Coarse Mesh Finite Difference Method Research Articles

A new three-level CMFD method based on the loosely coupled parallel strategy

In the whole-core heterogeneous transport calculations with massive parallel, the computational cost of the Coarse Mesh Finite Difference (CMFD) method might become the most time-consuming part if directly using the traditional CMFD method. To accelerate the CMFD calculations, a new three-level CMFD method based on the loosely coupled parallel strategy is developed in the high-fidelity neutronics code NECP-X. Two aspects are considered to accelerate the CMFD calculations, one is reducing the CMFD matrix size and another is minimizing the number of outer iteration numbers. The three-level CMFD acceleration method includes: (1) the multi-group pin-level CMFD (MG-Pin-CMFD) for accelerating transport calculations, in which the cross sections and currents are obtained from the 2D-1D transport calculation; (2) the one-group pin-level CMFD (1G-Pin-CMFD) for accelerating the MG-Pin-CMFD calculations, and the 1G-Pin-CMFD is established by the group-condensed cross sections, flux and currents from the MG-Pin-CMFD; (3) the one-group assembly-level CMFD (1G-ASY-CMFD) for accelerating 1G-Pin-CMFD, and the assembly-wise parameters are from the spatial homogenization of the 1G-Pin-CMFD calculations. The three-level CMFD method can reduce the outer iterations of CMFDs, such as MG-Pin-CMFD and 1G-Pin-CMFD. In every level of CMFD, the group-wised CMFD linear system is constructed based on the loosely coupled spatial domain decomposition, and the serial Generalized Minimum RESsidual (GMRES) method is implemented to solve the linear system instead of the parallel GMRES method to minimize the communications. A set of benchmark problems are tested and the results show good performance and good accuracy in transport calculations.

Two-level time-dependent GET based CMFD acceleration for 3D whole core transient transport simulation using 2D/1D method

A pin-resolved kinetics transport simulation based on the transient fixed-source problem (TFSP) using 2D/1D method has been implemented in this work. The 3D transient fixed source problem is transformed into 2D TFSP and 1D TFSP coupled by the leakage term, while the MOC method and NEM method are used to solve the 2D and 1D TFSP respectively. And a global pin-level time-dependent generalized equivalence theory (GET) based coarse mesh finite difference method (CMFD) is used to synthesize the 2D radial MOC and 1D axial NEM transient calculations, and also to accelerate the iteration convergence of 3D whole-core transient transport calculation. Even more important, an advanced yet accurate two-level time-dependent CMFD acceleration technique is proposed, in which an equivalent one-group CMFD is established to accelerate the multi-group CMFD TFSP solutions, and then to accelerate the 3D whole-core transient transport calculation efficiently. 2D TWIGL and 3D C5G7-TD benchmarks are selected to verify the accuracy and the acceleration effect of the 2D/1D method and the two-level CMFD acceleration. Numerical results indicate that acceptable accuracy of 2D/1D transient calculations and superior acceleration of TL CMFD are achieved.

3D heterogeneous Cartesian cells for transport-based core simulations

We present in this paper a discrete-ordinates transport method to perform 3D PWR transport simulations. The numerical technique takes profit of the Cartesian modular construction of the PWR geometry. The spatial mesh of the proposed method is composed of Heterogeneous Cartesian Cells (HCC). HCCs are basic geometrical patterns delimited by a box and having an arbitrary number of locally-extruded heterogeneous regions. The source is spatially expanded by piece-wise linear approximation in each region. The faces of the box, composing the boundary of the HCC, are discretized with a uniform Cartesian mesh. This surface sub-mesh is the support of a piece-wise linear representation of the interface angular flux. The linear expansion of the sources allows for a considerable reduction of the number of regions. Because of the Cartesian nature of the geometry, the method uses the effective spatial sweeping based on progression by front. Results on three-dimensional core simulations show accurate power distribution while minimizing the number of degrees of freedom. Since parallel computing is mandatory to access high-fidelity flux distributions in a reasonable amount of time, a domain decomposition algorithm is applied at each power iteration. Also, because of the slow convergence of the parallel block-Jacobi iterations, outer power iterations are accelerated by the Coarse-Mesh Finite Difference method (CMFD). In the present work, both transport and outer CMFD share the same domain splitting configuration and perform local multigroup source iterations to stabilize the scattering source. This allows for non-intrusive coarse-grained hybrid parallelism based on MPI/OpenMP directives. A set of 3D benchmarks will be proposed to access the accuracy and the parallel efficiency of the implementation.

