SEARCH · Search NASA

Results for “Diffusion problems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Control-Affine Schrödinger Bridge and Generalized Bohm Potential

From a stochastic control perspective, the Schrödinger bridge is a density-valued continuous curve parameterized by time that connects a given pair of initial and terminal probability densities via minimum effort controlled Brownian motion. The control-affine Schrödinger bridge extends this idea to a generic control-affine Itô diffusion, possibly with an additive state cost. Here, in this letter, we recast the necessary conditions of optimality for the control-affine Schrödinger bridge problem as a two point boundary value problem for a quantum mechanical Schrödinger PDE with complex potential. This complex-valued potential is a generalization of the real-valued Bohm potential in quantum mechanics. Our derived potential is akin to the optical potential in nuclear physics where the real part of the potential encodes elastic scattering (transmission of wave function), and the imaginary part encodes inelastic scattering (absorption of wave function). The key takeaway is that the process noise that drives the evolution of probability densities induces an absorbing medium in the evolution of wave function. These results make new connections between control theory and non-equilibrium statistical mechanics through the lens of quantum mechanics.

Markov processes↗

DOE OSTI2022

A Statistical Interpolation Code for Ocean Analysis and Forecasting

Abstract We present a data assimilation package for use with ocean circulation models in analysis, forecasting, and system evaluation applications. The basic functionality of the package is centered on a multivariate linear statistical estimation for a given predicted/background ocean state, observations, and error statistics. Novel features of the package include support for multiple covariance models, and the solution of the least squares normal equations either using the covariance matrix or its inverse—the information matrix. The main focus of this paper, however, is on the solution of the analysis equations using the information matrix, which offers several advantages for solving large problems efficiently. Details of the parameterization of the inverse covariance using Markov random fields are provided and its relationship to finite-difference discretizations of diffusion equations are pointed out. The package can assimilate a variety of observation types from both remote sensing and in situ platforms. The performance of the data assimilation methodology implemented in the package is demonstrated with a yearlong global ocean hindcast with a 1/4° ocean model. The code is implemented in modern Fortran, supports distributed memory, shared memory, multicore architectures, and uses climate and forecasts compliant Network Common Data Form for input/output. The package is freely available with an open source license from www.tendral.com/tsis/ .

Srinivasan, Ashwanth↗

DOE OSTI2019

A Positive Asymptotic-Preserving Scheme for Linear Kinetic Transport Equations

We present a positive- and asymptotic-preserving numerical scheme for solving linear kinetic transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard spectral angular discretization and a classical micro-macro decomposition. The three main ingredients are a semi-implicit temporal discretization, a dedicated finite difference spatial discretization, and realizability limiters in the angular discretization. Under mild assumptions, the scheme becomes a consistent numerical discretization for the limiting diffusion equation when the scattering cross-section tends to infinity. The scheme also preserves positivity of the particle concentration on the space-time mesh and therefore fixes a common defect of spectral angular discretizations. The scheme is tested on the well-known line source benchmark problem with the usual uniform material medium as well as a medium composed of different materials that are arranged in a checkerboard pattern. We also tested the scheme on a Riemann problem with a nonuniform material medium. The observed order of space-time accuracy of the proposed scheme is reported.

nite difference methods↗

DOE OSTI2017

Simulations of anti-parallel reconnection using a nonlocal heat flux closure

The integration of kinetic effects in fluid models is important for global simulations of the Earth's magnetosphere. In particular, it has been shown that ion kinetics play a crucial role in the dynamics of large reconnecting systems, and that higher-order fluid moment models can account for some of these effects. Here, we use a ten-moment model for electrons and ions, which includes the off diagonal elements of the pressure tensor that are important for magnetic reconnection. Kinetic effects are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in the fluid framework. Moreover, the closure is tested using the island coalescence problem, which is sensitive to ion dynamics. We also demonstrate that the nonlocal closure is able to self-consistently reproduce the structure of the ion diffusion region, pressure tensor, and ion velocity without the need for fine-tuning of relaxation coefficients present in earlier models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

