Unstructured Tetrahedral Meshes Research Articles

Including geological orientation information into geophysical inversions with unstructured tetrahedral meshes

SUMMARY Minimum-structure, or Occam’s style of, inversion introduces a regularization function into the underdetermined geophysical inverse problems to stabilize the inverse problem and mitigate its non-uniqueness. The regularization function is typically designed such that it can incorporate a priori information into the inversion framework, thus constructing models that have more plausible representations of the true Earth’s subsurface structure. One type of a priori information is geological orientation information such as strike, dip and tilt angles of the subsurface structure. This type of information can be incorporated into inverse problems through the roughness operators. Designing such roughness operators for inversion frameworks using unstructured tetrahedral meshes is not as straightforward as for inversion frameworks using structured meshes due to the arbitrary and complex geometry of unstructured meshes. Researchers have developed methods which allow us to incorporate geological orientation information into inversion frameworks with unstructured tetrahedral meshes. The majority of these methods consider each cell in a package with its neighbours, hence, the constructed models are not as sharp as desired if the regularization function is measured using an $\ell _1$-type measure instead of the $\ell _2$ norm. To address this issue, we propose a method that calculates the directional derivatives of physical property differences between two adjacent cells normalized by the distance between the cell centroids. This approach is able to both incorporate geological orientation information into the inversion framework and construct models with sharp boundaries for the scenarios in which the regularization term is quantified by an $\ell _1$-type measure. This method is an integral-based approach, therefore, the roughness operators are scaled appropriately by the cell volumes, which is an important characteristic for the inversions with unstructured meshes. To assess the performance and the capability of the proposed method, it was applied to 3-D synthetic gravity and magnetotelluric examples. The gravity example was also used to investigate the impact of applying the depth weighting function inside and outside the roughness operators for the scenarios that the model objective function is measured by an $\ell _1$ norm. The examples show that the proposed method is able to construct models with a reasonable representation of the strike and dip directions of the true subsurface model with sharper boundaries if the regularization function is quantified by an $\ell _1$-type measure. The examples also demonstrate the proposed method behaves numerically well, and has a fast convergence rate.

DC3DPAFEM: An efficient and accurate 3-D direct current resistivity anisotropic forward modeling software for complex geological settings

Nowadays, there is a growing trend that direct current (DC) field surveys are shifting towards challenging areas characterized by mountainous topography and electrical anisotropy. Given these complex geological settings, there is an urgent need for 3-D DC forward modeling software capable of effectively addressing large-scale problems and delivering accurate modeling results to interpret field data. However, most open-source software packages face certain limitations, such as the high numerical cost to handle complex surface topography, the lack of consideration for anisotropic conductivity, the absence of mesh refinement techniques to guarantee accuracy in forward modeling, and the lack of parallel computing techniques to solve large-scale problems. In this study, we develop an efficient and highly accurate 3-D DC anisotropic forward modeling software, namely DC3DPAFEM, using the adaptive finite element algorithm based on the unstructured tetrahedral mesh. Firstly, we construct a strong compatible boundary value problem (BVP) for 3-D anisotropic DC problems by adopting a specialized secondary potential approach to handle the surface topography efficiently. Then, we develop a goal-oriented adaptive mesh refinement (AMR) technique to ensure accurate forward modeling results, even with a coarse initial mesh. To ensure time and memory efficiency, we employ a robust conjugate gradient (CG) algorithm preconditioned by the algebraic multigrid (AMG) solver to solve the large-scale linear system of equations resulting from complex geological structures. We aim to investigate the performance of the AMG scheme in anisotropic DC cases. Furthermore, we incorporate the domain decomposition technique into the iterative solution scheme for further efficiency gains. This technique significantly improves computing efficiency for large-scale problems in parallel clusters. Finally, we conduct comprehensive performance tests for DC3DPAFEM using a two-layer anisotropic model and a 3-D complex model with undulating terrain. The results of both examples validate the accuracy of DC3DPAFEM, as they closely align with the analytical solutions and the solutions obtained from the existing 3-D DC forward modeling code. Compared to traditional direct solver MUMPS and ILU-preconditioned iterative solvers, DC3DPAFEM exhibits highly scalable performance for large-scale problems, offering significant advantages in terms of memory and time consumption. Overall, DC3DPAFEM demonstrates substantial advances in efficiency, accuracy, and practicality through a series of numerical examples. This open-source code provides an efficient and available tool for developing a 3-D DC inversion method that can deal with large-scale problems involving intricate topography and anisotropic media.

