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At least 163 records · Page 9

MPACT Verification With Magnox Reactor Neutronics Progression Problems

MPACT is a state-of-the-art core simulator designed to perform high-fidelity analysis using whole-core, three-dimensional, pin-resolved neutron transport calculations on modern parallel computing hardware. MPACT was originally developed to model light water reactors, and its capabilities are being extended to simulate gas-cooled, graphite-moderated cores such as Magnox reactors. To verify MPACT’s performance in this new application, the code is being formally benchmarked using representative problems. Progression problems are a series of example models that increase in complexity designed to test a code’s performance. The progression problems include both beginning-of-cycle and depletion calculations. Reference solutions for each progression problem have been generated using Serpent 2, a continuous-energy Monte Carlo reactor physics burnup calculation code.Using the neutron multiplication eigenvalue ke as a metric, MPACT’s performance is assessed on each of the progression problems. Initial results showed that MPACT’s multi-group cross section libraries, originally developed for pressurized water reactor problems, were not sufficient to accurately solve Magnox problems. MPACT’s improved performance on the progression problems is demonstrated using this new optimized cross section library.

Luciano, Nicholas↗

Multimessenger signals of heavy axionlike particles in core-collapse supernovae: Two-dimensional simulations

Core-collapse supernovae are a useful laboratory to probe the nature of exotic particles. If axionlike particles (ALPs) are produced in supernovae, they can affect the transfer of energy and leave traces in observational signatures. In this work, we present results from two-dimensional supernova models including the effects of the production and the absorption of ALPs that couple with photons. It is found that the additional heating induced by ALPs can enhance the diagnostic energy of explosion, E diag . For example, for moderate ALP-photon coupling, we find explosion energies ~0.6×10 51 erg compared to our reference model without ALPs of ~0.4×10 51 erg in the first ~0.5 s postbounce explored in this work. Further, our findings indicate that when the coupling constant is sufficiently high, the neutrino luminosities and mean energies are decreased because of the additional cooling of the proto-neutron star via ALPs. The gravitational wave amplitude is also reduced because the mass accretion on the proto-neutron star is suppressed. Although the ALP-photon coupling can foster explodability, including enhancing the explosion energy closer to recent observations, more long-term simulations in three spatial dimensions are needed to draw robust conclusions.

79 ASTRONOMY AND ASTROPHYSICS↗

Reactor Simulator Testing Overview

Test Objectives Summary: a) Verify operation of the core simulator, the instrumentation & control system, and the ground support gas and vacuum test equipment. b) Examine cooling & heat regeneration performance of the cold trap purification. c) Test the ALIP pump at voltages beyond 120V to see if the targeted mass flow rate of 1.75 kg/s can be obtained in the RxSim. Testing Highlights: a) Gas and vacuum ground support test equipment performed effectively for operations (NaK fill, loop pressurization, and NaK drain). b) Instrumentation & Control system effectively controlled loop temperature and flow rates or pump voltage to targeted settings and ramped within prescribed constraints. It effectively interacted with reactor simulator control model and defaulted back to temperature control mode if the transient fluctuations didn't dampen. c) Cold trap design was able to obtain the targeted cold temperature of 480 K. An outlet temperature of 636 K was obtained which was lower than the predicted 750 K but 156 K higher than the minimum temperature indicating the design provided some heat regeneration. d) ALIP produce a maximum flow rate of 1.53 kg/s at 800 K when operated at 150 V and 53 Hz.

Schoenfeld, Michael P.↗

Implementation of a Spacer Grid Rod Thermal-Hydraulic Reconstruction (ROTHCON) Capability into the Thermal-Hydraulic Subchannel Code CTF