IFDF acceleration method with adaptive diffusion coefficients for SN nodal calculation in SARAX code system

SN nodal method has been successfully applied to fast reactor core neutronics analysis. The computational efficiency can be enhanced efficiently by the popular coarse-mesh finite difference (CMFD) method. However, the CMFD method suffers from the problem of instability, especially for optically thick problems. In this paper, another efficient nonlinear acceleration method, named interface flux discontinuity factor (IFDF) acceleration, was studied and improved for the SN nodal calculation in hexagonal prism and cuboid meshes. With adaptive diffusion coefficients, the IFDF is guaranteed to be positive and within a reasonable region, which makes the acceleration stable. It was found that the IFDF and CMFD methods obtained similar speedups for the tested fast reactor problems. However, the stability of the IFDF method was much better than the CMFD method even with artificial diffusion improvement. Additionally, the rebalance accelerated IFDF method was applied to the external-source multiplication problem besides the common eigenvalue problem.

A Novel and Efficient Hybrid RSILU Preconditioner for the Parallel GMRES Solution of the Coarse Mesh Finite Difference Equations for Practical Reactor Simulations

The solution of the large, nonsymmetric, sparse linear system resulting from the discretization of the Boltzmann transport equation can be computationally intensive, even when innovative coarse mesh finite difference (CMFD) acceleration methods are applied on a high-performance computer. The research reported here describes the development and implementation of an innovative hybrid Reduced Symmetric Successive Over-Relaxation (RSOR) and Incomplete Lower Upper (ILU) (RSILU) preconditioner for the preconditioned Generalized Minimal RESidual (GMRES) solution of the three-dimensional, whole-core, pin-resolved transport calculation of a nuclear reactor core. The preconditioner was designed specifically to improve parallel computing capability and minimize the computational burden for solution of the CMFD method on a high-end computing platform. The hybrid RSILU preconditioner is applied to the preconditioned GMRES method without multicolor reordering by utilizing the ILU preconditioner for internal elements on each processor and the RSOR preconditioner for boundary elements that would require interprocessor communication. The construction of the RSILU preconditioner requires only that the diagonal elements be modified, factorized, and stored, which is identical to serial ILU. The computational cost of RSILU is minimized since the factorized diagonal block requires minimal data preparation time for interprocessor communication and exchanges information only once in parallel computation. This paper reports first the serial performance of RSOR, and numerical results show that the new proposed RSOR is an effective preconditioner even for serial computing applications. The parallel performance of RSILU is then assessed and compared to conventional multicolor ILU preconditioners. The results show that RSILU provides comparable convergence rates to the Standard Incomplete Lower Upper (SILU) preconditioners, but it is easier to implement since it does not require multicolor ordering. Although the required iterations of RSILU preconditioned GMRES increase as the number of processors increases, only slightly more iterations are required than the SILU preconditioner for a practical nuclear reactor application. The number of iterations required by the RSILU preconditioner increases only slightly and significantly less than the increased number of iterations required when using conventional Block-Jacobi Incomplete Lower Upper or Symmetric Successive Over-Relaxation preconditioners. Overall, the RSILU is shown to be an efficient and practical preconditioner for the GMRES method for improving the parallel computing performance for large-scale applications.

Reactor core analysis through the SP3-ACMFD approach Part II: Transient solution

Abstract In this part, an implicit time dependent solution is presented for the Boltzmann transport equation discretized by the analytic coarse mesh finite difference method (ACMFD) over the spatial domain as well as the simplified P3 (SP3) for the angular variable. In the first part of this work we proposed a SP3-ACMFD approach to solve the static eigenvalue equations which provide the initial conditions for temp dependent equations. Having solved the 3D multi-group SP3-ACMFD static equations, an implicit approach is resorted to ensure stability of time steps. An exponential behavior is assumed in transverse integrated equations to establish a relationship between flux moments and currents. Also, analytic integration is benefited for the time-dependent solution of precursor concentration equations. Finally, a multi-channel one-phase thermal hydraulic model is coupled to the proposed methodology. Transient equations are then solved at each step using the GMRES technique. To show the sufficiency of proposed transient SP3-ACMFD approximation for a full core analysis, a comparison is made using transport peers as the reference. To further demonstrate superiority, results are compared with a 3D multi-group transient diffusion solver developed as a byproduct of this work. Outcomes confirm that the idea can be considered as an economic interim approach which is superior to the diffusion approximation, and comparable with transport in results.