Interfacial mixing in high-energy-density matter with a multiphysics kinetic model

We have extended here a recently developed multispecies, multitemperature Bhatnagar-Gross-Krook model [Haack et al., J. Stat. Phys. 168, 822 (2017)], to include multiphysics capabilities that enable modeling of a wider range of physical conditions. In terms of geometry, we have extended from the spatially homogeneous setting to one spatial dimension. In terms of the physics, we have included an atomic ionization model, accurate collision physics across coupling regimes, self-consistent electric fields, and degeneracy in the electronic screening. We apply the model to a warm dense matter scenario in which the ablator-fuel interface of an inertial confinement fusion target is heated, but for larger length and time scales and for much higher temperatures than can be simulated using molecular dynamics. Relative to molecular dynamics, the kinetic model greatly extends the temperature regime and the spatiotemporal scales over which we are able to model. In our numerical results we observe hydrogen from the ablator material jetting into the fuel during the early stages of the implosion and compare the relative size of various diffusion components (Fickean diffusion, electrodiffusion, and barodiffusion) that drive this process. We also examine kinetic effects, such as anisotropic distributions and velocity separation, in order to determine when this problem can be described with a hydrodynamic model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Evaluation of 3D Simulation Capabilities within xRAGE using a Suite of Test Problems

This presentation describes a 3D verification and validation suite for xRAGE. Three verification test problems for hydrodynamics are presented: the Kidder ball problem, the Verney shell problem, and a 5-material compression problem. There is excellent agreement between 2D and 3D XRAGE simulation results for these problems, and between the xRAGE results and the benchmark solutions. In addition, two 3D ICF test problems are presented, based on an OMEGA direct drive capsule experiment, and on a NIF indirect drive capsule experiment. These two ICF test problems are used to evaluate two hydrodynamic methods within xRAGE. In addition to hydrodynamics the simulations also include three temperature plasma physics, thermal conduction and radiation diffusion. When simulating either capsule in 3D the newer unsplit hydrodynamic method in xRAGE produces more vorticity relative to the older default method. For the indirect drive capsule the 3D simulations are in reasonable agreement with the experimental values of ion temperature and neutron production. Unstable 3D vortex rings are present near the DT ice/carbon interface which enhance the confinement of the DT ice.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

The role of native defects and their diffusivity in CdTe

CdTe is a leading thin-film technology for solar-cell applications. Basic features such as the optimum band gap of 1.5 eV and simple manufacturing process have been driving the research on improving the current record efficiency of 22% for CdTe solar cells toward the theoretical limit of 32%. Low p-type doping and short carrier lifetimes in the CdTe absorber have been suggested as the main limiting factors and attributed to defect compensation and carrier recombination. Understanding the role of point defects and impurities in CdTe is crucial to solving these problems. Despite many years of research, the sources of compensation and the microscopic recombination mechanisms are still unclear. By using hybrid density functional calculations with spin-orbit coupling and large supercells, we investigate the electronic properties, the formation energies, and the diffusivities of the native defects in CdTe. As possible sources of compensation for p-type conductivity, we discuss the structural and electronic properties of Cd interstitial, Te vacancies, and TeCd antisites. The stability of each defect is discussed in terms of both the defect formation energy and the migration barrier. We also address possible mechanisms that lead to non-radiative recombination.

