of cells as long as the perturbed cells can be described by logical expressions of spatial surface equations. The perturbation algorithm is compared with a direct difference method, the linear least-squares fitting method with central differences, for several typical geometric perturbations including translation, fixed-axis rotation, and uniform isotropic/anisotropic expansion transformations of planar, spherical, cylindrical, and conical surfaces. The differences between the two methods are not more than 3% and not more than 3 σ for the majority of the test examples. Even though the perturbation algorithm has higher figures of merit than the direct difference method for the majority of the test examples, there is no guarantee that the former can always be more efficient than the latter. The limitation in the efficiency of the perturbation algorithm was demonstrated by the totally reflecting light water reactor pin model. [ABSTRACT FROM AUTHOR]

• This paper introduces a transient-state coupling method using the Monte Carlo Code RMC (Reactor Monte Carlo Code) and the Computational Fluid Dynamic (CFD) code ANSYS FLUENT. • This coupling multi-physics method was applied to reproduce TREAT reactor behaviour in time for short transients where the sudden reactivity was 2.5–5.4 dollars. • Calculated results were compared with power measured during temperature limited transients, and the deviation at peak power was less than 30%. This paper introduces a transient-state coupling method using the Monte Carlo Code RMC (Reactor Monte Carlo Code) and the Computational Fluid Dynamic (CFD) code ANSYS FLUENT. RMC employs the Predictor-Corrector Quasi-Static (PCQS) method to solve space- and time-dependent neutron transport problems and uses the on-the-fly target motion sampling (TMS) for Doppler broadening. This method was performed for simulation of transients in the Transient Reactor Test Facility (TREAT). Time evolutions of power were reproduced and qualitative assessment of the model was performed by comparison with the measured power. This method successfully reproduced the experimental results of transients in TREAT reactor, and the deviation at peak power was less than 30%. [ABSTRACT FROM AUTHOR]

Sensitivity analysis is an important way for us to know how the input parameters will affect the output of a system. Therefore, recently, there is an increased interest in developing sensitivity analysis methods in continuous-energy Monte Carlo Code due to the fact that Monte Carlo method can perform high-fidelity simulations of nuclear reactor. Previous studies mainly focused on developing sensitivity analysis method suitable for analyze eigenvalue. There are relatively few researches for performing sensitivity analysis of generalized response function by using continuous-energy Monte Carlo code. So, in this work, the differential operator method (DOM) has been investigated and implemented in continuous-energy Reactor Monte Carlo code (RMC) to perform sensitivity analysis of generalized response function in the form of ratios of reaction rate. The DOM implemented in RMC is based on the analog Monte Carlo transport mode and non-analog Monte Carlo transport mode. The correctness of the newly implemented method has been verified by comparing the results with those calculated by using the collision history-based method through the Jezeble and Flattop benchmark problems. In general, the results given by the DOM agree well with those obtained by the collision history-based method with an accuracy of 5%. Moreover, it is also shown that the non-analog Monte Carlo transport mode can obtain lower relative standard deviation of the sensitivity coefficients than the analog Monte Carlo transport mode.

The multipole representation provides an analytical way of Doppler broadening cross sections for neutron interactions and relies on a partial fraction decomposition that represents R-matrix resonance parameters by poles and residues. The windowed multipole method selectively broadens impactful poles and approximates the rest to increase the efficiency of the process. However, this process requires knowledge of the resonance parameters and certain limitations occur when additional channels are opened in the defined resolved resonance region such that only 2/3 of the ENDF/B-VII.1 nuclides can be processed. Some important nuclides needed in reactor applications such as Oxygen-16 and Hydrogen-1 are directly represented in point-wise form in the evaluation nuclear data library hindering the practicality of this approach. This paper presents a new fitting method for nuclear point-wise cross sections data that yields a pole and residue form analogous to the multipole representation. The Vector Fitting technique which originates from the field of signal processing was applied to the fitting of point-wise cross sections. Poles and residues from Vector Fitting were generated for Oxygen-16, Hydrogen-1, Boron-10 and Boron-11 and processed in the windowed multipole format. These new libraries were tested by direct comparison of the microscopic cross sections before and after Doppler Broadening, and by integral comparisons using a typical PWR pin cell from the BEAVRS benchmark. Results indicate that the new libraries are equivalent to the point-wise representation with the added benefit of allowing on-the-fly Doppler broadening without the need for temperature interpolation. Runtimes are approximately ∼28% slower using the multipole representation on this example problem compared to a single temperature ACE file. [ABSTRACT FROM AUTHOR]

