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FY-2013 FES (Fusion Energy Sciences) Joint Research Target Report

The H-mode confinement regime is characterized by a region of good thermal and particle confinement at the edge of the confined plasma, and has generally been envisioned as the operating regime for ITER and other next step devices. This good confinement is often interrupted, however, by edge-localized instabilities, known as ELMs. On the one hand, these ELMs provide particle and impurity flushing from the plasma core, a beneficial effect facilitating density control and stationary operation. On the other hand, the ELMs result in a substantial fraction of the edge stored energy flowing in bursts to the divertor and first wall; this impulsive thermal loading would result in unacceptable erosion of these material surfaces if it is not arrested. Hence, developing and understanding operating regimes that have the energy confinement of standard H-mode and the stationarity that is provided by ELMs, while at the same time eliminating the impulsive thermal loading of large ELMs, is the focus of the 2013 FES Joint Research Target (JRT): Annual Target: Conduct experiments and analysis on major fusion facilities, to evaluate stationary enhanced confinement regimes without large Edge Localized Modes (ELMs), and to improve understanding of the underlying physical mechanisms that allow acceptable edge particle transport while maintaining a strong thermal transport barrier. Mechanisms to be investigated can include intrinsic continuous edge plasma modes and externally applied 3D fields. Candidate regimes and techniques have been pioneered by each of the three major US facilities (C-Mod, D3D and NSTX). Coordinated experiments, measurements, and analysis will be carried out to assess and understand the operational space for the regimes. Exploiting the complementary parameters and tools of the devices, joint teams will aim to more closely approach key dimensionless parameters of ITER, and to identify correlations between edge fluctuations and transport. The role of rotation will be investigated. The research will strengthen the basis for extrapolation of stationary regimes which combine high energy confinement with good particle and impurity control, to ITER and other future fusion facilities for which avoidance of large ELMs is a critical issue. Data from the Alcator C-Mod tokamak (MIT), DIII-D tokamak (General Atomics), and NSTX spherical tokamak (PPPL) contribute to this report. Experiments specifically motivated by this research target were conducted on DIII-D, with a national team of researchers from GA, LLNL, PPPL, MIT and ORNL contributing. Both the Alcator C-Mod and NSTX-U teams contributed analysis of previously collected data, as those two facilities did not operate in FY2013. Within each of the three research groups, members from both the host institutions and collaborating institutions made critical contributions. Highlights from these research activities are provided, with additional details.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Flux stabilization in neutron problems with fixed sources

Although critical core calculations are the most common in design and safety analysis, fixed source calculations are needed for specific applications, e.g. to compute ex-core detector response functions, to develop new methodologies for dilution and reload error accidents and more in general for all situations involving sub-critical shut-down states. It is well known that the source problem becomes difficult to be solved with core configuration close to criticality, i.e. with the multiplication factor approaching unity, for the occurrence of numerical ill-conditioning and very high number of iterations, possibly leading to failure in the flux convergence. In this work, the Wielandt Eigen-shift technique used in iterative methods of critical problems is developed for source problems too, in order to stabilize the solution. The mathematical basis and the proof of the convergence are discussed. Compared to the existing methods, this technique allows also more control to avoid singular behavior at inner iterations. Numerical tests with a 1D analytical benchmark are reported to prove the robustness of the technique. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Results from tight and loose coupled multiphysics in nuclear fuels performance simulations using BISON