A highly parallel algorithm for simulating the elastodynamics of a patient-specific human heart with four chambers using a heterogeneous hyperelastic model

In this paper a highly parallel method is developed for simulating the elastodynamics of a four-chamber human heart with patient-specific geometry. The heterogeneous hyperelastic model is discretized by a finite element method in space and a fully implicit adaptive method in time, and the resulting nonlinear algebraic systems are solved by a scalable domain decomposition algorithm. The deformations of the cardiac muscles are quite complex due to the realistic geometry, the heterogeneous hyperelasticity of the cardiac tissue, and the myocardial fibers with active stresses. Moreover, the deformations in different chambers and at different phases of the cardiac cycle are very different. To simulate all the muscle movements including the atrial diastole, the atrial systole, the isovolumic contraction, the ventricular ejection, the isovolumic relaxation, and the ventricular filling, the temporal-spatial mesh needs to be sufficiently fine, but not too fine so that the overall computing time is manageable, we introduce a baseline mesh in space and a two-level time stepping strategy including a uniform baseline time step size to obtain the desired time accuracy and an adaptive time stepping method within a baseline time step to guarantee the convergence of the nonlinear solver. Through numerical experiments, we investigate the performance of the proposed method with respect to the material coefficients, the fiber orientations, as well as the mesh sizes and the time step sizes. For an unstructured tetrahedral mesh with more than 200 million degree of freedoms, the method scales well for up to 16,384 processor cores for all steps of an entire cardiac cycle.

Joint inversion of potential field data with adaptive unstructured tetrahedral mesh

Inverting potential field data presents a significant challenge due to its ill-posed nature, often leading to nonunique model solutions. Addressing this, our work focuses on developing a robust joint inversion method for potential field data, aiming to achieve more accurate density and magnetic susceptibility distributions. Unlike most previous work that used regular meshes, our approach adopts an adaptive, unstructured tetrahedral mesh, offering enhanced capabilities in handling the inverse problem of potential field methods. During inversion, the tetrahedral mesh is refined in response to the model update rate. We integrate a Gramian constraint into the objective function, allowing the enforcement of model similarity in terms of either the model parameters or their spatial gradients on an unstructured mesh. In addition, we use the moving least-squares method for gradient operator computation, which is essential for model regularization. Our model studies indicate that this method effectively inverts potential field data, yielding reliable subsurface density and magnetic susceptibility distributions. The joint inversion approach, compared with individual data set inversion, produces coherent geophysical models with enhanced correlations. Notably, it significantly mitigates the nonuniqueness problem, with the recovered anomaly locations aligning more closely with actual ground truths. Applying our methodology and algorithm to field data from the Ring of Fire area in Canada, the joint inversion process has generated comprehensive geophysical models with robust correlations, offering potential benefits for mineral exploration in the region.

Simulation of two-phase flow in 3D fractured reservoirs using a projection-based Embedded Discrete Fracture Model on Unstructured tetrahedral grids (pEDFM-U)