Pinwise Diffusion Solution of Partially MOX-Loaded PWRs with the GPS (GET PLUS SPH) Method

The generalized equivalence theory (GET) plus superhomogenization (SPH) [GET Plus SPH (GPS)] method, which is a new leakage correction method for the pin-by-pin reactor analysis of light water reactors, has been applied to benchmarks for partial loading of mixed oxide (MOX) fuel in pressurized water reactor (PWR) cores. In the GPS method, the pinwise, cross section–dependent SPH factors are parameterized as a function of normalized leakage, i.e., current-to-flux ratio. As partially MOX-loaded PWRs usually have a stiff gradient of neutron flux on nodal interfaces, the original GPS functions for UO2 cores are slightly modified to take into account the strong spectral interaction. To determine the coefficients of the GPS function, several colorset models are considered to obtain fitting data. In this work, the two-dimensional method of characteristics–based DeCART2D code is used for both colorsets and reference core calculations. The GPS method is implemented in an in-house, pin-by-pin diffusion solver with the pinwise coarse mesh finite difference method. To evaluate the performance of the GPS method on partially MOX-loaded PWRs, the Korea Advanced Institute of Science and Technology (KAIST) 1A benchmark is analyzed in this work. In addition, various small and large variants of the KAIST 1A benchmark are also analyzed using the same GPS functions to demonstrate the general applicability of the predetermined GPS functions. Based on the comprehensive results of this work, it is concluded that the GPS method can clearly improve the accuracy of the conventional GET-based, two-step, pin-by-pin core analyses.

3D Real-Time Simulation of Reactor Core based on Discontinuity Factor Ratio

During the development of full scope simulator (FSS) in nuclear power plant, it is difficult to satisfy with high precision and efficiency of the 3D distribution calculation of reactor power. The accuracy of conventional coarse mesh finite difference method (CMFD) cannot meet the requirement if the nodal size is large. According to the generalized equivalence theory (GET), the finite difference solution of diffusion equation based on discontinuity factor correction was deduced, the calculation method of the discontinuity factor and boundary albedo are presented through the process of assembly homogenization. Through the calculation of typical LMW benchmark problem, the simulation results showed that using CMFD with discontinuity factor ratio (CMFD-DFR) to solve the time-dependent neutron kinetic equation, can not only improve the simulation precision, and can keep the calculation speed, and can meet the requirement of reactor core real-time model of FSS.

3D whole-core neutron transport simulation using 2D/1D method via multi-level generalized equivalence theory based CMFD acceleration

A new 2D/1D method with multi-level generalized equivalence theory (GET) based coarse mesh finite difference (CMFD) acceleration was proposed for the whole core transport calculation in this paper. Fouressential features of this new 2D/1D methods are as follows: (1) Two new defined factors, nodal discontinuity factor (NDF) and modified diffusion coefficient factor (MDF), were defined in this new GET based CMFD method to achieve equivalence between CMFD and the transport solutions and especially insure that only positive coupling coefficients would occur in the CMFD linear system; (2) For accelerating the convergence of the CMFD, a multi-level acceleration scheme was implemented and an innovative self-developed RSILU preconditioned GMRES solver was developed to solve the CMFD linear system; (3) Within the new CMFD framework, 2D MOC and 1D two-node nodal expansion solvers were developed for 3D whole core transport calculation and the sub-plane technique was applied to minimize the nodal error successfully while maintain a reasonable computing time; (4) For implementation, transverse leakage splitting technique was applied to avoid the total source to become negative, and domain decomposition method based on MPI was implemented to take advantages of high performance clusters. The accuracy of this 2D/1D method via multi-level GET based CMFD and the effectiveness and acceleration performance of the multi-level CMFD method were examined for the well-known C5G7 benchmarks problems. The numerical results demonstrate that superior accuracy is achievable and the multi-level acceleration schemeis efficient and enhances the converge speed of both the GET based CMFD acceleration and the MOC calculation.