14 SOLAR ENERGY↗

DOE OSTI2018

Lumping Techniques for Mixed Finite Element Diffusion Discretizations

We are interested in positivity preserving spatial discretizations applicable to arbitrary order mixed finite element spatial discretizations of the radiative diffusion equations. Though not guaranteed to yield strict positivity, matrix lumping is appealing as a method of increasing solution positivity because unlike ad hoc fixups or strictly non-negative, non-linear solution representations, matrix lumping keeps the mixed finite element diffusion equations as a linear system of equations. Self-lumping schemes have previously been shown to be a generalization of more traditional matrix lumping techniques. Self-lumping schemes restrict integration quadrature points to the interpolation points used to define interpolatory finite element basis functions. As shown previously, the positivity and order of accuracy of self-lumping schemes are directly related to the choice of finite element interpolation point. Here, we develop self-lumping schemes for arbitrary order, mixed finite element spatial discretizations of the diffusion equation in Cartesian geometry. After introducing several possible self-lumping schemes appropriate for mixed finite elements, we test the ability of each scheme to increase solution positivity relative to an unlumped discretization using a simple test problem designed to induce negative solutions, evaluating efficacy as a function of finite element order and finite element interpolation point type. The method of manufactured solutions is then used to evaluate order of convergence for promising self-lumping schemes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Anderson acceleration stability in NDA-accelerated k-eigenvalue problems

Anderson acceleration (AA) has been used to improve the stability and convergence rate of multiphysics iterative methods for reactor analysis. Most applications studied assume a tightly converged solution for the different physics problems, and AA is usually applied to state variables like temperature, density, and heat generation rate. In this paper, we study the theoretical performance of AA in NDA-accelerated k-eigenvalue problems. The problems and algorithms studied are simplified from the coupled iteration scheme adopted by MPACT and many other high-fidelity whole-core reactor codes. Compared to previous analyses of AA for these iteration schemes, we study the case with a partially converged neutronics solution and possibly partially converged nonlinear diffusion acceleration (NDA)/coarse mesh finite difference (CMFD) solutions. We observe that the performance of the iteration scheme with AA is very sensitive to the initial guess and is affected by the partially converged CMFD solutions. When the NDA solution is fully converged, using AA cannot achieve the optimal convergence rate in large-sized problems. Conversely, if the NDA solution is partially converged, the iteration scheme with AA can diverge or converge extremely slowly. It is found that the loss of robustness for AA is due to the fact that it is applied to the iterative subspace of state variables rather than the fundamental unknowns of the governing equations. To improve the robustness, the scalar flux should also be considered in the implementation of AA. After considering the residuals of flux, we observe that the stability is regardless of the partial convergence of NDA solutions. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

Implementation of CMFD Acceleration Scheme in PROTEUS-MOC

The PROTEUS-MOC code is a three-dimensional (3D) transport code, which is being developed at Argonne National Laboratory under the DOE-NE's Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. It provides a fully consistent 3D discretization of the transport equation by combining the two-dimensional (2D) method of characteristics (MOC) for the planar direction with the discontinuous Galerkin method for the treatment of the axial variable. PROTEUS-MOC uses the unstructured finite element method (FEM) and thus allows the explicit representation of any extruded geometries. It also has a capability of massively parallel computation in energy group, angle, plane, and space using a top-level GMRES linear algebra solver. For parallel computation in space, it uses an unstructured domain decomposition by adapting METIS. The computational burden for direct heterogeneous core calculations based on unstructured geometries is excessive for practical reactor problems, and hence it is essential to implement an efficient acceleration scheme in PROTEUS-MOC. Recently, the coarse mesh finite difference (CMFD) method, which was originally applied to the nodal diffusion methods, has been successfully applied to the MOC transport solvers, resulting in a remarkable reduction in the number of fission source iterations. In addition, a modified CMFD method has been developed to overcome the limitation of the conventional CMFD that is applicable only to neutronics solvers with a conservative discretization. This CMFD method was derived to be consistent with the FEM, which is based on a nonconservative discretization. In this method, the neutron balance in each coarse mesh is enforced by introducing a pseudo absorption cross section (PAXS), and the well-established alternating solution process of CMFD and transport calculations is employed to accelerate source convergence. This modified CMFD acceleration scheme was adopted in PROTEUS-MOC to accelerate the fission source iteration. Pin-cell and assembly based CMFD schemes have been implemented by defining individual pin cells or assemblies as a coarse mesh. For this, an algorithm to map the finite elements to coarse meshes was developed, and the routines were developed to determine the coupling coefficients and PAXS of the CMFD equations from the transport solution. Preliminary performance tests were carried out using the C5G7 benchmark problem. This paper presents the main features of this CMFD acceleration scheme and the preliminary test results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2019

