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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Phase field benchmark problems for nucleation

In this work, we present nucleation phase field model benchmark problems, expanding on our previous benchmark problems on diffusion, precipitation, dendritic growth, linear elasticity, fluid flow and electrochemistry. Nucleation is the process in which either a new thermodynamic phase or a new structure is created, such as solidification from the melt, or self-assembly of particulates. Based on where the nucleation occurs, it can be divided into two main categories: homogeneous nucleation and heterogeneous nucleation. In the first nucleation benchmark problem, we focus on homogeneous nucleation for both single seed under different initial conditions and multiple seeds. The second nucleation benchmark problem focuses on athermal heterogeneous nucleation and nucleation behavior near the free growth limit with different undercooling driving forces.

36 MATERIALS SCIENCE↗
DOE OSTI2025

An Optimization-Based Coupling of Reduced Order Models with an Efficient Reduced Adjoint Basis Generation Approach

Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problems has been hindered by the computational cost of finding the stationary points of the associated Lagrangian, which requires primal and adjoint solves. This issue can be mitigated by using OBC in conjunction with computationally efficient reduced order models (ROMs). To demonstrate the potential of this combination, in this paper, we develop an optimization-based ROM-ROM coupling for a transient advection-diffusion transmission problem. We pursue the “optimize-then-reduce” path toward solving the minimization problem at each time step and solve reduced space adjoint system of equations, where the main challenge in this formulation is the generation of adjoint snapshots and reduced bases for the adjoint systems required by the optimizer. One of the main contributions of the paper is a new technique for an efficient adjoint snapshot collection for gradient-based optimizers in the context of optimization-based ROM-ROM couplings. In conclusion, we present numerical studies demonstrating the accuracy of the approach along with comparison between various approaches for selecting a reduced order basis for the adjoint systems, including decay of snapshot energy, average iteration counts, and timings.

coupled problems↗
NASA NTRS1992

Effect of the geomagnetic field on the diffusion of meteor trains

A solution to the problem of the diffusion of a meteor train in the geomagnetic field from an initial line density may be written in closed form in terms of effective diffusion coefficients depending on direction, enabling detailed calculations across the entire range of angle of train to field and relevant heights. While the effective diffusion coefficient in the plane of train and field then remains close to the zero field ambipolar value right up to 90 deg, the effective coefficient in the direction of the normal to plane of train and field drops steadily to its theta = 0 value at theta = 90 deg. At 95 km this corresponds to a change of almost 5 km, in 'diffusion height', that is, the height of an underdense meteor calculated on the basis of the exponential decay of its radar echo. We have estimated the consequent changes in the expected distribution of diffusion heights for various orientations of radar antenna and find the dependence on azimuth is very marked. The effect of the field is relatively minor for a south pointing beam but very strong if the beam is pointing north.

Jones, William↗
DOE OSTI2016

Two-fluid and finite Larmor radius effects on helicity evolution in a plasma pinch

The evolution of magnetic energy, helicity, and hybrid helicity during nonlinear relaxation of a driven-damped plasma pinch is compared in visco-resistive magnetohydrodynamics and two-fluid models with and without the ion gyroviscous stress tensor. Magnetic energy and helicity are supplied via a boundary electric field which initially balances the resistive dissipation, and the plasma undergoes multiple relaxation events during the nonlinear evolution. The magnetic helicity is well conserved relative to the magnetic energy over each event, which is short compared with the global resistive diffusion time. The magnetic energy decreases by roughly 1.5% of its initial value over a relaxation event, while the magnetic helicity changes by at most 0.2% of the initial value. The hybrid helicity is dominated by magnetic helicity in low-β pinch conditions and is also well conserved. Differences of less than 1% between magnetic helicity and hybrid helicity are observed with two-fluid modeling and result from cross helicity evolution. The cross helicity is found to change appreciably due to the first-order finite Larmor radius effects which have not been included in contemporary relaxation theories. The plasma current evolves towards the flat parallel current state predicted by Taylor relaxation theory but does not achieve it. Plasma flow develops significant structure for two-fluid models, and the flow perpendicular to the magnetic field is much more substantial than the flow along it.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Scalable Matrix-Free Adaptive Product-Convolution Approximation for Locally Translation-Invariant Operators