The modeling of fluid flow in heterogeneous, anisotropic and fractured porous media is relevant in many applications, including hydrocarbon and groundwater extraction, dispersion of contaminants, hydrogen or carbon dioxide (CO2) storage. Thus, accurate and scalable simulation of fluid flow through these formations continues to be a great challenge. The presence of fractures that are explicitly modeled, ranging from flow barriers to highly conductive channels, significantly increases the complexity of the numerical simulation. The Embedded Discrete Fracture Model (EDFM) produces results that can be as accurate as those obtained using equidimensional Discrete Fracture Models (DFM) at a much lower computational cost for highly conductive fractures, but it is not adequate for impermeable barriers. In contrast, the pEDFM (projection-based Embedded Discrete Fracture Model) produces accurate results for both, channels and barriers by using additional matrix-fracture connectivities. In its current versions, it is restricted to cartesian and corner-point grid geometries and to the classical Two Point Flux Approximation (TPFA) scheme. In this work, for the first time, the pEDFM is extended to handle unstructured tetrahedral meshes (pEDFM-U). In addition, interface fluxes are approximated by using the Multipoint Flux Approximation method with a Diamond stencil (MPFA-D). This allows for simulation of highly heterogeneous and anisotropic geo-models. The developed method is robust and can deal with full permeability tensors on arbitrary tetrahedral meshes. The advective terms are discretized considering an implicit First Order Upwind (FOU) method. Our method is implemented within the DARSim (Delft Advanced Reservoir Simulation) open-source simulator framework. Through several test cases, the proposed method showed to be robust and capable to accurately capture the effects of both high and low permeability fractures for general tetrahedral meshes, under arbitrary heterogeneous and anisotropic permeability tensors for the rock matrix.

Aircraft Simulations Using the New CFD Software from ONERA, DLR, and Airbus

This paper presents a thorough comparison between RANS simulations performed with the computational fluid dynamics by ONERA, DLR, and Airbus (CODA) new-generation flow solver and reference legacy codes TAU (DLR) and elsA (ONERA) for high-speed cruising NASA Common Research Model (CRM) configurations that were considered in the context of the 5th, 6th, and 7th Drag Prediction Workshops. The solver’s accuracy is assessed with several meshing strategies, including block-structured, hybrid-structured/unstructured, and fully unstructured tetrahedral meshes. This solver features both a cell-centered finite-volume (FV) scheme suited to arbitrary meshes as well as a modern high-order discontinuous Galerkin (DG) scheme. We show that for all cases considered, the FV component recovers an equivalent accuracy compared to elsA (cell-centered FV) on block-structured meshes and TAU (node-centered FV) on hybrid and unstructured meshes. The high-order DG scheme (third-order accurate) is found to significantly enhance the drag prediction on coarse meshes compared to legacy FV methods, both for structured and unstructured meshes.

Two-step multi-resolution reconstruction-based compact gas-kinetic scheme on tetrahedral mesh

This paper presents the development of a third-order compact gas-kinetic scheme (GKS) for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme utilizes a time-dependent gas distribution function at a cell interface to not only calculate the fluxes needed for updating the cell-averaged flow variables but also to evaluate the flow variables at the cell interface. This leads to the evolution of cell-averaged gradients of flow variables. The success of this scheme heavily relies on the initial data reconstruction techniques, with an emphasis on their application to the tetrahedral mesh. Employing a conventional second-order unlimited least-square reconstruction directly on the cell-averaged flow variables of von Neumann neighbouring cells can introduce linear instability into the scheme. However, by using the updated cell-averaged gradients, the GKS with a third-order compact smooth reconstruction remains linearly stable under a large CFL number when applied to a tetrahedral mesh. To enhance the robustness of the high-order compact GKS for capturing a discontinuous solution, we propose a novel two-step multi-resolution weighted essentially non-oscillatory (WENO) reconstruction. This innovative approach overcomes the stability issues associated with a second-order compact reconstruction by incorporating a pre-reconstruction step. Additionally, it simplifies the third-order non-linear reconstruction process by adding a single large stencil to those used in the second-order one. A high-order wall boundary condition is achieved by fusing the constrained least-square technique with the WENO procedure, where a quadratic element is used in the reconstruction for cells with a curved boundary. Numerical tests involving both the second-order and third-order compact GKS are presented, encompassing both inviscid and viscous flows at both low and high speeds. The results demonstrate that the proposed third-order compact scheme possesses robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.

Multi-compartment head modeling in EEG: Unstructured boundary-fitted tetra meshing with subcortical structures.