With the rapid development of computational power and parallel algorithms, Monte Carlo method has been widely investigated and used in neutron transport simulations due to its advantages in geometry modelling and usage of continuous energy point-wise cross sections. Monte Carlo codes can also be coupled with thermal-hydraulics codes to consider feedbacks. One of the most important aspects of thermal-hydraulics feedback is the detailed temperature distribution, which results in the demands of updates of temperature dependent cross sections in neutron transport simulations. For thermal reactors such as PWR and HTGR, two neutron energy regions should be carefully considered: the resolved resonance region (RRR) and the thermal energy region, especially the resolved resonance region. Besides, the temperature dependence of cross sections in the unresolved resonance energy region (URR) is also important for fast reactors and some experimental critical assemblies. In this paper, the on-the-fly temperature treatment of cross sections in the RRR was implemented in RMC code. The on-the-fly method for the URR was also proposed and implemented in RMC code, which was also combined with the on-the-fly temperature treatments for resolved resonance energy. The proposed method was applied to Monte Carlo transport and depletion calculations. The accuracy and efficiency are compared for different combinations of methods of RRR and URR. The results show that the on-the-fly treatment has high efficiency and satisfactory fidelity. The probability tables with equiprobable bands were also developed to reduce the memory consumption, with keeping the same accuracy of original probability tables. [ABSTRACT FROM AUTHOR]

• Three mesh-free SW-based methods are proposed to capture the FSD random error term's 1 m feature. • A mesh-free source convergence auto-diagnosis algorithm is introduced utilizing the 1 m feature. • The algorithm can automatically save 58% to 81% of the computational time to reach a converged fission source in models with a dominance ratio of around 0.99. The Monte Carlo algorithm commonly adopts the power iteration (PI) process in criticality calculations. Previous studies have shown that random error term in the PI process significantly influences the source convergence diagnosis and variance underestimation phenomenon. This paper uses the Sliced Wasserstein (SW) distance of the fission source distributions (FSDs) to estimate the error terms in the PI process. Three mesh-free SW-based methods are proposed to capture the random error term's 1 m feature for the OECD source convergence fissile slab model, sphere array model, and the BEAVRS model. Then, a mesh-free source convergence auto-diagnosis algorithm is introduced based on the methods. The algorithm sets the batch size at five stages. The 1 m feature of the random error term is utilized to achieve auto-diagnosis at the target batch size. Numerical calculation results show that the auto-diagnosis algorithm is practical and efficient for source convergence diagnosis and acceleration, which can automatically save 58 % to 81 % of the computational time to reach a converged fission source in models with the dominance ratio of around 0.99. [ABSTRACT FROM AUTHOR]

Monte Carlo method can provide high fidelity neutronic analysis of different types of nuclear reactors, owing to its advantages of the flexible geometry modeling and the use of continuous-energy nuclear cross sections. It can also be coupled with thermal-hydraulics codes to consider feedbacks. Due to the effect of thermal motion of target nucleus known as Doppler effect, special treatments have to be used for cross sections at different temperature points. The traditional approach of pre-generated cross sections has difficulty of memory footprint when the number of temperature points is large. The target motion sampling (TMS) method was proposed and developed in Serpent code for temperature treatment based on the Woodcock tracking. In this paper, the TMS method was developed in RMC code based on the ray tracking. Moreover, Doppler-broadening rejection correction (DBRC) technique was also implemented in RMC to consider the effect of thermal motion on scattering kinematics. The pre-generated technique was proposed and applied to accelerate the calculation of TMS method. The results show that TMS method is equivalent to the exact cross-sections with DBRC, while TMS in RMC has higher efficiency in the cases of PWR and HTGR, no matter that the number of nuclides is small or large. [ABSTRACT FROM AUTHOR]