The behavior of nuclear fuel in the reactor environment is affected by multiple physics, most notably heat conduction and solid mechanics, which can have a strong influence on each other. To provide credible solutions, a fuel performance simulation code must have the ability to obtain solutions for each of the physics, including coupling between them. Solution strategies for solving systems of coupled equations can be categorized as loosely-coupled, where the individual physics are solved separately, keeping the solutions for the other physics fixed at each iteration, or tightly coupled, where the nonlinear solver simultaneously drives down the residual for each physics, taking into account the coupling between the physics in each nonlinear iteration. In this paper, we compare the performance of loosely and tightly coupled solution algorithms for thermomechanical problems involving coupled thermal and mechanical contact, which is a primary source of interdependence between thermal and mechanical solutions in fuel performance models. The results indicate that loosely-coupled simulations require significantly more nonlinear iterations, and may lead to convergence trouble when the thermal conductivity of the gap is too small. We also apply the tightly coupled solution strategy to a nuclear fuel simulation of an experiment in a test reactor. Studying the results from these simulations indicates that perhaps convergence for either approach may be problem dependent, i.e., there may be problems for which a loose coupled approach converges, where tightly coupled won't converge and vice versa. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Movable geometry and eigenvalue search capability in the MC21 Monte Carlo code

A description of a robust and flexible movable geometry implementation in the Monte Carlo code MC21 is described along with a search algorithm that can be used in conjunction with the movable geometry capability to perform eigenvalue searches based on the position of some geometric component. The natural use of the combined movement and search capability is searching to critical through variation of control rod (or control drum) position. The movable geometry discussion provides the mathematical framework for moving surfaces in the MC21 combinatorial solid geometry description. A discussion of the interface between the movable geometry system and the user is also described, particularly the ability to create a hierarchy of movable groups. Combined with the hierarchical geometry description in MC21 the movable group framework provides a very powerful system for inline geometry modification. The eigenvalue search algorithm implemented in MC21 is also described. The foundations of this algorithm are a regula falsi search though several considerations are made in an effort to increase the efficiency of the algorithm for use with Monte Carlo. Specifically, criteria are developed to determine after each batch whether the Monte Carlo calculation should be continued, the search iteration can be rejected, or the search iteration has converged. These criteria seek to minimize the amount of time spent per iteration. Results for the regula falsi method are shown, illustrating that the method as implemented is indeed convergent and that the optimizations made ultimately reduce the total computational expense. (authors)

97 MATHEMATICS AND COMPUTING↗

Nonlinear diffusion acceleration for the multigroup transport equation discretized with S{sub N} and continuous FEM with rattlesnake

Nonlinear diffusion acceleration (NDA) can improve the performance of a neutron transport solver significantly especially for the multigroup eigenvalue problems. The high-order transport equation and the transport-corrected low-order diffusion equation form a nonlinear system in NDA, which can be solved via a Picard iteration. The consistency of the correction of the low-order equation is important to ensure the stabilization and effectiveness of the iteration. It also makes the low-order equation preserve the scalar flux of the high-order equation. In this paper, the consistent correction for a particular discretization scheme, self-adjoint angular flux (SAAF) formulation with discrete ordinates method (S{sub N}) and continuous finite element method (CFEM) is proposed for the multigroup neutron transport equation. Equations with the anisotropic scatterings and a void treatment are included. The Picard iteration with this scheme has been implemented and tested with RattleS{sub N}ake, a MOOSE-based application at INL. Convergence results are presented. (authors)

97 MATHEMATICS AND COMPUTING↗

Hybrid S{sub n}-Diffusion and S{sub n}-P{sub 3} transport calculations

We investigate coupling and preconditioning techniques for 1-D hybrid neutronics calculations. Each problem is represented by two spatial regions with S{sub n} used in one region and either diffusion or P{sub 3} used in the other. For each of these two cases we define one coupling scheme and two preconditioned systems. These systems are solved with both fixed-point iteration and the GMRES Krylov method. The solution techniques are compared in terms of iteration count and CPU time per iteration. Preconditioning with a global diffusion operator is found to be very effective for the most difficult problems. (authors)

