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At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A FFT-based numerical implementation of mesoscale field dislocation mechanics: Application to two-phase laminates

In this study, we present an enhanced crystal plasticity elasto-viscoplastic fast Fourier transform (EVPFFT) formulation coupled with a phenomenological Mesoscale Field Dislocation Mechanics (MFDM) theory here named MFDM-EVPFFT formulation. In contrast with classic CP-EVPFFT, the model is able to tackle plastic flow and hardening due to polar dislocation density distributions or geometrically necessary dislocations (GNDs) in addition to statistically stored dislocations (SSDs). The model also considers GND mobility through a GND density evolution law numerically solved with a recently developed filtered spectral approach, which is here coupled with stress equilibrium. The discrete Fourier transform method combined with finite differences is applied to solve both lattice incompatibility and Lippmann-Schwinger equations in an augmented Lagrangian numerical scheme. Numerical results are presented for two-phase laminate composites with plastic channels and elastic second phase. It is shown that both GND densities and slip constraint at phase boundaries influence the overall and local hardening behavior. In contrast with the CP-EVPFFT formulation, a channel size effect is predicted on the shear flow stress with the present MFDM-EVPFFT formulation. The size effect originates from the progressive formation of continuous screw GND pile-ups from phase boundaries to the channel center. The effect of GND mean free path on local and global responses is also examined for the two-phase composite.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Numerical stability of relativistic beam multidimensional PIC simulations employing the Esirkepov algorithm

Rapidly growing numerical instabilities routinely occur in multidimensional particle-in-cell computer simulations of plasma-based particle accelerators, astrophysical phenomena, and relativistic charged particle beams. Reducing instability growth to acceptable levels has necessitated higher resolution grids, high-order field solvers, current filtering, etc. except for certain ratios of the time step to the axial cell size, for which numerical growth rates and saturation levels are reduced substantially. This paper derives and solves the cold beam dispersion relation for numerical instabilities in multidimensional, relativistic, electromagnetic particle-in-cell programs employing either the standard or the Cole–Karkkainnen finite difference field solver on a staggered mesh and the common Esirkepov current-gathering algorithm. Good overall agreement is achieved with previously reported results of the WARP code. In particular, the existence of select time steps for which instabilities are minimized is explained. Additionally, an alternative field interpolation algorithm is proposed for which instabilities are almost completely eliminated for a particular time step in ultra-relativistic simulations.

43 PARTICLE ACCELERATORS↗
DOE OSTI2014

A numerical method for the quasi-incompressible Cahn–Hilliard–Navier–Stokes equations for variable density flows with a discrete energy law

In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities [48]. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a C{sup 0} finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy law (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with C{sup 0} finite element. A Newton method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier–Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Stabilization of numerical interchange in spectral-element magnetohydrodynamics

In this study, auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C 0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate of the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. Lastly, the projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code [C. R. Sovinec, et al., J. Comput. Phys. 195 (2004) 355-386], provided that the projections introduce numerical dissipation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution of dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

A model and numerical method for compressible flows with capillary effects

A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results on droplet breakup induced by a shock wave.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

On numerical energy conservation for an implicit particle-in-cell method coupled with a binary Monte-Carlo algorithm for Coulomb collisions

We report conventional particle-in-cell (PIC) methods suffer from enhanced numerical heating (explicit PIC) or cooling (semi-implicit PIC) when coupled with a binary Monte-Carlo algorithm for Coulomb collisions. In this work, a fully-implicit θ-PIC scheme (with adjustable time-biasing parameter 1/2 ≤ θ ≤) is considered. The discrete change in energy of a closed system after a time step for this scheme scales with (1/2 - θ)C θ , where C θ is a positive definite quantity that depends on the frequency spectrum of the energy in the fields. Collisions lead to additional energy in the field fluctuations associated with high-frequency light waves produced by a numerical Bremsstrahlung process, which can result in a large increase in the numerical cooling rate for θ > 1/2. However, for θ = 1/2, energy is exactly conserved. The energy in the field fluctuations on long time scales agrees with that calculated using the equipartition theorem for a classical system in thermodynamic equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency

Here, we consider a kinetic description of multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In this model, the Maxwellians typically used in standard BGK operators are replaced by a generalization of such target functions, which are defined by a variational procedure. In this paper we present a numerical method for simulating this model, which uses an Implicit-Explicit (IMEX) scheme to minimize a certain potential function, mimicking the Lagrange functional that appears in the theoretical derivation. We show that theoretical properties such as conservation of mass, total momentum and total energy as well as positivity of the distribution functions are preserved by the numerical method, and illustrate its usefulness and effectiveness with numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Numerical evaluation of photosensitive tracers as a strategy for separating surface and subsurface transient storage in streams