The Consortium for Advanced Simulation of Light Water Reactors is developing a core simulator capability known as the Virtual Environment for Reactor Applications (VERA) to address nuclear industry challenge problems such as crud-induced power shift (CIPS). The CTF thermal-hydraulic (T/H) subchannel code provides thermal feedback in the coupled neutronics, T/H, crud chemistry simulation that VERA performs. It has been discovered that the coarse meshing approach used by CTF (in which fuel rods are discretized into four azimuthal segments) can be a source of error in predicting crud growth and boron distribution in VERA CIPS calculations. Spacer grid effects lead to complex rod-to-fluid heat transfer behavior that, when not resolved, can lead to error in the prediction of crud growth and boron deposition. A higher-fidelity computational fluid dynamics approach can be used instead of CTF, but this leads to excessive simulation times. This paper presents an approach for using high-fidelity computational fluid dynamics data to create shape functions that are used in CTF to reconstruct rod surface heat transfer behavior as a function of spacer grid geometry. The approach is demonstrated for a 5 × 5 rod bundle facility with five mixing vane grids under a range of operating conditions encountered in nominal pressurized water reactor conditions. Furthermore, it is demonstrated that the grid heat transfer maps are successful at introducing a higher-fidelity heat transfer modeling capability into CTF.

CFD-informed↗

Steady-State Gyrokinetics Transport Code (SSGKT), A Scientific Application Partnership with the Framework Application for Core-Edge Transport Simulations, Final Report

This project initiated the development of TGYRO - a steady-state Gyrokinetic transport code (SSGKT) that integrates micro-scale GYRO turbulence simulations into a framework for practical multi-scale simulation of conventional tokamaks as well as future reactors. Using a lightweight master transport code, multiple independent (each massively parallel) gyrokinetic simulations are coordinated. The capability to evolve profiles using the TGLF model was also added to TGYRO and represents a more typical use-case for TGYRO. The goal of the project was to develop a steady-state Gyrokinetic transport code (SSGKT) that integrates micro-scale gyrokinetic turbulence simulations into a framework for practical multi-scale simulation of a burning plasma core ? the International Thermonuclear Experimental Reactor (ITER) in particular. This multi-scale simulation capability will be used to predict the performance (the fusion energy gain, Q) given the H-mode pedestal temperature and density. At present, projections of this type rely on transport models like GLF23, which are based on rather approximate fits to the results of linear and nonlinear simulations. Our goal is to make these performance projections with precise nonlinear gyrokinetic simulations. The method of approach is to use a lightweight master transport code to coordinate multiple independent (each massively parallel) gyrokinetic simulations using the GYRO code. This project targets the practical multi-scale simulation of a reactor core plasma in order to predict the core temperature and density profiles given the H-mode pedestal temperature and density. A master transport code will provide feedback to O(16) independent gyrokinetic simulations (each massively parallel). A successful feedback scheme offers a novel approach to predictive modeling of an important national and international problem. Success in this area of fusion simulations will allow US scientists to direct the research path of ITER over the next two decades. The design of an efficient feedback algorithm is a serious numerical challenge. Although the power source and transport balance coding in the master are standard, it is nontrivial to design a feedback loop that can cope with outputs that are both intermittent and extremely expensive. A prototypical feedback scheme has already been successfully demonstrated for a single global GYRO simulation, although the robustness and efficiency are likely far from optimal. Once the transport feedback scheme is perfected, it could, in principle, be embedded into any of the more elaborate transport codes (ONETWO, TRANSP, and CORSICA), or adopted by other FSP-related multi-scale projects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Coupling neutrino oscillations and simulations of core-collapse supernovae

At the present time even the most sophisticated, multidimensional simulations of core-collapse supernovae do not (self-consistently) include neutrino flavor transformation. This physics is missing despite the importance of neutrinos in the core-collapse explosion paradigm. Because of this dependence, any flavor transformation that occurs in the region between the protoneutron star and the shock could result in major effects upon the dynamics of the explosion. Here, we present the first hydrodynamic core-collapse supernova simulation which simultaneously includes flavor transformation of the free-streaming neutrinos in the neutrino transport. These oscillation calculations are dynamically updated and evolve self-consistently alongside the hydrodynamics. Using a M = 20 M ⊙ progenitor, we find that while the oscillations have an effect on the neutrino emission and the heating rates, flavor transformation alone does not lead to a successful explosion of this progenitor in spherical symmetry.