“On the fly” stabilization of the Coarse-Mesh Finite Difference acceleration for multidimensional discrete-ordinates transport calculations

In this paper, the Jacobian matrix of the Coarse-Mesh Finite Difference (CMFD) method is analyzed. Both the homogenization and the current preservation effects are studied in heterogeneous multidimensional configurations. Some bounding values of the spectral radius are also given. An analytical stability analysis is carried on an interface slab problem. This analysis leads to the computation of the stability parameter introduced in the Generalized Coarse Mesh Rebalancing method. A dynamical stabilization technique is proposed for multidimensional neutron lattice calculations. Numerical calculations show that the proposed technique dumps the unstable modes, in particular in optically thick configurations, where the classical CMFD method fails to converge.

Unstructured coarse mesh finite difference method to accelerate k-eigenvalue and fixed source neutron transport calculations

Unstructured coarse mesh finite difference (CMFD) method was implemented to accelerate the k-eigenvalue and fixed source neutron transport calculations in the nodal SN transport code DNTR, which was based on arbitrary triangular-z meshes. The same triangular-z meshes were adopted in the CMFD calculation to accommodate the arbitrary problem boundaries and simplify the coarse mesh generation and mapping processes. Two-level CMFD formulations were derived for the k-eigenvalue problems, and the few-group CMFD calculation was used to speed up the convergence of the multigroup CMFD calculation. For the fixed source problems in the neutronics analyses of subcritical reactors or transient neutron transport calculations, a special ks iteration method by introducing the source multiplication factor ks was employed in the SN transport calculation to remove the dependence of the convergence rate on the subcriticality. Multigroup CMFD formulations were established to accelerate the convergence of the ks iteration procedure in the fixed source neutron transport calculation. The acceleration effects of CMFD on the k-eigenvalue and fixed source calculations were verified using four representative neutron transport problems, i.e. the small fast breeder reactor with Cartesian boundaries, the BN-600 fast reactor with hexagonal boundaries, the space nuclear power reactor with cylindrical boundaries, and the accelerator driven subcritical reactor with hexagonal boundaries. The numerical results showed that for the first three eigenvalue problems, the multigroup CMFD achieved a speedup of total computation time by a factor of 2–5, and the two-level CMFD reduced the computation time by a factor of 3–7. It was also shown that the multigroup CMFD was able to accelerate the ks iteration procedure in the fixed source problems by a factor of about 6. The implementation of the unstructured CMFD method turns the DNTR code into an efficient neutron transport solver with flexible geometry treatment capability for both k-eigenvalue and fixed source problems.

A modified predictor-corrector quasi-static method in NECP-X for reactor transient analysis based on the 2D/1D transport method

The 2D/1D transport method is a widely applied method for the whole-core heterogeneous transport calculation. The transient simulation based on the pin-resolved 2D/1D method is implemented in the high-fidelity code NECP-X. The 3D transient fixed source problem (TFSP) is transformed into 2D TFSP and 1D TFSP coupled by leakage, and the pin-based coarse mesh finite difference method (CMFD) is used to accelerate convergence of the 2D/1D TFSP. In this paper, a modified predictor-corrector quasi-static (mPCQS) method is developed to provide better reactivity prediction for PK calculations. Furthermore, the simplified source scaling method (SSSM) is used to accelerate the convergence of the CMFD TFSP iterations. The results of three problems are presented including the 2D C5G7-TD benchmark, a MiniCore-3D rod-ejection problem and a 3D heterogeneous rod-ejection problem. Numerical results reveal that the SSSM method can significantly reduce the number of CMFD iterations without increasing the computational complexity, and the mPCQS method can provide better results than the standard PCQS for step perturbation transient event and rod ejection transient event no matter in the homogeneous case or in the heterogeneous case.