Monte Carlo method can provide high fidelity neutronic analyses of different types of nuclear reactors, because of its advantages of the flexible geometry modeling and the use of continuous-energy nuclear cross sections. MC codes can also couple with depletion solver and thermal-hydraulics codes simultaneously for the “transport-burnup-thermal-hydraulics” coupled calculations. In this paper, the target motion sampling (TMS) method was developed in RMC code to consider the Doppler broadening effect in resolved resonance energy region, and the on-the-fly interpolation of thermal scattering data was developed to consider the thermal scattering and bound effect in the thermal energy region. Moreover, TMS method was applied to reaction rate tally and depletion calculation for power generation feedback and nuclide density evolutions. This is the first time that a Monte Carlo code is developed for on-the-fly temperature treatment in MC depletion calculations. The results show that TMS method and on-the-fly interpolation of thermal scattering have high efficiency and accuracy in the cases of PWR assembly calculation. With TMS method, the reaction rate can be tallied with temperature feedback. Temperature feedback in each burnup step can also be considered, allowing for the high fidelity “transport-burnup-thermal-hydraulics” coupled calculation. [ABSTRACT FROM AUTHOR]

Recently, there is a need to develop advanced methods of computing eigenvalue sensitivity coefficients to nuclear data in the continuous-energy Monte Carlo codes. One of these methods is the iterated fission probability (IFP) method, which is adopted by most of Monte Carlo codes of having the capabilities of computing sensitivity coefficients, including the Reactor Monte Carlo code RMC. Though it is accurate theoretically, the IFP method faces the challenge of huge memory consumption. Therefore, it may sometimes produce poor sensitivity coefficients since the number of particles in each active cycle is not sufficient enough due to the limitation of computer memory capacity. In this work, two algorithms of the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method, namely, the collision-event-based algorithm (C-CLUTCH) which is also implemented in SCALE and the fission-event-based algorithm (F-CLUTCH) which is put forward in this work, are investigated and implemented in RMC to reduce memory requirements for computing eigenvalue sensitivity coefficients. While the C-CLUTCH algorithm requires to store concerning reaction rates of every collision, the F-CLUTCH algorithm only stores concerning reaction rates of every fission point. In addition, the fission matrix method is put forward to generate the adjoint fission source distribution for the CLUTCH method to compute sensitivity coefficients. These newly proposed approaches implemented in RMC code are verified by a SF96 lattice model and the MIT BEAVRS benchmark problem. The numerical results indicate the accuracy of the F-CLUTCH algorithm is the same as the C-CLUTCH algorithm while the F-CLUTCH algorithm requires less memory and has higher computational efficiency. [ABSTRACT FROM AUTHOR]

Simulation of particle transport in random media poses a challenge for traditional deterministic transport methods, due to the significant effects of spatial and energy self-shielding. Monte Carlo method plays an important role in accurate simulation of random media, owing to its flexible geometry modeling and the use of continuous-energy nuclear cross sections. Three stochastic geometry modeling methods including Random Lattice Method, Chord Length Sampling and explicit modeling approach with mesh acceleration technique, have been developed in RMC to simulate the particle transport in the dispersed fuels. The verifications of the accuracy and the investigations of the calculation efficiency have been carried out. The stochastic effects of the randomly dispersed fuel particles are also analyzed. The results show that all three stochastic geometry modeling methods can account for the effects of the random dispersion of fuel particles, and the explicit modeling method can be regarded as the best choice. [ABSTRACT FROM AUTHOR]