97 MATHEMATICS AND COMPUTING↗

Evolution of US DOE Performance Assessments Over 20 Years - 13597

Performance assessments (PAs) have been used for many years for the analysis of post-closure hazards associated with a radioactive waste disposal facility and to provide a reasonable expectation of the ability of the site and facility design to meet objectives for the protection of members of the public and the environment. The use of PA to support decision-making for LLW disposal facilities has been mandated in United States Department of Energy (US DOE) directives governing radioactive waste management since 1988 (currently DOE Order 435.1, Radioactive Waste Management). Prior to that time, PAs were also used in a less formal role. Over the past 20+ years, the US DOE approach to conduct, review and apply PAs has evolved into an efficient, rigorous and mature process that includes specific requirements for continuous improvement and independent reviews. The PA process has evolved through refinement of a graded and iterative approach designed to help focus efforts on those aspects of the problem expected to have the greatest influence on the decision being made. Many of the evolutionary changes to the PA process are linked to the refinement of the PA maintenance concept that has proven to be an important element of US DOE PA requirements in the context of supporting decision-making for safe disposal of LLW. The PA maintenance concept is central to the evolution of the graded and iterative philosophy and has helped to drive the evolution of PAs from a deterministic compliance calculation into a systematic approach that helps to focus on critical aspects of the disposal system in a manner designed to provide a more informed basis for decision-making throughout the life of a disposal facility (e.g., monitoring, research and testing, waste acceptance criteria, design improvements, data collection, model refinements). A significant evolution in PA modeling has been associated with improved use of uncertainty and sensitivity analysis techniques to support efficient implementation of the graded and iterative approach. Rather than attempt to exactly predict the migration of radionuclides in a disposal unit, the best PAs have evolved into tools that provide a range of results to guide decision-makers in planning the most efficient, cost effective, and safe disposal of radionuclides. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Investigation of the Effects of Hydrogen Atoms Concentration on the Tungsten Sigma 5 (310) Symmetric Tilt Grain Boundary Strength

Recently, strict policies are being made by several government agencies, environmentalists, and some people against the usage of fossil fuels as the source of energy generation. Not only because its supply does not meet the booming human population all around the world but also it is not pollution-free; just to mention a few. These setbacks attached to fossil fuels make nuclear fusion energy an important means of energy generation; it is characterized with clean and easy means of energy generation compared to other methods of power production such as hydropower and solar power. The success of fusion power depends on the design of modern fusion materials and the selection of the plasma facing materials (PFMs). ITER and Demonstration Power plant (DEMO) considered Tungsten (W) as part of their PFMs. W is the most preferred plasma facing material (PFM) for the future nuclear fusion reactors such as in the proposed DEMO and ITER- which is at the moment the largest Tokamak nuclear fusion reactor under construction in the world. Tungsten has excellent thermal properties, low-sputtering yield, and high melting point. Hydrogen (H) atoms have an affinity for tungsten grain boundary, and are trapped there permanently. In addition, it makes W prone to failure. In a fusion environment, W is exposed to extremely high fluences of H isotopes and irradiation. The low-energy H isotopes will be retained in the tungsten material leading to the formation of blisters in W and cause degradation of the mechanical and thermal properties of W. For safety reason, the effect of hydrogen atoms concentration at the tungsten S5 (310) grain boundary (GB) needs to be investigated and it will aid in better designing of fusion wall materials. Σ5 (310) is considered in this work because it is one of the most important and dominant GBs in the atomic distribution of materials. GBs affect the strength of W as well. The GBs with superior properties can be increased in the atomic distribution of W relative to others in order to achieve high overall material properties. GBs play a role in determining the properties of materials such as the thermal and electrical conductivity of a material. The crystallography description of the Σ5 (310) grain boundary comprises of Σ, tilt type- symmetric, crystallographic direction [001] and the GB plane. The Σ is related to the coincidence site lattice (CSL) model, which denotes that in a certain orientation between two grains, there are numbers of points where the atoms coincide. For the case of Σ5 (310), the misorientation between the two crystals is 36.9 degree along [001] direction and the GB plane is (310). GB properties differ as result of different sigma values and Σ is the reciprocal of CSL. Thus, Σ5 GB has 1/5 of the atoms in coincident sites. For the case of a tilt boundary, the lattice vector is embedded in the GB plane. Also for a tilt-symmetric GB, the grains directions are mirrored against the GB plane. The classic molecular dynamics method (MD) is an accurate numerical approach that adopts Newton's equation of motion to get atoms trajectories.Studies have been carried out on atomistic simulation of tungsten.The effect of H on GB migration in W was studied by using molecular dynamics simulation and it was discovered that H prevents the GB migration at different H concentrations and temperatures. Others investigated the migration, dissolution and trapping of H in W using MD and first principles method. Atomistic simulations have been used to predict the GB energy in Fe and Mo using embedded atom method (EAM) and it was concluded that the GB energies in the metals are affected more by the orientation of the GB plane than by the misorientation of the lattice. Study was done on symmetric and asymmetric tilt grain boundaries in Cu and Al using MD method and the GB structures and energies were established; EAM was adopted as well. The formation of hydrogen blisters and cracking processes for various tungsten materials were investigated and it was observed that, dopants increase the number of blisters and exfoliations for both stress relieved and recrystallized W. Investigation was carried out on the surface morphology changes in W caused by plasmas heat and particle loadings and their effects on material degradation in ITER. In addition, the study of interactions between low energetic hydrogen and tungsten surface was carried out using molecular dynamics simulations with analytical bond order potential (ABOP) and the results addressed irradiation damage in tungsten. Mechanism of blister formation on W surface was studied using experimental approach and it was observed that the amount of blisters formed depends on the beam fluence. This work investigates the effect of hydrogen atom concentrations at the W Σ5 (310) tilt-symmetric GB on the grain boundary energy and the GB pulling force. (authors)