One-node and two-node hybrid coarse-mesh finite difference algorithm for efficient pin-by-pin core calculation

Abstract This article presents a new global–local hybrid coarse-mesh finite difference (HCMFD) method for efficient parallel calculation of pin-by-pin heterogeneous core analysis. In the HCMFD method, the one-node coarse-mesh finite difference (CMFD) scheme is combined with a nodal expansion method (NEM)–based two-node CMFD method in a nonlinear way. In the global-local HCMFD algorithm, the global problem is a coarse-mesh eigenvalue problem, whereas the local problems are fixed source problems with boundary conditions of incoming partial current, and they can be solved in parallel. The global problem is formulated by one-node CMFD, in which two correction factors on an interface are introduced to preserve both the surface-average flux and the net current. Meanwhile, for accurate and efficient pin-wise core analysis, the local problem is solved by the conventional NEM-based two-node CMFD method. We investigated the numerical characteristics of the HCMFD method for a few benchmark problems and compared them with the conventional two-node NEM-based CMFD algorithm. In this study, the HCMFD algorithm was also parallelized with the OpenMP parallel interface, and its numerical performances were evaluated for several benchmarks.

A Local Adaptive Coarse-Mesh Nonlinear Diffusion Acceleration Scheme for Neutron Transport Calculations

In order to improve the effectiveness and stability of the coarse-mesh finite difference method (CMFD), we developed a new nonlinear diffusion acceleration scheme for solving neutron transport equations. This scheme, called LR-NDA, employs a local refinement approach on the framework of CMFD by solving a local boundary value problem of the scalar flux on the coarse-mesh structure to replace the piecewise constant scalar flux obtained by CMFD. The refined flux is then used to update the scalar flux in the neutron transport source iteration. In this paper, a detailed convergence study of LR-NDA is carried out based on a two-dimensional fixed-source problem, and it shows that LR-NDA is much more effective and stable than CMFD for a wide range of optical thicknesses. In addition, we demonstrate that LR-NDA is a local adaptive method. LR-NDA does not necessarily require local refinement for all the coarse-mesh cells on the problem domain, i.e., it can be used only for relatively optically thick regions where the standard CMFD scheme would encounter the convergence problem.

Fourier Convergence Analysis of the Infinite Homogenous Multigroup Time-Dependent Boltzmann Transport Equation Using Discrete Ordinates Formulation

Fourier analysis of the continuous infinite homogenous multigroup (MG) formulation is investigated in this paper for the time-dependent Boltzmann transport equation using discrete ordinates formulation. In addition, a continuous two-group (2G) and one-group (1G) Fourier analysis is performed to generate an analytical spectral radius and provide the basis for a theoretical analysis of the convergence. The discrete 1G formulation is then presented, and the theoretical analysis is found to predict the same spectral radius as the continuous 1G formulation. A typical pressurized water reactor pin cell problem with 47-group library is then homogenized with reflective boundary conditions, and the numerical spectral radius is calculated using the MPACT code. The theoretical predictions and the numerical results from the pin cell case agree very well and are found to have the following behavior: (1) The spectral radius is usually very close to unity for standard parameters for realistic transient application, (2) the spectral radius generally decreases as a function of inners per outer M, (3) the spectral radius generally decreases as a function of time-step size and then increases beyond unity for extremely small time steps, and (4) the spectral radius is almost constant as a function of the inserted reactivity. Good agreement is observed with the MG Fourier analysis. Finally, it is shown that the group sweeping coarse mesh finite difference method is theoretically and numerically very slow to converge the time-dependent neutron transport equation and that it is necessary to move the right-hand-side fission and transient source to the left-hand side and to solve the entire matrix form of the system.

Analysis of Stabilization Techniques for CMFD Acceleration of Neutron Transport Problems

The coarse-mesh finite difference (CMFD) method is one of the most widely used methods for accelerating the convergence of numerical transport solutions. However, in some situations, iterative methods using CMFD can become unstable and fail to converge. We present and evaluate three different modifications of the CMFD scheme that provide enhanced stability: multiple transport sweeps, artificial diffusion, and relaxing the flux update. We present the Fourier analysis on each of these schemes for an idealized problem to characterize the stability and rate of convergence for both fixed-source and fission-source problems. Comparisons of the effectiveness of these methods are also performed numerically for a variety of benchmark boiling water reactor and pressurized water reactor problems using the Consortium for Advanced Simulation of Light Water Reactors neutronics code MPACT. We demonstrate a means of stabilizing CMFD by modifying the diffusion coefficient to make the iteration behave more like the partial-current CMFD (pCMFD) method, which is unconditionally stable, and show through a sequence of numerical experiments that the CMFD method performs similarly to the pCMFD method for the selected benchmark problems. We also show, both theoretically and experimentally, that modifying the diffusion coefficient in the CMFD equations is similar to underrelaxing the scalar flux update. The theoretical and experimental results show that many of the known techniques for stabilizing CMFD are fundamentally very closely related.