We present an adaptive grid matrix-free operator approximation scheme based on a "product-convolution" interpolation of convolution operators. This scheme is appropriate for operators that are locally translation-invariant, even if these operators are high rank or full rank. Such operators arise in Schur complement methods for solving partial differential equations (PDEs), as Hessians in PDE-constrained optimization and inverse problems, as integral operators, as covariance operators, and as Dirichlet-to-Neumann maps. Constructing the approximation requires computing the impulse responses of the operator to point sources centered on nodes in an adaptively refined grid of sample points. A randomized a posteriori error estimator drives the adaptivity. Once constructed, the approximation can be efficiently applied to vectors using the fast Fourier transform. The approximation can be efficiently converted to hierarchical matrix (H-matrix) format, then inverted or factorized using scalable H-matrix arithmetic. The quality of the approximation degrades gracefully as fewer sample points are used, allowing cheap lower quality approximations to be used as preconditioners. Furthermore, this yields an automated method to construct preconditioners for locally translation-invariant Schur complements. We directly address issues related to boundaries and prove that our scheme eliminates boundary artifacts. We test the scheme on a spatially varying blurring kernel, on the nonlocal component of an interface Schur complement for the Poisson operator, and on the data misfit Hessian for an advection dominated advection-diffusion inverse problem. Numerical results show that the scheme outperforms existing methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A mineral precipitation model based on the volume of fluid method

A novel volume of fluid method is presented for mineral precipitation coupled with fluid flow and reactive transport. The approach describes the fluid-solid interface as a smooth transitional region, which is designed to provide the same precipitation rate and viscous drag force as a sharp interface. Specifically, the governing equation of mineral precipitation is discretized by an upwind scheme, and a rigorous effective viscosity model is derived around the interface. The model is validated against analytical solutions for mineral precipitation in channel and ring-shaped structures. It also compares well with interface tracking simulations of advection-diffusion-reaction problems. Here, the methodology is finally employed to model mineral precipitation in fracture networks, which is challenging due to the low porosity and complex geometry. Compared to other approaches, the proposed model has a concise algorithm and contains no free parameters. In the modeling, only the pore space requires meshing, which improves the computational effciency especially for low-porosity media.

58 GEOSCIENCES↗
DOE OSTI2023

Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. In this report we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate speed-up over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Dynamic Mode Decomposition of Solids

Dynamic mode decomposition (DMD) is a method that has gained notoriety in the field of turbulent fluid flows as a method for decomposing the flow field into modes that could be further deconstructed to understand their influence on the overall dynamics of the system. Forays into solids and non-linear systems were considered, but not applied. In this work, DMD was applied for the first time to the heat-diffusion and reactive heat diffusion equations on a random particle pack of uniform solid spheres. A verification of a linear heat-diffusion test problem was successful, showing equality between the normal modes and Koopman modes obtained from DMD. Further application to a non-linear reactive system revealed stability limits of the underlying modes which are dependent on microstructure and chemical kinetics. This work will enable the development of reactive material models based on further analysis using DMD to quantify the statistical dependencies of transient response on microstructural characteristics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1981

Residual fields from extinct dynamos

The generation of magnetic fields in convective zones of declining vigor and/or thickness is considered, the goal being to explain the magnetic fields observed in A-stars. The investigation is restricted to kinematical dynamos in order to show some of the many possibilities, which depend on the assumed conditions of decline of the convection. The examples illustrate the quantitative detail required to describe the convection in order to extract any firm conclusions concerning specific stars. The first example treats the basic problem of diffusion from a layer of declining thickness. The second has a buoyant rise added to the field in the layer. The third deals with plane dynamo waves in a region with declining eddy diffusivity, dynamo coefficient, and large-scale shear. It is noted that the dynamo number may increase or decrease with declining convection, with an increase expected if the large-scale shear does not decline as rapidly as the eddy diffusivity. It is shown that one of the components of the field may increase without bound even when the dynamo number declines to zero.