This paper introduces an automated approach for generating a finite element (FE) discretization of a multi-compartment human head model for electroencephalographic (EEG) source localization. We aim to provide an adaptable FE mesh generation tool for EEG studies. Our technique relies on recursive solid angle labeling of a surface segmentation coupled with smoothing, refinement, inflation, and optimization procedures to enhance the mesh quality. In this study, we performed numerical meshing experiments with the three-layer Ary sphere and a magnetic resonance imaging (MRI)-based multi-compartment head segmentation which incorporates a comprehensive set of subcortical brain structures. These experiments are motivated, on one hand, by the sensitivity of non-invasive subcortical source localization to modeling errors and, on the other hand, by the present lack of open EEG software pipelines to discretize all these structures. Our approach was found to successfully produce an unstructured and boundary-fitted tetrahedral mesh with a sub-one-millimeter fitting error, providing the desired accuracy for the three-dimensional anatomical details, EEG lead field matrix, and source localization. The mesh generator applied in this study has been implemented in the open MATLAB-based Zeffiro Interface toolbox for forward and inverse processing in EEG and it allows for graphics processing unit acceleration.

Determination of cryogenic temperature loads for finite-element model of LNG bunkering ship under LNG release accident

Abstract The rising demand for liquefied natural gas (LNG)-fueled ships requires the LNG bunkering facility that partially uses a ship-to-ship operation. The bunkering process of LNG fuel may have a greater risk due to LNG volatility. The cryogenic temperature of LNG poses a threat to the personnel and structural embrittlement to ships. Therefore, cryogenic spill protection optimization was introduced concerning the structural strength analysis using finite element (FE) by utilizing cryogenic temperature loads provided by the computational fluid dynamics (CFD) model of an LNG release. This study aims to build a platform for transferring the temperature load profile from CFD to FE software accurately. The CFD model usually uses a structured Cartesian grid, and the FE method adopts an unstructured tetrahedral or hexahedral mesh. As a result, both configurations store results at different positions, and it is not preferred for the load profile to be transferred directly. The error will be greater due to the variance of positions. Random Forest, a machine learning method, has been employed that uses a regression technique to deal with a continuous variable. An accurate load profile for the FE model can be obtained by adopting decision tree learning in Random Forest. The procedure for determining the temperature load profile is presented in this article.

Computational Study of a Swirl Stabilized Flame in a Gas Turbine Combustor

Size of recirculation zone and temperature field is examined in a swirl stabilized aero gas turbine combustor using computational fluid dynamics. A sector of 22.5° of an annular combustor is modeled for the study. Unstructured tetrahedral meshes comprising 1.2x106 elements are employed in the model where the governing equations are solved using CFD flow solver CFX. Grid sensitivity study and code validation through limited test data has also been carried out. The effect of pressure and fuel-air ratio on the size of recirculation zone and apparent size of flame zone has been studied at steady state conditions. The heat release rate due to combustion is found to affect the length of recirculation zone as well as the velocity field inside the combustion liner.

The Thermal Plumbing System of Stromboli Volcano, Aeolian Islands (Italy) Inferred From Electrical Conductivity and Induced Polarization Tomography

AbstractWe performed the first 3D island‐scale tomography of the electrical conductivity of Stromboli volcano (Aeolian Islands, Italy) using 2D acquisition lines (37.2 km) and a total of 18,880 measurements and 2,402 unique electrode locations. This 3D data set was inverted using a Gauss‐Newton algorithm, parallel‐processing on an unstructured tetrahedral mesh containing 678,420 finite‐element nodes and 3,580,145 elements to account for the topography of the volcanic island. The tomogram exhibits a conductive body (10−2–1.0 S m−1) consistent with the location of CO2 and temperature anomalies observed at the ground surface. It corresponds to the hydrothermal system with high electrical conductivity associated with alteration. In order to confirm this interpretation, a 2.5D large‐scale induced polarization tomography was performed crossing the volcano. The joint interpretation of the conductivity and normalized chargeability is done with a petrophysical model previously tested and verified at both shield‐ and strato‐volcanoes. This model implies that alteration (through the effect of the cation exchange capacity associated with clay minerals and zeolites) plays a strong role in both controlling the electrical conductivity and normalized chargeability at Stromboli volcano. A temperature tomogram, derived from the geoelectrical measurements, is consistent with surface temperature anomalies and the Very Long Period (VLP) seismicity related to the mild‐explosive activity. This survey displays at 600 m a.s.l. a lateral shift in the highest temperature location, also corresponding to the source of VLP seismicity. Structural boundaries have a major role in the hottest hydrothermal fluids rising below the active crater terrace of Stromboli volcano.