• An improved direct kinetic simulation method has been developed in RMC. • The equivalence between the initial neutron distribution of the direct kinetic simulation method and the time absorption source distribution in the static calculation mode of the PCQS method is proved. • The polynomial fitting method is used to reduce the big fluctuation of the calculated results, and the effect is remarkable. With the continuous development of supercomputing, a direct kinetic simulation based on Monte Carlo method has received more attention owing to its high fidelity. In this paper, an improved direct kinetic simulation capability is developed based on the Reactor Monte Carlo (RMC) code. Several new techniques that are different from other Monte Carlo codes have been proposed, including a new method of obtaining the neutron distribution at the initial moment, and a theoretically more accurate time-dependent tally method. The newly-developed kinetic capability was tested and verified using a point reactor benchmark and a complex three-dimensional C5G7 kinetic benchmark. The numerical results demonstrate that the relative differences of the relative power at all time points between such direct kinetic simulation capability and the reference in the C5G7 benchmark are within 5.15%. [ABSTRACT FROM AUTHOR]

• A new diagnostic method for Monte Carlo (MC) source convergence is proposed based on the Wasserstein distance (WD) metric. • The usage of the WD-based indicator is almost input-free and particularly requires no spatial meshing. • The WD-based indicator is intuitive and easy to implement. • The proposed indicator is more conservative than the existing entropy-based indicators. The power iteration technique is commonly used in Monte Carlo (MC) criticality simulations to obtain converged neutron source distributions. Entropy is a typical indicator used to examine source distribution convergence. However, spatial meshing is required to calculate entropy, and the performance of a convergence diagnostic is sensitive to the chosen meshing scheme. A new indicator based on the Wasserstein distance (WD) measure is proposed; it is intuitive and easy to implement in MC codes. In addition, the usage of the WD-based indicator is almost input-free, which not only lowers the thresholds that users must meet but also reduces modeling errors. Numerical tests are conducted with typical source convergence problems and a full-core problem. The results show that the WD-based indicator is more conservative and reliable than the existing entropy-based indicators. For the BEAVRS problem, the average relative errors of the axial fission rate obtained using the entropy-based indicator are larger than 4%, while it is less than 1% when using the WD-based indicator. An extra computational cost is required to calculate the WD values, but the performance penalty is acceptable, with the slowdown less than 2% for large-scale problems. [ABSTRACT FROM AUTHOR]

• An innovative single neutron tracking method for calculating POS based on the Reactor Monte Carlo (RMC) code is proposed. • Both new and traditional methods for calculating POS are developed in RMC. • The new method does not need to control the number of particles which is a better method than the neutron bank tracking method in terms of accuracy and user friendliness. In a weak neutron source system, the neutron chains rarely overlap, and hence the neutrons should be described by stochastic kinetics. The probability of survival (POS) is a quantity that is often calculated in the field of stochastic kinetics and is also a simple index to test the correctness of the method of describing weak source systems. The general Monte Carlo method for calculating POS needs to control the number of simulated particles, which introduces deviations. In this work, an innovative single neutron tracking method for calculating POS based on the Reactor Monte Carlo (RMC) code is proposed, and it does not need to control the number of particles. The relative difference between the POS calculated by RMC and those calculated by MCATK are less than 6%. The new method is more accurate and user-friendly than the traditional method. [ABSTRACT FROM AUTHOR]