79 ASTRONOMY AND ASTROPHYSICS↗

Reactivity-initiated accident simulation to inform transient testing of candidate advanced cladding

This paper leverages three-dimensional reactor-core-simulation capabilities to provide information on appropriate experimental test conditions for candidate advanced cladding materials in a control-rod-ejection event. These test conditions use three-dimensional nodal kinetics simulations of a reactivity-initiated accident (RIA) in a representative state-of-the-art pressurized water reactor with both nuclear-grade iron-chromium-aluminum (FeCrAl) and silicon-carbide (SiC-SiC)-based cladding materials. The effort yields boundary conditions for experimental mechanical tests, specifically peak cladding strain during the power pulse following the rod ejection. The impact of candidate cladding materials on the reactor kinetics behavior of RIA progression versus that of reference Zr cladding is predominantly due to differences in -1) fuel mass/volume/specific power density, -2) spectral effects due to parasitic neutron absorption, -3) control rod worth due to hardened (or softened) spectrum, and -4) initial conditions due to power peaking and neutron transport cross sections in the equilibrium cycle cores resulting from hardened (or softened) spectrum. This study shows minimal impact of SiC-SiC-based cladding configurations on the transient response versus reference Zircaloy cladding. However, the FeCrAl cladding response indicates similar energy deposition, but with significantly shorter pulses of higher magnitude. Therefore, the FeCrAl-based cases have a more rapid fuel thermal expansion rate, and the resultant pellet-cladding interaction occurs more rapidly. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

The effects of temperatures on the pebble flow in a pebble bed high temperature reactor

The core of a pebble bed high temperature reactor (PBHTR) moves during operation, a feature which leads to better fuel economy (online refueling with no burnable poisons) and lower fuel stress. The pebbles are loaded at the top and trickle to the bottom of the core after which the burnup of each is measured. The pebbles that are not fully burned are recirculated through the core until the target burnup is achieved. The flow pattern of the pebbles through the core is of importance for core simulations because it couples the burnup distribution to the core temperature and power profiles, especially in cores with two or more radial burnup 'zones '. The pebble velocity profile is a strong function of the core geometry and the friction between the pebbles and the surrounding structures (other pebbles or graphite reflector blocks). The friction coefficient for graphite in a helium environment is inversely related to the temperature. The Thorium High Temperature Reactor (THTR) operated in Germany between 1983 and 1989. It featured a two-zone core, an inner core (IC) and outer core (OC), with different fuel mixtures loaded in each zone. The rate at which the IC was refueled relative to the OC in THTR was designed to be 0.56. During its operation, however, this ratio was measured to be 0.76, suggesting the pebbles in the inner core traveled faster than expected. It has been postulated that the positive feedback effect between inner core temperature, burnup, and pebble flow was underestimated in THTR. Because of the power shape, the center of the core in a typical cylindrical PBHTR operates at a higher temperature than the region next to the side reflector. The friction between pebbles in the IC is lower than that in the OC, perhaps causing a higher relative flow rate and lower average burnup, which in turn yield a higher local power density. Furthermore, the pebbles in the center region have higher velocities than the pebbles next to the side reflector due to the interaction between the pebbles and the immobile graphite reflector as well as the geometry of the discharge conus near the bottom of the core. In this paper, the coupling between the temperature profile and the pebble flow dynamics was analyzed by using PEBBED/THERMIX and PEBBLES codes by modeling the HTR-10 reactor in China. Two extreme and opposing velocity profiles are used as a starting point for the iterations. The PEBBED/THERMIX code is used to calculate the burnup, power and temperature profiles with one of the velocity profiles as input. The resulting temperature profile is then passed to PEBBLES code to calculate the updated pebble velocity profile taking the new temperature profile into account. If the aforementioned hypothesis is correct, the strong temperature effect upon the friction coefficients would cause the two cases to converge to different final velocity and temperature profiles. The results of this analysis indicates that a single zone pebble bed core is self-stabilizing in terms of the pebble velocity profile and the effect of the temperature profile on the pebble flow is insignificant. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Framework Application for Core Edge Transport Simulation (FACETS)