36 MATERIALS SCIENCE↗

Test facility for fission chamber assemblies - 239

The Institution -Project Center ITER- with participation of the National Research Nuclear University MEPhI are developing the neutron diagnostics -Divertor Neutron Flux Monitor- (DNFM) for the International Thermonuclear Experimental Reactor (ITER). This diagnostics shall ensure measurement of the total neutron yield and ITER fusion power. Assemblies of fission chambers (FC) with different fissile materials and sensitivities are planned to be used for the neutron flux measurement. Study of fission chambers characteristics and acceptance testing of the diagnostic system will be carried out at the testing facility of the neutronic laboratory of the 'TRINITI' Institute. The facility includes: compact powerful neutron generator with the power, control and monitoring system; remote handling system for FCs positioning and movement; novel three channels data acquisition and processing system. Each acquisition channel contains some measuring circuits with signal processing. This set of circuits provides neutron flux measurement in the range of at least 10 decades for each single FC. Data acquisition and processing system features are: signal digitizing with sample rate up to 125 MHz; real time data processing with computation and data update cycle from 0.1 ms. This paper examines the structure, composition and specification of the test facility. Application software, hardware solutions and the results of fission chambers prototypes tests are discussed. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Fourier Analysis of the Multilevel QD Method with {alpha}-Approximation For Time-Dependent Radiative Transfer Problems

Thermal radiation transfer (TRT) problems describe interaction of photon radiation with matter. They are defined by the time-dependent radiative transfer (RT) equation for the specific intensity I coupled with the energy balance (EB) equation. This class of problems is characterised by high dimensionality, multiple scales and strong nonlinearity. In this paper we analyze the multilevel quasi-diffusion (QD) method for solving TRT problems. This is a nonlinear method of moments with exact closures. The QD method enables one to reduce dimensionality of the original radiative transfer problem. It is formulated by a nonlinear system of equations consisting of (i) the high-order RT (HORT) equation for the intensity of photon radiation and (ii) low-order equations for the angular and energy moments of the intensity. The nonlinear closures are formulated by means of stable factors. The low-order problem brings the radiative transfer model to the level of multi-physics equations. The multilevel QD (MLQD) method possesses attractive features for efficient multi-physics coupling. To calculate the high-order RT solution we apply the {alpha}-approximation which assumes that the intensity changes exponentially in time over a time step. The {alpha}-approximation leads to the steady-state RT equation with a modified opacity and enables one to avoid storing the high-dimensional solution from the previous time step. The rate of change is evaluated by the solution of the time-dependent low-order QD (LOQD) equations for moments. We note that the HORT equation in the {alpha}-approximation contains an extra nonlinear term. It affects the iterative behaviour of the MLQD method. The obtained computational results indicated that the rate of convergence is slower compared to the rate when the time-dependent HORT is used to calculate the intensity. In this paper we perform an iterative stability analysis of the MLQD method in a discretized form and analyze convergence of outer (transport) iterations on a time step. We consider multigroup TRT problems in 1D slab geometry. The fully implicit scheme is used to discretize equations in time. The HORT equation is approximated with the method of step characteristics. A finite volume method is applied for spatial discretization of multigroup LOQD equations. The grey (one-group) LOQD equations are algebraically consistent with the multigroup LOQD equations. To perform Fourier analysis a model TRT problem in an infinite homogeneous medium is considered. The system of nonlinear equations of the MLQD method is linearized near an equilibrium solution at some given temperature. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Analysis of Shutdown Dose Rate in Fusion Energy Systems Using Hybrid Monte Carlo/Deterministic Techniques - Paper 138