For this work, we numerically evaluated photosensitive tracers as a potential strategy for separating the effects of surface and hyporheic storage zones (SSZs and HSZs, respectively) on stream corridor transport. Correctly separating HSZ and SSZ effects is critical to estimating the hydro-biogeochemical function of a stream because HSZs and SSZs expose solutes to significantly different biogeochemical conditions, like sunlight exposure, microbial processes, and oxygen availability. Our numerical experiments used a multiscale river-corridor transport model implemented in the ATS code, which accommodates multiple storage zones with distinct travel time distributions and biogeochemical reactions. For parameter inferences, we used Bayesian inverse modeling. We found that breakthrough curves for photo-decaying tracers from day and night injection can delineate surface and hyporheic transient storage contributions, but only when interpreted jointly through a two-storage zone model. Numerical experiments that used only daytime injection or interpreted breakthrough curves with a single storage zone model yielded good fit to breakthrough curves, but parameter estimates were biased and controlling processes misattributed, examples of good model fits for the wrong reasons. Using those biased parameter estimates in reactive transport simulations resulted in significantly different projections of denitrification, which underscores the potential for stream function to be mischaracterized if tracer tests are interpreted through an inappropriately simplified model for transient storage. More generally, this study highlights the role of modeling in evaluating the experimental design and identifying the potential of system mischaracterization and its implications.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗
DOE OSTI2023

A hybrid analytical and numerical model for cross-over and performance decay in a unit cell vanadium redox flow battery

Developing an accurate and efficient model for cross-over is critical for improving the long-term performance of redox flow batteries (RFBs). Here, this work presents a hybrid analytical and numerical model that combines a two-dimensional analytical solution to the active species, a one-dimensional analytical model for cross-over mechanisms, and a zero-dimensional numerical model for outlet concentrations of reactants. By comparing with experiment over 41 cycles (ca. 144 h), the model reported a mean voltage difference of 0.0089 V, mean time difference of 14 s per cycle (of 3.5 h), maximum relative difference for capacity and energy of 1.34% and 1.63%, respectively. The predicted mean concentrations for V 2+ , V 3+ , and VO$_{2}^{+}$ in membrane are 65%~77% of measured values from the literature. Upon validation, the model reproduced behaviors in electrolyte imbalance similar to those observed in experiments and numerical models, and revealed the control of cross-over, self-discharge, stoichiometry of side reactions, and Coulombic efficiency on electrolyte imbalance. The model also demonstrates excellent computational efficiency for simulating 41 cycles (around 37,000 points) within 3~4 s. The demonstrated efficiency and accuracy for predicting cross-over and its impacts on voltage, capacity&energy decay, membrane concentrations, and electrolyte imbalance makes it a reliable tool for optimizing RFBs’ long-term performance.

25 ENERGY STORAGE↗
DOE OSTI2017

A fast numerical integrator for relativistic charged particle tracking

In this paper, we report on a fast second-order numerical integrator to solve the Lorentz force equations of a relativistic charged particle in electromagnetic fields. This numerical integrator shows less numerical error than the popular Boris algorithm in tracking the relativistic particle subject to electric and magnetic space-charge fields and requires less number of operations than another recently proposed relativistic integrator.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Numerical study of multi-component flow and mixing in a scaled fission product venting system

Numerical simulation of isothermal multi-component gas flow was conducted to study fluid flow and mixing in a scaled low-pressure, low-temperature test facility for the fission product venting system (FPVS) of a gas cooled fast reactor (GFR). The geometry of FPVS test facility was an open loop including gradual expansion coupling and two 90°pipe elbows. First, the validation of large eddy simulation (LES) wall-adapting local eddy-viscosity (WALE) turbulent model was performed for transitional flow in a circular pipe with gradual expansion. The reactingFOAM solver in OpenFOAM v8 was employed. By introducing appropriate turbulence disturbance at the flow inlet, such as turbulence intensity, the numerical results showed good agreement in (1) the velocity profile downstream of the pipe expansion measured by particle image velocimetry (PIV) in this study, and (2) the reattachment length reported in the literature. Using this validated model, the numerical simulation of flow and component mixing was performed for the FPVS with an inlet flowrate corresponding to a Reynolds number of 2,400 to investigate the flow behavior and component mixing. Standard deviation of the mass fraction of component, referred to as absolute mixing index (AMI), was calculated to quantify the mixing of components, showing that the component mixing length determined by AMI is related to the reattachment length downstream of the expansion. Additionally, this study was able to identify the best location in the FPVS test facility to measure the velocity and concentration profies where multicomponent flow is well mixed.