The FACETS (Framework Application for Core-Edge Transport Simulations) project of Scientific Discovery through Advanced Computing (SciDAC) Program was aimed at providing a high-fidelity whole-tokamak modeling for the U.S. magnetic fusion energy program and ITER through coupling separate components for each of the core region, edge region, and wall, with realistic plasma particles and power sources and turbulent transport simulation. The project also aimed at developing advanced numerical algorithms, efficient implicit coupling methods, and software tools utilizing the leadership class computing facilities under Advanced Scientific Computing Research (ASCR). The FACETS project was conducted by a multi-discipline, multi-institutional teams, the Lead PI was J.R. Cary (Tech-X Corp.). In the FACETS project, the Applied Plasma Theory Group at the MAE Department of UCSD developed the Wall and Plasma-Surface Interaction (WALLPSI) module, performed its validation against experimental data, and integrated it into the developed framework. WALLPSI is a one-dimensional, coarse grained, reaction/advection/diffusion code applied to each material boundary cell in the common modeling domain for a tokamak. It incorporates an advanced model for plasma particle transport and retention in the solid matter of plasma facing components, simulation of plasma heat power load handling, calculation of erosion/deposition, and simulation of synergistic effects in strong plasma-wall coupling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Verification and validation of the Alternative Nonlinear Two-phase Subchannel (ANTS) code

The Alternative Nonlinear Two-phase Subchannel solver (ANTS) code was written to provide a fast-running, steady-state, pin-resolved modeling and simulation tool for analysis of common boiling water reactor (BWR) geometry and common operating conditions. ANTS has been integrated into the Virtual Environment for Reactor Application (VERA) core simulator software, where it can be used to provide a thermal/hydraulic (T/H) subchannel solution that is then used to provide neutronic feedback as well as perform the fuel depletion and temperature solution. Herein, this paper presents the rigorous analysis performed on the ANTS code, which includes both code and solution verification testing, benchmarking with the existing two-phase subchannel capability in VERA, CTF, and validation testing using popular two-phase experiments such as PWR Sub-channel and Bundle Tests (PSBT), BWR Full-size Fine-mesh Bundle Tests (BFBT), Risø, and FRIGG. This assessment was used to qualify ANTS for its intended applications before its use for core-scale, multiphysics BWR simulations. In general, it was found that agreement with experimental data was good; errors were within the range of experimental data uncertainty. Furthermore, code and solution verification confirmed that the governing equations and the most important closure terms were correctly implemented and behaving as expected.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A study on the impact of using a subchannel resolution for modeling of large break loss of coolant accidents

The nuclear industry is investigating the feasibility of transitioning from 18- to 24-month fuel cycles because of the positive impact it would have on the operational costs for the current fleet of light-water reactors. A challenge to making this change is the increased risk of fuel fragmentation, relocation, and dispersal (FFRD) due to the known potential for ceramic fuel to pulverize into fine particles at the higher discharge burnups. Previous work has been performed by the Nuclear Energy Advanced Modeling and Simulation program to assess FFRD risk in high-burnup cores using the BISON fuel performance code and a coarse mesh thermal hydraulics (T/H) solution for a loss-of-coolant accident (LOCA) using the TRACE system T/H code. Because of the importance of the T/H solution for FFRD assessment, this study seeks to investigate the impact of using higher-fidelity subchannel techniques for modeling of the LOCA transient. CTF was used to model a subregion of a high-burnup core that was depleted by the Virtual Environment for Reactor Applications (VERA) multiphysics core simulator. Both coarse-mesh and pin-resolved models were created in CTF, and a consistent coarse-mesh TRACE model was also developed to allow for benchmarking the code results. Further, a large-break loss-of-coolant accident (LBLOCA) reflood transient was simulated using these three models, and results were compared. Results showed some consistent differences between the CTF and TRACE coarse models, including a higher peak cladding temperature (PCT) prediction in CTF and later quenching in CTF; however, the transient clad temperature behavior was similar, and these differences are likely due to post-critical heat flux heat transfer modeling differences and minimum film boiling temperature model differences. The pin-resolved results indicate that the PCT in the lumped model is often under-predicted by as much as 70 °C and that PCT occurs at a different location than the high-power pin in the assembly. The lumped model predicts a difference of 10 °C or less between the average and hot pins in the assembly, whereas the pin-resolved model predicts a range of over 100 °C. These results indicate that higher-fidelity T/H results may have an impact on predicted core behavior during LOCA, which may be important to consider when assessing FFRD risk.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOMINO: A fast 3D cartesian discrete ordinates solver for reference PWR simulations and SPN validation