Development of a Tetrahedral Mesh Generator Based on Constrained Delaunay Triangulation

The article describes the basic principles of operation of the finite element mesh generator SMCMGrid, which is an integral part of the SMCM software package designed to solve problems in the mechanics of composite materials and structures, which was developed at the Scientific-educational center on supercomputer modeling and software engineering of Bauman Moscow State Technical University (BMSTU SIMPLEX CENTER). The paper describes a software pipeline for constructing high-quality tetrahedral unstructured meshes for arbitrary shape B-rep models based on constrained Delaunay triangulation. We have presented the main algorithms for generating meshes on the edges and surfaces of the model, which make it possible to create the so-called simplicial complex, for which it is then possible to construct a constrained Delaunay triangulation and create the final tetrahedral mesh of the required quality. The mesh is generated in a Riemannian space with a given metric that takes into account the required characteristics of the mesh at each point of the geometric model. We gave examples of finite element meshes for various geometric models of engineering structure elements, including composite materials, and also demonstrated the adequacy of the results of solving the elasticity problem on a mesh built using the SMCMGrid generator. The results of the work led to the conclusion that the presented generator can be used to solve problems of engineering analysis and modeling.

Aerodynamic Analysis of Variable Cant Angle Winglets for Higher Mach regimes

The performance of the aircraft is reduced due to induced drag generated at the wingtip. The vortices are generated at the wingtip in the turbulent flow. For the reduction of the vortices the small device with the positive or negative cant angle called winglet is introduced. This paper describes Computational Fluid Dynamics (CFD) analysis, performed on a trapezoidal wing prototype with a winglet of NACA 63(2)-215 airfoil section. The White comb geometry is used for the parametric values of the winglet. The objectives of the analysis were to compare the aerodynamic characteristics and to investigate the performance of winglets at cant angles -15°, 0°, 15°, 30° and 450 at the constant angle of attack (AOA) 0°. The entire wing works on around 0.5 Mach .The CFD simulations were performed in ANSYS fluent. 3-dimensional unstructured tetrahedral meshes were used to compute the flow around the model. The parameters like pressure, velocity are found and analyzed at different cant angles.

Eikonal equation-based earthquake location with irregular surfaces

SUMMARYEarthquake location is a basic seismological problem and has a key role in many quantitative seismic analyses. The significant anomaly of traveltimes observed in mountainous areas with irregular surfaces has made earthquake location a challenge. To cope with this problem, we develop an effective eikonal equation-based earthquake location method based on unstructured mesh for 2-D/3-D isotropic and anisotropic media with irregular surfaces. First, the location misfit function is established by the reciprocity principle. Then, we use a global search algorithm to find the optimal origin times and hypocentres. Afterward, we apply eikonal equation-based master-event relocation method to relocate earthquakes on lateral boundaries of the region where the location results may be biased. To accurately compute the traveltime in 3-D vertically transversely isotropic and tilted transversely isotropic models with irregular surfaces or interfaces, we also propose a 3-D iterative fast sweeping method for eikonal equation on the unstructured tetrahedral mesh. Finally, we verify the proposed method by performing numerical experiments in 2-D/3-D irregular isotropic and anisotropic models. The numerical tests indicate that the proposed eikonal equation-based earthquake location method provides an effective way to find accurate hypocentre and origin time in 2-D/3-D isotropic and anisotropic media with irregular surfaces, even for inhomogeneous complex structures. In addition, the eikonal equation-based master-event location method has also yielded promising relocation results.