Multi-scale topology optimization of multi-material structures with controllable geometric complexity — Applications to heat transfer problems

This study presents a topology optimization method to design assemblies of periodic cellular materials with controllable geometric complexity. The framework is based on a novel multi-scale and multi-material design model in which the structure, the layout of the material subdomains, and their micro-structures are optimized concurrently. To allow a tight control over its geometrical complexity, the layout at the macro-scale is described by level-set fields, parameterized by geometric primitives. The micro-scale geometry is represented through a density approach. A nonlinear programming algorithm drives the optimization process using design sensitivities computed by the discrete adjoint method. The proposed design framework is studied with heat transfer problems. Practical design problems, such as a heat sink and a thermal storage unit with phase change are discussed. The macro-scale analysis model relies on a generalized transient diffusion equation. At the micro-scale, homogenization is used to compute equivalent material properties. The numerical examples in this study show that the optimized multi-scale multi-material layouts outperform the corresponding mono-scale structures while maintaining geometric simplicity at the macro-scale level.

42 ENGINEERING↗

DOE OSTI2018

OPTIMIZATION OF FAST FISSION GAS RELEASE MODEL PARAMETERS USING MACHINE LEARNING ACCELERATED EVOLUTIONARY ALGORITHMS

Fission gas release models used in FRAPCON and FAST are based on equations that describe the physical transport phenomena that control release from the fuel pellet to the rod void volume of fission gas produced during irradiation. Although these models are physically based, many of the parameters that control the release such as the impact of burnup on diffusion and bubble formation and saturation are critical to the accurate prediction of fission gas release, but cannot be measured in any quantitative way. To overcome this problem, these parameters have been empirically derived to provide a best fit to the available data that includes rod puncture data and electron probe microanalysis (EMPA) and X-ray fluorescence (XRF) data of radial location of residual gas within the pellet. In general, a heuristic approach for deriving these parameters via practical implementation of expert analyses on just a few dependent variables has been shown to perform quite well in most situations. In this paper, we present an approach for applying machine learning to expedite model development. This approach is based on developing a deep artificial neural network which describes FRAPCON’s fission gas release models, and optimizes parameters by a differential evaluation algorithm. This approach allows us to quickly and accurately tune physical models based on expert judgment, and works as a human-in-the-loop approach, to assist the modeler in identifying and addressing regions of high uncertainty in a multi-parameter space. Results of the updated fission gas release model will be shown for all the FAST assessment data.

Johns, Jesse M.↗

DOE OSTI2022

Minimum stabilizing energy release for mixing processes

Diffusive operations, which mix the populations of different elements of phase space, can irreversibly transform a given initial state into any of a spectrum of different states from which no further energy can be extracted through diffusive operations. We call these ground states. Here, the lower bound of accessible ground-state energies represents the maximal possible release of energy. This lower bound, sometimes called the diffusively accessible free energy, is of interest in theories of instabilities and wave-particle interactions. On the other hand, the upper bound of accessible ground-state energies has escaped identification as a problem of interest. Yet, as demonstrated here, in the case of a continuous system, it is precisely this upper bound that corresponds to the paradigmatic “quasilinear plateau” ground state of the bump-on-tail distribution. Although for general discrete systems the complexity of calculating the upper bound grows rapidly with the number of states, using techniques adapted from treatments of the lower bound, the upper bound can in fact be computed directly for the three-state discrete system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

Countercations Control Local Specific Bonding Interactions and Nucleation Mechanisms in Concentrated Water-in-Salt Solutions

One of the continuing challenges presented in aqueous salt solutions is to understand ion association reactions driving dynamic demixing from solvation, complexation and solute clustering. The problems understanding this phenomenon are exacerbated in the highly-concentrated water-in-salt electrolytes, where the deficiency of water leads to a dramatic retardation of solvating water and formation of extended solvent-solute clustering networks. By probing microscopic dynamics of water and prenucleation clusters using quasi-elastic neutron scattering and proton nuclear magnetic resonance spectroscopy, we observed contrasting mechanistic specifics of ion-water mobilities in highly-concentrated Na+- vs. K+-based aluminate solutions (diffusion coefficients of 0.2 vs. 2.6?10-10m2s-1 at 293 K, respectively). The magnitude of the differences is far beyond the kosmotropic (Na+) and chaotropic (K+) effects typically understood at low ionic concentrations. The distinct crystallization mechanisms observed in analogous deuterated systems further imply that different prenucleation cluster dynamics and network packing morphologies can either frustrate or promote crystallization, as described by non-classical nucleation theory.