Accurate assessments of shutdown dose rate (SDDR) are critical to support operation, maintenance, and waste disposal planning and to guide possible design changes of critical components in fusion energy systems. An SDDR calculation involves three steps: 1. a neutron transport calculation to determine the space and energy neutron flux distributions, 2. an activation calculation for computing the photon source distribution, and 3. a photon transport calculation for the estimation of the final SDDR. A companion paper describes the challenges of SDDR computations in fusion energy systems and the status of the techniques that are currently being used in SDDR analysis. Of these techniques, the rigorous 2-step (R2S) computational system entails Monte Carlo (MC) neutron and photon transport calculations coupled with a comprehensive activation step using a dedicated inventory code and library. The use of global MC variance reduction techniques was suggested for accelerating the SDDR MC neutron transport calculation. These techniques, which attempt to calculate MC tallies with nearly uniform relative uncertainties in both the low-flux space-energy regions and the high-flux space-energy regions, do not preferentially focus the MC computational efforts toward space-energy regions of high importance to the final decay dose. The ability of these approaches to accurately predict SDDR is inhibited by their prohibitive computational costs, which will be on the order of thousands of processor-years for full-scale modeling of an entire fusion plant. The companion paper describes the theoretical background of the Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) method, which has been proposed to speed up SDDR MC neutron calculations. The MS-CADIS method uses the CADIS method, which has been successfully used for more than a decade in shielding calculations, but focuses on multistep shielding calculations such as SDDR analyses. The companion paper also describes a new method for calculating the uncertainties in SDDR due to uncertainties in the MC neutron calculation. This new method of uncertainty propagation uses the MS-CADIS neutron adjoint source to propagate the uncertainties in the neutron fluxes to the SDDR. This paper describes the application of the MS-CADIS method for speeding up the SDDR MC calculations and for calculating the SDDR uncertainty due to the neutron flux uncertainties. A new metric for assessing the reliability of SDDR calculations was also suggested and used in this analysis. The ITER benchmark problem was used in this analysis. The problem resembles the configuration and geometrical arrangement of an upper port plug in ITER. The analysis compared the efficiency of the MS-CADIS method to the traditional approach of using global MC variance reduction techniques for speeding up SDDR MC neutron calculation. The application of the MS-CADIS method to SDDR calculations in fusion energy systems was tested using the ITER benchmark problem. Compared to the standard FW-CADIS method, the increase in the efficiency of the SDDR neutron MC calculation due to the use of the MS-CADIS method was between 18% and 69%. The MS-CADIS method also increases the fraction of non-zero-scoring mesh tally elements in the space-energy regions of high importance to the final SDDR. Implementation of the MS-CADIS method in the SCALE and the ADVANTG code systems is currently under way. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

Fast Scanning Probe Microscopy via Machine Learning: Non-Rectangular Scans with Compressed Sensing and Gaussian Process Optimization

