NECP-MCX: A hybrid Monte-Carlo-Deterministic particle-transport code for the simulation of deep-penetration problems

Highlights

• A new hybrid Monte-Carlo-Deterministic particle-transport code, NECP-MCX, has been developed.

• Development of NECP-MCX is focused on efficiency and high performance.

• The figure of merit of NECP-MCX is ~10³ higher than that of MCNP with weight window generator.

Abstract

A new particle-transport code NECP-MCX has been developed by Nuclear Engineering Computational Physics (NECP) laboratory of Xi’an Jiaotong University. NECP-MCX is aimed at the simulation of deep-penetration problems, including reactor radiation-shielding calculation, fusion reactor blanket calculation, etc. These problems are challenging for the Monte Carlo (MC) method, which needs a huge number of particles to obtain reliable results. For the problems mentioned above, it is also challenging for the deterministic method to obtain results with high precision due to discretization errors. To overcome these challenges, NECP-MCX has been developed based on a hybrid Monte-Carlo-Deterministic method from scratch. The hybrid Monte-Carlo-Deterministic method utilizes the deterministic method to generate consistent mesh-based weight-window and source-biasing parameters for the MC method to reduce variance. The numerical results demonstrate that NECP-MCX is able to simulate deep-penetration problems with higher efficiency compared to the conventional MC codes.

Introduction

In the field of particle transport, simulation of the deep-penetration problem has long been a challenge for the Monte Carlo (MC) method. For a typical deep-penetration problem, ex-core detector calculation for example, the flux decreases ~ 10⁷ times from the reactor core to the detector. A simulated particle in the MC method tends to be killed before reaching the detector, which makes the variance of the detector results unacceptably large with a reasonable number of particles. Two measures are needed to address the challenge in simulating deep-penetration problems: efficient variance-reduction technique and scalable parallel algorithm.

Much work has been done for variance reduction. In the MCNP code (X-5 Monte Carlo Team, 2003), variance-reduction techniques like geometry splitting and roulette, energy splitting and roulette, exponential transform, cutoff methods, source biasing and weight window are implemented. These are powerful techniques for variance reduction. However, selection and usage of these techniques require much experience of the users, which results in the variance-reduction techniques difficult to use. To address this problem, the weight-window generator (WWG) is implemented in MCNP. The WWG generates weight window automatically by iterative MC calculations and largely reduces the requirement of users’ experience. However, it is still dependent on the users’ experience to judge whether the generated weight window is reasonable or not.

Other codes that are able to generate variance-reduction parameters automatically are MAVRIC (Peplow, 2011) and ADVANTG (Mosher et al., 2015). In these codes, the consistent adjoint-driven importance sampling (CADIS) method and the forward-weighted CADIS (FW-CADIS) method (Wagner, 1997, Zheng et al., 2018, Wagner et al., 2009) are implemented. The CADIS method generates consistent weight-window and source-biasing parameters by adjoint fluxes calculated by the S_N method. The CADIS method is suitable for variance reduction of the single-detector problem, while the FW-CADIS method biases the adjoint source by forward fluxes calculated by the S_N method, taking multiple detectors into account. The S_N solver of used by MAVRIC is DENOVO (Thomas et al., 2010), which is suitable for massive parallel computation. The MC code used by MAVRIC is MONACO (Peplow, 2009), a fixed-source multi-group MC shielding code, which introduces approximation due to the self-shielding effect. The MC code used by ADVANTG is MCNP, which is reported to be not suitable for future parallel computer architectures due to its master-slave parallel algorithm.

Much wok has been done on other excellent MC codes like OpenMC (Romano and Forget, 2013), RMC (Wang et al., 2015), JMCT (Deng, 2014), Serpent (Leppanen et al., 2015), MCS (Lee et al., 2020), SuperMC (Wu et al., 2015), etc. to improve the efficiency of the MC method. In these codes, only OpenMC is open-source. However, OpenMC aims at performing high-fidelity reactor-core physics calculation and is not planned to be applied to deep-penetration problems. WWG is a commonly-used variance-reduction technique in these codes. However, WWG needs several times of iteration and user’s experience to determine whether the variance-reduction parameters are applicable or not.

Another type of the method to solve particle-transport equation is the deterministic method. The deterministic method that is widely used for deep-penetration calculation is the S_N method. The S_N method discretizes space, energy and angle variables and solves discretized particle-transport equation. Generally, the efficiency of the S_N method is higher than that of the MC method because of discretization. However, discretization will introduce approximations in solving the particle-transport equation. The energy variable is split into multiple energy groups, namely, the multi-group approximation. The self-shielding effect is hard to be treated precisely under multi-group approximation. The angular discretization will introduce ray effects. Besides, use of rectangular grids introduces approximations in modelling the curve surface. The S_N code ANISN (Engle, 1967), DORT (Rhoades et al., 1979) and TORT (Rhoades and Simpson, 1997) developed by the Oak Ridge National Laboratory, have been widely used. However, these codes are all serial codes and hence not applicable to large-scale problems. NECP-Hydra (Xu et al., 2017) is an in-house three-dimensional parallel discrete ordinate transport code developed by the Nuclear Engineering Computational Physics (NECP) laboratory of Xi’an Jiaotong University. Similar to DENOVO, NECP-Hydra scales well on parallel computers.

To address the challenges of deep-penetration calculations faced by the conventional MC codes and the motivation to perform independent academic research and knowledge-transfer education based on a self-developed in-house code for easy maintenance and enhancement, a hybrid Monte-Carlo-Deterministic code NECP-MCX has been developed for the simulation of deep-penetration problems. The hybrid Monte-Carlo-Deterministic method (hybrid method in short) is based on the CADIS and FW-CADIS methods. NECP-MCX combines the advantages of the MC method and the S_N method. Since the precision requirement of the weight-window and source-biasing parameters for variance reduction of the MC method is relative low, these parameters can be quickly computed by the S_N method and then utilized by the MC method to perform deep-penetration calculation with higher efficiency. The MC code and the S_N code NECP-Hydra are incorporated into one code system. The code is well designed for deep-penetration calculation and make the users free of selection and usage of different variance-reduction techniques. Besides, state-of-art acceleration techniques for the MC method have also been implemented in NECP-MCX. The hash-based energy lookup algorithm (Bown, 2014) is used to accelerate energy lookup. The hash-based mapping algorithm is used to handle massive tallies. The nearest-neighbors algorithm is implemented to reduce communication in fission-bank synchronization.

Except the capability of deep-penetration simulation, the capabilities of neutron-photon coupling calculation and criticality calculation based on Monte Carlo method have also been developed in NECP-MCX. The capabilities of burnup, activation, source-term and multi-physics calculation are currently under development for wider applications of the code in the future.

The rest of the paper is organized as follows. Section 2 introduces the methods of NECP-MCX, including the hybrid Monte-Carlo-Deterministic method and its implementation. Section 3 demonstrates the performance of NECP-MCX by calculating eigenvalue problems and fixed-source problems. Section 4 provides the summary.