An optimally diffusive Coarse Mesh Finite Difference method to accelerate neutron transport calculations

A new optimally diffusive Coarse Mesh Finite Difference (odCMFD) method is proposed. The new method generalizes the Coarse Mesh Finite Difference (CMFD) and partial current-based CMFD (pCMFD) methods by adding an artificial term to the diffusion coefficient. The standard CMFD and pCMFD methods preserve the net current and partial currents respectively and can greatly reduce the spectral radius for solving neutron transport problems. Linearized Fourier analysis shows that these methods essentially differ only by the definition of the diffusion coefficient – the pCMFD diffusion coefficient contains an additional “artificial” term, usually taken to be ¼ the coarse mesh size. In this paper, the magnitude of the artificially diffusive term is numerically investigated and optimized using Fourier analysis. The results show that the optimal coefficient increases as the coarse cell optical thickness increases. Also, the optimal value is always smaller than the pCMFD value. This indicates that the pCMFD method overcorrects the diffusion coefficient which increases the spectral radius. A simple polynomial fitting was found for implementing the odCMFD in the MPACT code to perform calculations for realistic problems. Numerical MPACT results for a two-region homogeneous problem, a 2D C5G7 problem, a VERA problem 5 and a 2D BWR Peach Bottom Unit 2 core problem agree well with the Fourier analysis and confirm previous research results that: (1) CMFD converges faster than pCMFD for optically thin coarse grids, but CMFD diverges for optically thick coarse grids; (2) pCMFD is unconditionally stable for all coarse grids; and show that the newly proposed odCMFD is the most efficient among these three methods for all cases. The new method has a similar convergence rate as CMFD for optically thin coarse grids, is faster than both CMFD and pCMFD for coarse grids with intermediate optical thickness, and is unconditionally stable and faster than pCMFD for optically thick coarse grids.

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also noted that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.

The Relationship between the Coarse-Mesh Finite Difference and the Coarse-Mesh Diffusion Synthetic Acceleration Methods

The coarse-mesh finite difference (CMFD) and the coarse-mesh diffusion synthetic acceleration (CMDSA) methods are widely used, independently developed methods for accelerating the iterative convergence of deterministic neutron transport calculations. In this paper, we show that these methods have the following theoretical relationship: If the standard notion of diffusion synthetic acceleration as a fine-mesh method is straightforwardly generalized to a coarse-mesh method, then the linearized form of the CMFD method is algebraically equivalent to a CMDSA method. We also show theoretically (via Fourier analysis) and experimentally (via simulations) that for fixed-source problems, the CMDSA and CMFD methods have nearly identical convergence rates. Our numerical results confirm the close theoretically predicted relationship between these methods.

Resolution of the Generalized Eigenvalue Problem in the Neutron Diffusion Equation Discretized by the Finite Volume Method

Numerical methods are usually required to solve the neutron diffusion equation applied to nuclear reactors due to its heterogeneous nature. The most popular numerical techniques are the Finite Difference Method (FDM), the Coarse Mesh Finite Difference Method (CFMD), the Nodal Expansion Method (NEM), and the Nodal Collocation Method (NCM), used virtually in all neutronic diffusion codes, which give accurate results in structured meshes. However, the application of these methods in unstructured meshes to deal with complex geometries is not straightforward and it may cause problems of stability and convergence of the solution. By contrast, the Finite Element Method (FEM) and the Finite Volume Method (FVM) are easily applied to unstructured meshes. On the one hand, the FEM can be accurate for smoothly varying functions. On the other hand, the FVM is typically used in the transport equations due to the conservation of the transported quantity within the volume. In this paper, the FVM algorithm implemented in the ARB Partial Differential Equations solver has been used to discretize the neutron diffusion equation to obtain the matrices of the generalized eigenvalue problem, which has been solved by means of the SLEPc library.