15 GEOTHERMAL ENERGY↗
DOE OSTI2020

Measurement of flow properties coupled to experimental and numerical analyses of dense, granular flows for solar thermal energy storage

Granular flows of sintered bauxite proppants were researched along an inclined plane for solar thermal energy storage applications. Granular flow properties needed to drive numeric granular models were measured for improved numerical model predictions for Carbobead CP 50/140, 40/100, and 30/60 particles. Particle shape and size distributions were determined by coupling optical microscopy to an in-house image processing algorithm. The impulse excitation technique was used to measure elastic and shear moduli, and compute Poisson’s ratio. The coefficient of static sliding friction was measured using the slip-stick method, and the static rolling friction was determined from measured shear on particles positioned between two hot-pressed plates. The coefficient of restitution was measured by dropping particles on a surface and determining the kinetic energy before and after impact with the surface using high resolution particle tracking velocimetry. Particle size did not significantly impact the coefficients of restitution and static rolling friction, however, particle shape distribution resulted in a large variation in measurements. An inclined flow experiment was performed to characterize granular flows of Carbobead CP 30/60 particles using particle image velocimetry. Numerical models of the experiment using discrete element method were generated with the measured mechanical properties as inputs for comparison with experimental results. A constant directional torque rolling friction model best predicted bulk granular flow behavior. Furthermore, good agreement between the model and experiment was achieved at ambient, steady state conditions, with average velocity differences <10%.

14 SOLAR ENERGY↗
DOE OSTI2017

Numerical study of variable density turbulence interaction with a normal shock wave

Accurate numerical simulations of shock–turbulence interaction (STI) are conducted with a hybrid monotonicity-preserving–compact-finite-difference scheme for a detailed study of STI in variable density flows. Theoretical and numerical assessments of data confirm that all turbulence scales as well as the STI are well captured by the computational method. Linear interaction approximation (LIA) convergence tests conducted with the shock-capturing simulations exhibit a similar trend of converging to LIA predictions to shock-resolving direct numerical simulations (DNS). The effects of density variations on STI are studied by comparing the results corresponding to an upstream multi-fluid mixture with the single-fluid case. Here the results show that for the current parameter ranges, the turbulence amplification by the normal shock wave is much higher and the reduction in turbulence length scales is more significant when strong density variations exist. Turbulent mixing enhancement by the shock is also increased and stronger mixing asymmetry in the postshock region is observed when there is significant density variation. The turbulence structure is strongly modified by the shock wave, with a differential distribution of turbulent statistics in regions having different densities. The dominant mechanisms behind the variable density STI are identified by analysing the transport equations for the Reynolds stresses, vorticity, normalized mass flux and density specific volume covariance.

42 ENGINEERING↗
DOE OSTI2015

Tokamak elongation – how much is too much? Part 2. Numerical results

We report the analytic theory presented in Paper I is converted into a form convenient for numerical analysis. A fast and accurate code has been written using this numerical formulation. The results are presented by first defining a reference set of physical parameters based on experimental data from high performance discharges. Scaling relations of maximum achievable elongation (κ max ) versus inverse aspect ratio (ε) are obtained numerically for various values of poloidal beta (β p ), wall radius (b/a) and feedback capability parameter (γ τ w ) in ranges near the reference values. It is also shown that each value of κ max occurs at a corresponding value of optimized triangularity (δ), whose scaling is also determined as a function of ε. The results show that the theoretical predictions of κ max are slightly higher than experimental observations for high performance discharges, as measured by high average pressure. The theoretical δ values are noticeably lower. We suggest that the explanation is associated with the observation that high performance involves not only n = 0 MHD stability, but also n ≥ 1 MHD modes described by β N in the Troyon limit and transport as characterized by τ E . Operation away from the n = 0 MHD optimum may still lead to higher performance if there are more than compensatory gains in β N and τ E . Unfortunately, while the empirical scaling of β N and τ E with the elongation (κ) has been determined, the dependence on δ has still not been quantified. This information is needed in order to perform more accurate overall optimizations in future experimental designs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