Fast scanning probe microscopy enabled via machine learning allows for a broad range of nanoscale, temporally resolved physics to be uncovered. However, such examples for functional imaging are few in number. Here, using piezoresponse force microscopy (PFM) as a model application, a factor of 5.8 reduction in data collection using a combination of sparse spiral scanning with compressive sensing and Gaussian process regression reconstruction is demonstrated. It is found that even extremely sparse spiral scans offer strong reconstructions with less than 6% error for Gaussian process regression reconstructions. Further, the error associated with each reconstructive technique per reconstruction iteration is analyzed, finding the error is similar past ≈15 iterations, while at initial iterations Gaussian process regression outperforms compressive sensing. Finally, this study highlights the capabilities of reconstruction techniques when applied to sparse data, particularly sparse spiral PFM scans, with broad applications in scanning probe and electron microscopies.

36 MATERIALS SCIENCE↗

Progress of Divertor Heat and Particle Flux Control in EAST for Advanced Steady-State Operation in the Last 10 Years

Active control of the excessively high heat and particle fluxes on the divertor target plates is of fundamental importance to the steady state operation of tokamaks, especially for fusion reactors. A series of experiments have been carried out on this critical issue to relieve the plasma-wall interactions in the experimental advanced superconducting tokamak (EAST) in the last ten years, not only contributing to the long pulse operation of EAST itself, but also providing physical understandings and potential techniques to the next-generation devices like ITER. Here we have characterized the power deposition pattern and broadened the divertor footprint width effectively. The plasma-wetted area is actively handled using either 3-dimentional edge magnetic topology or advanced plasma equilibrium, thereby peak heat flux around the strike point is reduced. Active control of detachment or radiation compatible with core plasma performance has progressed significantly in very recent years, with a series of active feedback control modules developed and utilized successfully, based on the divertor physics advances with both experiments and simulation. The upper divertor of EAST was upgraded from graphite to active water-cooling ITER-like tungsten in 2014, exhibiting much enhanced heat removal capability. As for the particle exhaust including both fueling and impurity particles, in addition to wall conditioning and impurity source control, the efficiency of particle flux exhaust is optimized by making full use of the divertor closure and the plasma drifts in both scrape-off layer and divertor volume. These heat and particle exhaust advances contribute greatly to a series of EAST achievements like H-mode operation over 100 s. A brief near-term plan on the integrated control of divertor plasma-wall interactions in long-time scale will also be introduced, aiming to provide favorable divertor operation solution for ITER and CFETR.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems

In this paper, we propose nonoverlapping localized exponential time differencing (ETD) methods for diffusion problems. The model time-dependent diffusion equation is first reformulated on subdomains based on the nonoverlapping domain decomposition, in which Neumann boundary conditions are imposed on the interfaces for the subdomain problems and Dirichlet type conditions are enforced to form a space-time interface problem. After spatial discretization by standard central finite differences and temporal integration with the first or second order ETD methods, the fully discrete interface problem is obtained. Such an interface problem is then solved iteratively either at each time step or over the whole time interval: the former involves the solution of stationary problems in each subdomain at each iteration while the latter involves the solution of time-dependent subdomain problems at each iteration. For both approaches, we prove that localized ETD solutions conserve mass exactly and converge in time to the exact space semidiscrete solution. Numerical experiments in two dimensions are also presented to illustrate the performance of the proposed methods.

Mass conservation↗

Retracted Article: Distributed energy management for networked microgrids in a three-phase unbalanced distribution network