Parker, E. N.↗
NASA NTRS1982

Solar reflection from a regular array of horizontally finite clouds

The reflected flux from a regular array of 2- and 3-D clouds has been computed to estimate the effect of fractional cloud cover on albedos and the solar flux available to heat the earth's surface. The broken clouds are represented by a regular array of identical cuboids for the 3-D problem and equally spaced, infinitely long, bars for the 2-D problem. A diffusion approximation to the radiative transfer equation is used to compute the fluxes leaving each face of the cloud. Interaction between clouds is simulated by assuming diffuse exitance from the cloud faces and applying angle factors to obtain modified boundary conditions on each cloud face.

Weinman, J. A.↗
NASA NTRS1983

Acceleration and transport processes - Verification and observations

The general problem of diffusive transport and acceleration of energetic charged particles is considered. The transport of solar-flare particles, solar modulation of galactic cosmic rays and shock acceleration processes on the solar wind are examined and observational tests are summarized. It is concluded that the basic diffusive transport equation is a useful approximation in situations like the solar wind, where turbulent scattering by magnetic irregularities is sufficient to maintain near isotropy. The application of this equation to the interstellar medium andd other, more distant astrophysical regimes is then discussed and implications for gamma-ray astrophysics are outlined. Finally the evidence for interstellar turbulence is reviewed and its consequences briefly discussed.

Jokipii, J. R.↗
NASA NTRS1986

Solar wind helium, neon and argon released by oxidation of metal grains from the Weston chondrite

A set of experiments were carried out to test the feasibility of determining unfractionated elemental and isotopic ratios for the noble gases in the presumably ancient solar wind present in the gas rich meteorites. The problems of diffusive loss was avoided by analyzing metal rather than the usual silicates. In order to avoid chemical, and even harsh physical, treatment of the sample, which might have affected the surfaces of metal grains, a means of analyzing the metal in the presence of residual silicate not removed by gentle crushing and magnetic separation was devised. Preliminary results given were obtained by taking advantage of the differing properties of metal and silicates with regard to diffusion. The results suggests that, with some modifications in the choice of pyrolysis and combustion temperatures and in the amount of O2 used, it should be possible, by oxidizing the surfaces of metal grains from gas rich meteorites, to obtain data on solar wind that has not been fractionated by diffusive loss.

Becker, R. H.↗
NASA NTRS1985

An internal variable assisted formulation of moisture sorption models for polymers and composites

The purpose of the paper is to demonstrate that constitutive equations for moisture sorption and swelling can be obtained with an internal variable method which is rooted in the theory of irreversible thermodynamics. Realism is injected into the model through the concept of free volume. The power of the method is illustrated by the solution of the formidable nonlinear boundary value problem for diffusion with swelling-stress dependent diffusivity.

Hiel, C. C.↗
NASA NTRS1987

Hydrodynamical constraints on cosmic-ray acceleration in relativistic shocks

A two-fluid hydrodynamical model governing the transport of cosmic rays in a relativistically moving background plasma is developed. The equations are used to discuss the time asymptotic structure of a relativistic, plane-parallel shock wave significantly modified by first-order Fermi acceleration of cosmic rays. The model allows for an anisotropic cosmic-ray pressure tensor with pressure components parallel and perpendicular to the shock normal. It is surmised that the well-known energy threshold problem for diffusive shock acceleration that downstream particles have a large enough velocity to overtake the shock and subsequently scatter in the upstream medium before returning to the downstream medium may be expressed hydrodynamically by the condition V less than V(cr), where V is the fluid velocity relative to the shock and V(cr) is the relativistic cosmic-ray sound speed. Astrophysical implications of the results are briefly discussed.

Webb, G. M.↗