3D joint inversion of airborne ZTEM and ground MT data using the finite element method with unstructured tetrahedral grids

As an airborne electromagnetic method induced by natural sources, the Z-axis tipper electromagnetic (ZTEM) system can primarily recover near-surface shallow structures, due to band-limited frequencies (usually 30–720 Hz) of the airborne survey and high sample rate acquisition along the terrain. In contrast, traditional ground magnetotellurics (MT) allows better recovery of deep structures as the data acquired are typical of large site intervals (usually higher than 1 km) and lower frequencies (usually lower than 400 Hz). High-resolution MT surveys allow for shallow small and deep large anomalies to be adequately interpreted but need large site intervals and broadband frequency range, which are seldom used as they are quite costly and laborious. ZTEM data are tippers that relate local vertical to orthogonal horizontal fields, measured at a reference station on the ground. As the 1D structures produce zero vertical magnetic fields, ZTEM is not sensitive to background resistivity. Thus, in general, ZTEM can only reveal relative resistivities and not real resistivities. A combination of the ZTEM and MT methods can be an effective technique, alleviating the shortcomings of the individual methods. At present, complex underground structures and topography introduce difficulties for data inversion and interpretation, as conventional ZTEM and MT forward modeling are generally used on structured grids with limited accuracy. To effectively recover complex underground structures with topography, we developed a 3D framework for joint MT and ZTEM inversion with unstructured tetrahedral grids. The finite element method is used for the forward problem because of its flexibility with unstructured tetrahedral meshes. The limited-memory quasi-Newton algorithm (L-BFGS) for optimization is used to solve the joint inverse problem, which saves memory and computational time by avoiding the explicit calculation of the Hessian matrix. To validate our joint inversion algorithm, we run numerical experiments on two synthetic models. The first synthetic model uses two conductive anomalous bodies of different sizes and depths. At the same time, a simple quadrangular is used for comparing the inversions with and without topography. In contrast, the second synthetic model represents a realistic topography with two different conductivities and the same depth. Both single-domain and joint inversions of the ZTEM and MT data are carried out for the two synthetic models to demonstrate the complementary advantages of joint inversion, while the second model is also used to test the adaptability of the joint inversion to complex topography. The results demonstrate the effectiveness of the finite element method with unstructured tetrahedral grids and the L-BFGS method for joint MT and ZTEM inversion. In addition, the inversion results prove that joint MT and ZTEM inversion can recover deep structures from the MT data and small near-surface structures from the ZTEM data by alleviating the weaknesses of the individual methods.

Modeling 3-D Elastic Wave Propagation in TI Media Using Discontinuous Galerkin Method on Tetrahedral Meshes

Transversely isotropic (TI) medium is a widely studied anisotropic solid medium in seismology. The numerical simulation of seismic wave propagation in TI media is an effective tool to analyze the mechanism of seismic waves in complex anisotropic media. In this study, we introduce a double-weighted Runge-Kutta discontinuous Galerkin (RKDG) method for numerically solving wave propagation problems in 3D TI media with surface topography. This method incorporates the discontinuous Galerkin spatial discretization with an explicit double-weighted two-step iteration time discretization. The local Lax-Friedrichs flux is used as the numerical flux in the formulations. This method can solve the first-order velocity-stress seismic wave equations including TI media as well as more general anisotropic media. Due to the large scale of 3D problems, the parallel technology is adopted. Regions with irregular boundaries are discretized into unstructured tetrahedral meshes. Numerical experiments for various anisotropic media including the vertical and tilted TI media are presented. The results demonstrate the effectiveness of the double-weighted RKDG method in wavefield simulations in 3D complicated anisotropic media.