Owing to increased penetration of three-phase and single-phase microgrids, distributed energy resources (DERs), and responsive loads, the maintenance of a three-phase balance by distribution networks is a significant challenge. Existing literature on distributed energy management for networked microgrids generally neglects the distribution network or employs a simplified phase balanced distribution network; thus, these evaluations are not applicable. Further, the underlying mutual coupling between the different phases of distribution feeders results in a more challenging situation. Here, to solve this issue, this study sought to propose distributed energy management based on a three-phase unbalanced distribution network. Various three-phase or single-phase microgrids, utility-owned DERs, and responsive loads were coordinated through iteratively adjusted price signals. Based on the price signals received, the microgrid controllers (MCs) and distribution management system (DMS) updated the schedules of the DERs and responsive loads under their jurisdiction separately. The price signals were then updated according to the generation-load mismatch at each node and distributed to the corresponding MCs and DMS for the next iteration. The iteration continued until a sufficiently small generation-load mismatch was achieved at all nodes, that is, a balanced generation and load at all nodes under the agreed price signals. Considering a three-phase unbalanced distribution network, the price signals were determined per phase per node. Overall, the proposed distributed energy management coordinates microgrids, utility-owned DERs, responsive loads with guaranteed network constraints, and preserves the privacy of microgrid customers. This distributed energy management method was further demonstrated through various case studies on a three-phase networked microgrid test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A O(1/k{sup 3/2}) hybrid proximal extragradient primal–dual interior point method for nonlinear monotone mixed complementarity problems

We present a Newton-type hybrid proximal extragradient primal–dual interior point method for solving smooth monotone mixed complementarity problems. Dual variables for the nonnegativity constraints are introduced. The ergodic complexity of the method is O(1/k{sup 3/2}). The method performs two types of iterations: underelaxed hybrid proximal extragradient iterations and short-steps primal–dual interior point iterations.

97 MATHEMATICS AND COMPUTING↗

Newton trust-region methods with primary variable switching for simulating high temperature multiphase porous media flow

Coupling multiphase flow with energy transport due to high temperature heat sources introduces significant new challenges since boiling and condensation processes can lead to dry-out conditions with subsequent re-wetting. The transition between two-phase and single-phase behavior can require changes to the primary dependent variables adding discontinuities as well as extending constitutive nonlinear relations to extreme physical conditions. Practical simulations of large-scale engineered domains lead to Jacobian systems with a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. Performance assessment of potential nuclear repositories, carbon sequestration sites and geothermal reservoirs can require numerous Monte-Carlo simulations to explore uncertainty in material properties, boundary conditions, and failure scenarios. Due to the numerical challenges, standard NR iteration may not converge over the range of required simulations and require more sophisticated optimization method like trust-region. In this study, we use the open-source simulator PFLOTRAN for the important practical problem of the safety assessment of future nuclear waste repositories in the U.S. DOE geologic disposal safety assessment Framework. The simulator applies the PETSc parallel framework and a backward Euler, finite volume discretization. We demonstrate failure of the conventional NR method and the success of trust-region modifications to Newton’s method for a series of test problems of increasing complexity. Trust-region methods essentially modify the Newton step size and direction under some circumstances where the standard NR iteration can cause the solution to diverge or oscillate. Furthermore, we show how the Newton Trust-Region method can be adapted for Primary Variable Switching (PVS) when the multiphase state changes due to boiling or condensation. The simulations with high-temperature heat sources which led to extreme nonlinear processes with many state changes in the domain did not converge with NR, but they do complete successfully with the trust-region methods modified for PVS. This implementation effectively decreased weeks of simulation time needing manual adjustments to complete a simulation down to a day. Finally, we show the strong scalability of the methods on a single node and multiple nodes in an HPC cluster.

54 ENVIRONMENTAL SCIENCES↗

Accelerating the solution of the S N equations with highly anisotropic scattering using the Fokker-Planck approximation

The discrete ordinates method can model forward-peaked transport problems accurately. However, convergence of discrete ordinates solution can become arbitrarily slow upon use of standard iterative procedures like source iteration. Standard zeroth and first moment-based acceleration methods like nonlinear diffusion acceleration and diffusion synthetic acceleration are ineffective in accelerating such problems because these methods do not correct higher order Legendre-moments of angular flux. In this paper, we explore the idea of using the Fokker-Planck approximation as a preconditioner to accelerate the convergence of solution of forward-peaked transport problems. Finally, we observe that such preconditioning can successfully reduce the iteration count by up to four orders of magnitude, and solver runtime by up to three orders of magnitude when compared to diffusion synthetic acceleration.

42 ENGINEERING↗