Wang, Hsiu-Wen↗

DOE OSTI2020

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Resonance broadened quasi-linear (RBQ) model for fast ion distribution relaxation due to Alfvénic eigenmodes

The burning plasma performance is limited by the confinement of the super-alfvénic fusion products such as alpha particles and the auxiliary heating ions capable of exciting the Alfvénic eigenmodes (AEs) (Gorelenkov et al 2014 Nucl. Fusion 54 125001). Here in this work the effect of AEs on fast ions is formulated within the quasi-linear (QL) theory generalized for this problem recently (Duarte 2017 PhD Thesis University of São Paulo, Brazil). The generalization involves the resonance line broadened interaction of energetic particles (EP) with AEs supplemented by the diffusion coefficients depending on EP position in the velocity space. A new resonance broadened QL code (or RBQ1D) based on this formulation allowing for EP diffusion in radial direction is built and presented in details. In RBQ1D applications we reduce the wave particle interaction (WPI) dynamics to 1D case when the particle kinetic energy is nearly constant. The diffusion equation for EP distribution evolution is then solved simultaneously for all particles along the angular momentum direction. We make initial applications of the RBQ1D to a DIII-D plasma with elevated q-profile where the beam ions show stiff transport properties (Collins et al (The DIII-D Team) 2016 Phys. Rev. Lett. 116 095001). In conclusion, AE driven fast ion profile relaxation is studied for validations of the QL approach in realistic conditions of beam ion driven instabilities in DIII-D.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

Multilevel Sequential Monte Carlo Samplers for Normalizing Constants

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the discrete approximation error must be balanced. A multilevel strategy is utilized to substantially reduce the cost to obtain a given error level in the approximation as compared to standard estimators. Two estimators are considered and relative variance bounds are given. The theoretical results are numerically illustrated for two Bayesian inverse problems arising from elliptic partial differential equations (PDEs). The examples involve the inversion of observations of the solution of (i) a 1-dimensional Poisson equation to infer the diffusion coefficient, and (ii) a 2-dimensional Poisson equation to infer the external forcing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Diffusion bonding of tungsten-vanadium-zirconium using vacuum hot pressing for the development of a low decay heat cladding solution for tungsten spallation targets

Tantalum has been used as cladding material for water-cooled solid tungsten targets at many leading spallation neutron production facilities thanks to its high neutron yield, manageable radiation damage behavior, and excellent corrosion/erosion resistance in radiation environments. However, from a safety hazard perspective, thermal neutron capture of tantalum in spallation environments causes a high specific decay heat in the target volume, which often becomes a limiting factor in increasing the beam power on the target. In this paper, we studied vacuum hot pressing (VHP) parameters to diffusion bond zirconium to tungsten to explore the feasibility of using zirconium alloys as an alternative cladding material to tantalum. Zirconium alloys have long been used as cladding material for early generation solid spallation targets, and nuclear fuel rods. In spallation environments zirconium has significantly lower decay heat with shorter decay time compared to tantalum. The hot isostatic pressing (HIP) of zirconium and tungsten is known to produce limited bonding quality due to the formation of the brittle ZrW2 intermetallic layer. To overcome this problem, placing a vanadium interlayer between tungsten and zirconium has been proposed by exploring parameter space in binary alloy phase diagrams. Under the VHP conditions, 860 ◦C at 70 MPa for 4 hours, Zr-V and V-W showed good diffusion bonding, which demonstrates the feasibility of a single step HIP process to make the zirconium alloy clad tungsten spallation volumes.

Lee, Yong Joong↗