A Bernstein–Bézier Lagrange–Galerkin method for three-dimensional advection-dominated problems

We present a high-order Bernstein–Bézier finite element discretization to accurately solve three-dimensional advection-dominated problems on unstructured tetrahedral meshes. The key idea consists of implementing a modified method of characteristics to discretize the advection terms in a Bernstein–Bésier finite element framework. The proposed Bernstein–Bézier Lagrange–Galerkin method has been designed so that the Courant–Friedrichs–Lewy condition is strongly relaxed using semi-Lagrangian time discretization. A low complexity procedures in building finite element matrices and load vectors is also achieved in the present work by both the analytical rule and the sum factorization method using the tensorial feature of Bernstein polynomials. Several numerical examples including advection–diffusion equations with known analytical solutions and the viscous Burgers problem are considered to illustrate the accuracy, robustness and performance of the proposed approach. The computed results support our expectations for a stable and highly accurate Bernstein–Bézier Lagrange–Galerkin finite element method for three-dimensional advection-dominated problems.

A novel time‐domain numerical methodology for the electromagnetic analysis of an H‐plane tee power divider

A time-domain numerical methodology for the transient analysis of multisection waveguide power dividers is proposed. Waveguide power dividers are essential components of microwave systems for high-power applications. A numerical strategy based on the 3D discontinuous Galerkin time-domain finite element method is used to estimate the electromagnetic propagation inside a power divider with three ports. The proposed approach leads to simulations that are fast, robust, and accurate, this being the result of a parallel local discretisation of the full-wave time-domain Maxwell's equations on unstructured tetrahedral meshes. The stability of the overall numerical scheme is obtained using an upwind numerical flux, an implicit second-order accurate time integration scheme, and Whitney's edge elements. Good agreements are obtained when the computed results are compared with other HFSS simulation results, and with measurement results found in the literature.

STRAUM-MATXST: A code system for multi-group neutron-gamma coupled transport calculation with unstructured tetrahedral meshes

In this paper, a new multi-group neutron-gamma transport calculation code system STRAUM-MATXST for complicated geometrical problems is introduced and its development status including numerical tests is presented. In this code system, the MATXST (MATXS-based Cross Section Processor for SN Transport) code generates multi-group neutron and gamma cross sections by processing MATXS format libraries generated using NJOY and the STRAUM (SN Transport for Radiation Analysis with Unstructured Meshes) code performs multi-group neutron-gamma coupled transport calculation using tetrahedral meshes. In particular, this work presents the recent implementation and its test results of the Krylov subspace methods (i.e., Bi-CGSTAB and GMRES(m)) with preconditioners using DSA (Diffusion Synthetic Acceleration) and TSA (Transport Synthetic Acceleration). In addition, the Krylov subspace methods for accelerating the energy-group coupling iteration through thermal up-scatterings are implemented with new multi-group block DSA and TSA preconditioners in STRAUM.

Development of unstructured mesh tally capability in cosRMC and application to shutdown dose rate analysis

Accurate estimation of shutdown dose rate (SDDR) is one of the key issues in the neutronics calculation of fusion reactors. cosRMC R2S was developed based on the Rigorous two-step (R2S) method using a mesh tally for shutdown dose rate calculation, which requires higher transport calculation accuracy in complex geometry. However, the traditional method in this approach was based on the orthogonal structured mesh. The orthogonal structured mesh does not necessarily coincide with geometry and material boundaries, which can introduce large errors in activation calculation and reduce the calculation accuracy of shutdown dose rate. To solve this problem, the unstructured mesh tally capability was developed in the Monte Carlo code cosRMC. On this basis, cosRMC R2S was further developed, using unstructured meshes to replace structured meshes. Due to the geometry particularity of the unstructured tetrahedral mesh, the rejection sampling strategy was adopted to sample the position of the decay gamma source. In order to verify the reliability and validity of the code, the verification analyses were carried out on the ITER port plug benchmark and the FNG ITER shutdown dose rate benchmark respectively. The results obtained with unstructured meshes were compared with those obtained with structured meshes, and the reliability of the code was preliminarily verified. The results showed that the maximum discrepancy between experimental results was 10.1% with unstructured meshes, which was closer to experimental results than that with structured meshes, indicating that the computational accuracy of the result was improved effectively. It is demonstrated that the code developed in this paper is capable of accurate shutdown dose field calculations and has the potential to be applied to complex shielding devices.