• A perturbation method is developed to calculate the fuel temperature coefficients. • Gauss-Hermite quadrature is adopted to on-the-fly calculate XS derivatives to temperature. • The free-gas model is used to analyse the perturbation of the scattering process. A negative fuel temperature reactivity coefficient is an important reactor physical parameter that indicates the inherent reactor operating safety. However, existing Monte Carlo perturbation methods still cannot accurately and efficiently predict the derivative of the k-eigenvalue with respect to temperature. The main difficulty lies in calculating the derivatives of the microscopic cross-section with respect to the temperature. This paper presents a Temperature Perturbation Method (TPM) that incorporates on-the-fly cross-section treatment as well as the free gas model into the differential operator method to calculate derivatives of the k-eigenvalue with respect to fuel temperature. TPM was then used to predict the k-eigenvalue at various temperatures for the Mosteller pin model. The differences between TPM and the direct difference method are less than 3% within 3 times of standard deviation. The results indicate that TPM can accurately and efficiently estimate the derivatives of the k-eigenvalue with respect to the fuel temperature. [ABSTRACT FROM AUTHOR]

• The superhistory based new GPT formulation was developed in RMC. • The sensitivity coefficients are shown to agree within 5% of reference results. • Uncertainty of the uncertainty quantification method agree with the stochastic sampling method. The capability of performing nuclear data sensitivity and uncertainty analysis of reaction rates has been developed in continuous-energy Reactor Monte Carlo (RMC) code. The sensitivity coefficients of reaction rates are calculated by using new generalized perturbation theory (GPT) formulation which is also implemented in McCARD. The superhistory based generalized perturbation theory (SH-GPT) formulation is developed in this paper to overcome the huge memory consumption problem encountered by the new GPT formulation. This newly developed capability is tested on several benchmark problems. The sensitivity coefficients are shown to agree within 5% of reference results for most cases. Moreover, the region-specified sensitivity analysis capability enables RMC to be the first continuous-energy Monte Carlo code that can use the first-order uncertainty quantification method to perform uncertainty analysis of the power distribution. The uncertainty results calculated by first-order uncertainty quantification method also agree well with those obtained by using stochastic sampling method. [ABSTRACT FROM AUTHOR]

• An on-the-fly homogenization method coupled with depletion was proposed. • HTTR benchmark was chosen to test the method. • Different energy structures and spatial homogenization schemes were compared. • OTFHom method captures double heterogeneity effect accurately with 1/3 ~ 1/5 time. An on-the-fly homogenization (OTFHom) method coupled with depletion based on Monte Carlo method was proposed and implemented in Reactor Monte Carlo code (RMC), which uses continuous energy cross sections to generate multi-group cross sections for specified problems and then uses them in Monte Carlo multi-group calculations to get more convergent results. In order to coupling with depletion, some modifications are made in continuous energy and multi-group calculation procedures to get one-group depletion cross sections and flux for each depletion region. A verification of OTFHom method is carried out to investigate the accuracy and efficiency using HTTR benchmark, which is a prismatic block-type high temperature gas cooled reactor designed by Japan. The criticality and depletion results show that OTFHom method can capture double heterogeneity effect accurately and reduce calculation time considerably because of the spatial homogenization of massive TRISO particles embedded in the graphite matrix. In terms of HTTR model, the time used by CE calculation is about 3 times of that used by OTFHom calculations. [ABSTRACT FROM AUTHOR]

• GEAR-MC method was extended to perform geometric sensitivity analysis. • Sensitivity coefficients estimated by GEAR-MC method agree with reference results. • The intergenerational term should be considered correctly in practical application. GEneralized Adjoint Responses in Monte Carlo (GEAR-MC) method has been developed to perform sensitivity analysis of reaction rate ratios, which was to compute sensitivity coefficients of reaction rate ratios to nuclear data e.g. nuclear cross sections. In this work, the GEAR-MC method is extended to calculate sensitivity coefficients of reaction rate ratios to geometric parameters for the first time and is implemented in the Reactor Monte Carlo (RMC) code. This newly developed geometric sensitivity analysis capability is tested by four benchmark problems. The results are shown to agree within 4% and 3 σ with reference results obtained by the direct perturbation method for all cases. Moreover, the contributions from different terms to the sensitivity results are compared. It is shown that, for Godiva, Hemisphere Godiva and Jezebel benchmarks, the intergenerational term contributes much to sensitivity coefficients, and this term is necessarily considered correctly in the practical application. [ABSTRACT FROM AUTHOR]