As part of its activity, EDF R and D is developing a new nuclear core simulation code named COCAGNE. This code relies on DIABOLO, a Simplified PN (SPN) method to compute the neutron flux inside the core for eigenvalue calculations. In order to assess the accuracy of SPN calculations, we have developed DOMINO, a new 3D Cartesian SN solver. The parallel implementation of DOMINO is very efficient and allows to complete an eigenvalue calculation involving around 300 x 10{sup 9} degrees of freedom within a few hours on a single shared-memory supercomputing node. This computation corresponds to a 26-group S{sub 8} 3D PWR core model used to assess the SPN accuracy. At the pin level, the maximal error for the SP{sub 5} DIABOLO fission production rate is lower than 0.2% compared to the S{sub 8} DOMINO reference for this 3D PWR core model. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Stellar Mass Black Hole Formation and Multimessenger Signals from Three-dimensional Rotating Core-collapse Supernova Simulations

We present self-consistent 3D core-collapse supernova simulations of a 40 ${M}_{\odot }$ progenitor model using the isotropic diffusion source approximation for neutrino transport and an effective general relativistic potential up to `0.9 s postbounce. We consider three different rotational speeds with initial angular velocities of ${{\rm{\Omega }}}_{0}=0$, 0.5, and 1 rad s -1 and investigate the impact of rotation on shock dynamics, black hole (BH) formation, and gravitational wave (GW) signals. The rapidly rotating model undergoes an early explosion at ~250 ms postbounce and shows signs of the low $T/| W| $ instability. We do not find BH formation in this model within ~460 ms postbounce. In contrast, we find BH formation at 776 ms postbounce and 936 ms postbounce for the nonrotating and slowly rotating models, respectively. The slowly rotating model explodes at ~650 ms postbounce, and the subsequent fallback accretion onto the proto–neutron star (PNS) results in BH formation. In addition, the standing accretion shock instability induces rotation of the PNS in the model that started with a nonrotating progenitor. Assuming conservation of specific angular momentum during BH formation, this corresponds to a BH spin parameter of a = J/M = 0.046. However, if no explosion sets in, all the angular momentum will eventually be accreted by the BH, resulting in a nonspinning BH. The successful explosion of the slowly rotating model drastically slows down the accretion onto the PNS, allowing continued cooling and contraction that results in an extremely high GW frequency (f ~ 3000 Hz) at BH formation, while the nonrotating model generates GW signals similar to our corresponding 2D simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

Convergence studies of deterministic methods for LWR explicit reflector methodology

The standard approach in modem 3-D core simulators, employed either for steady-state or transient simulations, is to use Albedo coefficients or explicit reflectors at the core axial and radial boundaries. In the latter approach, few-group homogenized nuclear data are a priori produced with lattice transport codes using 2-D reflector models. Recently, the explicit reflector methodology of the deterministic CASMO-4/SIMULATE-3 code system was identified to potentially constitute one of the main sources of errors for core analyses of the Swiss operating LWRs, which are all belonging to GII design. Considering that some of the new GIII designs will rely on very different reflector concepts, a review and assessment of the reflector methodology for various LWR designs appeared as relevant. Therefore, the purpose of this paper is to first recall the concepts of the explicit reflector modelling approach as employed by CASMO/SIMULATE. Then, for selected reflector configurations representative of both GII and GUI designs, a benchmarking of the few-group nuclear data produced with the deterministic lattice code CASMO-4 and its successor CASMO-5, is conducted. On this basis, a convergence study with regards to geometrical requirements when using deterministic methods with 2-D homogenous models is conducted and the effect on the downstream 3-D core analysis accuracy is evaluated for a typical GII deflector design in order to assess the results against available plant measurements. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Ex-Core Radiation Transport Modeling with VERA User Manual

It is important to be able to accurately predict the neutron flux outside the immediate reactor core for a variety of safety and material analyses. Monte Carlo radiation transport calculations are required to produce these high–fidelity ex-core responses. The Virtual Environment for Reactor Applications (VERA) provides the automated capability to launch independent Shift fixed-source and eigenvalue Monte Carlo (MC) calculations for user-specified state points during a standard Virtual Environment for Reactor Applications (VERA) calculation. VERA couples MPACT with COBRA-TF (CTF) to Shift to perform ex-core tallies for multiple state points concurrently, with each component capable of parallel execution on independent processor domains. In these ex-core calculations, MPACT is coupled to CTF and performs the in-core depletion and heat transfer calculation, followed by a fixed-source Shift transport calculation including ex-core regions to produce ex-core responses. The fission source, fuel pin temperatures, moderator temperature and density, boron concentration, and fuel pin depleted isotopic compositions can be transferred to Shift from the MPACT calculation. Specifically, VERA performs fluence calculations in the core barrel outward to the end of the pressure vessel and detector response calculations in ex-core detectors. It also performs the requested tallies in any user-defined ex-core regions. VERA takes advantage of the General Geometry (GG) package in Shift. This gives VERA the flexibility to explicitly model features outside the core barrel, including detailed vessel models, detectors, and power plant details. A very limited set of experimental and numerical benchmarks is available for ex-core simulation comparison. The Consortium for Advanced Simulation of Light Water Reactors has developed a set of ex-core benchmark problems to include as part of the VERA verification and validation set of problems. The ex-core capability in VERA has been tested on small representative assembly problems, multi-assembly problems, as well as quarter-core and full-core problems. VERA View has also been extended to visualize these vessel fluence results from VERA. This manual serves to present a guide to VERA users about the methodology behind ex-core calculations and the details of input, output, and analysis of results from these calculations. Details in this version of the manual are based on features in VERA 4.0.1.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Modifications and Modelling of the Fission Surface Power Primary Test Circuit (FSP-PTC)

An actively pumped alkali metal flow circuit, designed and fabricated at the NASA Marshall Space Flight Center, underwent a range of tests at MSFC in early 2007. During this period, system transient responses and the performance of the liquid metal pump were evaluated. In May of 2007, the circuit was drained and cleaned to prepare for multiple modifications: the addition of larger upper and lower reservoirs, the installation of an annular linear induction pump (ALIP), and the inclusion of the Single Flow Cell Test Apparatus (SFCTA) in the test section. Performance of the ALIP, provided by Idaho National Laboratory (INL), will be evaluated when testing resumes. The SFCTA, which will be tested simultaneously, will provide data on alkali metal flow behavior through the simulated core channels and assist in the development of a second generation thermal simulator. Additionally, data from the first round of testing has been used to refine the working system model, developed using the Generalized Fluid System Simulation Program (GFSSP). This paper covers the modifications of the FSP-PTC and the updated GFSSP system model.

Garber, Ann E.↗

Improvements, enhancements, and optimizations of COBRA-TF

The Reactor Dynamics and Fuel Management Group (RDFMG) at The Pennsylvania State University (PSU) has become active in the Consortium for Advanced Simulation of Light Water Reactors (CASL) program by delivering, supporting, and further developing CTF, the PSU version of the Coolant Boiling in Rod Arrays - Two Fluids (COBRA-TF) Thermal/Hydraulic (T/H), sub-channel program. New development work on CTF was primarily geared towards decreasing the execution time of the code so that it may eventually be used for performing pin-by-pin, full-core simulations. Great gains have been made through targeting sections of source code for optimization. For example, wall clock time has been reduced for a one-assembly, three-dimensional model, containing {approx}9,400 mesh cells, from 9.2 min to 1 min. A further improvement has been reduction in code memory usage, which was previously prohibitive for large models. In conjunction with the run time speedups, this has enabled the simulation of a refined quarter-core model ({approx}460,000 mesh cells), which saw a reduction in memory usage from over 130 GB to less than 3 GB. In addition to the optimization work, RDFMG has also created a preprocessor utility for the fast and less error-prone generation of CTF input decks. Furthermore, basic post-processing capabilities have been implemented by creating a CTF subroutine for producing Visualization Tool-Kit (VTK) files that output mesh data and associated simulation results. These VTK files can be opened with visualization software. (authors)

97 MATHEMATICS AND COMPUTING↗