• A parallel code based on RMC program was developed on Sunway TaihuLight. • Improvements were offered for original RMC program. • Special implementation and optimization were applied based on Sunway architecture. • An effective parallel speedup performance was provided. • Stable weak scalability was shown with over 1 million cores. Heterogeneous parallel computing is being widely used for particle transport Monte Carlo codes on various platforms. However, there is currently no related research on the Sunway TaihuLight system, a heterogeneous supercomputer with a unique architecture. In this study, RMC, a key particle transport Monte Carlo code, was parallelized for use on Sunway TaihuLight. Some optimization methods including a thread-private k eff calculator mechanism based on Pthreads were introduced into RMC. The criticality computing module of the optimized RMC was then implemented on Sunway TaihuLight with an MPI-Athread parallel model and optimization methods oriented to the system's special architecture. The results were verified by comparison with the original RMC. The criticality calculation is 125.3 times faster with 512 core groups each with 65 cores than the original serial RMC on 1 core on an Intel Xeon X5670. Stable weak scalability of the parallel calculation is shown with over 1 million cores. [ABSTRACT FROM AUTHOR]

• The superhistory-based differential operator method (SH-DOM) is developed. • Results of SH-DOM agree well with those of collision history-based method. • The SH-DOM can greatly reduce the memory consumption. The differential operator method (DOM) has been developed to perform sensitivity analyses of generalized responses in the form of reaction rate ratios. In this method, the memory consumption required to store the source perturbation effect will become prohibitively large with a large number of particle histories. This work introduces the superhistory-based differential operator method (SH-DOM) to reduce the memory usage. In the superhistory algorithm, the source perturbation effect is estimated by following the source particle and its progenies over super-generations within a single particle history, which significantly reduces the memory usage. The new method is verified via the Jezebel, Flattop and the UAM TMI PWR pin cell benchmark problems calculated by the collision history-based method and the SH-DOM. Results show that the energy integrated sensitivity coefficients given by the present method agree within 5% with those of the collision history-based method and the SH-DOM can effectively reduce the memory consumption. [ABSTRACT FROM AUTHOR]

• An on-the-fly homogenization method based on MC code RMC was proposed. • This method allows for a simultaneous generation of MGXS for all regions. • Different energy structures and homogenization schemes were compared. • Kaist 1A benchmark and a simplified Lead-cooled reactor case were tested. The applications of traditional deterministic lattice codes are limited in certain cases because they cannot treat closely coupled neutron characteristics and peculiar geometry. Therefore, to use the continuous energy Monte Carlo method and full core homogenization to generate multi-group cross sections has attracted growing interests. In this paper, the on-the-fly homogenization method based on the Monte Carlo code RMC, which generates multi-group cross sections in the frame of full core continuous energy Monte Carlo calculation and then use them in the Monte Carlo multi-group calculation to obtain a more convergent solution, is proposed and implemented. Tests and comparisons for the use of such on-the-fly homogenization method in criticality calculations are conducted using Kaist 1A benchmark and a simplified Lead-cooled reactor. The results show that our on-the-fly homogenization method exhibits similar accuracy with continuous energy Monte Carlo calculation that uses the same number of neutron histories and only costs about half of the computational time. With respect to spatial homogenization schemes, the cell homogenization scheme is the best one which can predict the reference solution especially for problems with strong absorbers. Given a tradeoff between efficiency and accuracy, the hybrid Homogenization scheme, which treats strong absorbers with cell homogenization and others with pin homogenization, can take nearly as much time as the pin Homogenization while achieving nearly the same accuracy as the cell Homogenization. [ABSTRACT FROM AUTHOR]