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At least 847 records · Page 47

Implicit Space-Time Conservation Element and Solution Element Schemes

Artificial numerical dissipation is in important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate implicit numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The new schemes presented are two highly accurate implicit solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to convection-dominated equations with very small viscosity. The stability and consistency of the schemes are analysed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

Chang, Sin-Chung↗

A Phase-Field Model for In-Space Manufacturing of Binary Alloys

The integrity of the final printed components is mostly dictated by the adhesion between the particles and phases that form upon solidification, which is a major problem in printing metallic parts using available In-Space Manufacturing (ISM) technologies based on the Fused Deposition Modeling (FDM) methodology. Understanding the melting/solidification process helps increase particle adherence and allows to produce components with greater mechanical integrity. We developed a phase-field model of solidification for binary alloys. The phase-field approach is unique in capturing the microstructure with computationally tractable costs. The developed phase-field model of solidification of binary alloys satisfies the stability conditions at all temperatures. The suggested model is tuned for Ni-Cu alloy feedstocks. We derived the Ginzburg-Landau equations governing the phase transformation kinetics and solved them analytically for the dilute solution. We calculated the concentration profile as a function of interface velocity for a one-dimensional steady-state diffuse interface neglecting elasticity and obtained the partition coefficient, k, as a function of interface velocity. Numerical simulations for the diluted solution are used to study the interface velocity as a function of undercooling for the classic sharp interface model, partitionless solidification, and thin interface.

36 MATERIALS SCIENCE↗

Immobile Pore-Water Storage Enhancement and Retardation of Gas Transport in Fractured Rock

The effect of immobile pore-water on gas transport in fractured rock has implications for numerical modeling of soil vapor extraction, methane leakage, gaseous CO 2 leakage from sequestration operations, radionuclide transport from underground nuclear explosions, and nuclear waste disposal. While the ability for immobile pore-water storage to effect gas transport has been recognized in the past, the details and specific scenarios leading to enhanced, retarded, or unaffected gas transport have not been explored. In this paper, we performed numerical investigations into the enhancement and retardation of gas transport due to immobile pore-water storage in order to identify implications for gas transport applications. To do this, we developed a numerical approach to model gas transport with a single-phase flow solution coupled to the advection–dispersion equation modified to account for immobile pore-water storage. Other than the immobility of pore water, the formulation contains all other physics included in two-phase formulations (advective and diffusive gas transport in fractures and rock matrix and dissolution in immobile pore water). The assumption of immobile pore water is valid here since for many applications involving transport of soluble gases in fractured rock, the rate of aqueous transport is insignificant compared to gas transport. We verify our modeling approach with analytical solutions of: (1) 1D gas diffusion, (2) 1D gas advection, (3) barometric pumping of a fracture, and (4) gas transport with uniform fracture flow and diffusion into the matrix. We account for pore-water storage in our model by implementing a kinetic formulation of gas dissolution wherein the dissolved (aqueous) phase is considered an immobile constituent. Using this formulation, we model the effect of dissolution rate and saturation on the retardation of gas transport during pure diffusion and pure advection. We also demonstrate that although it is commonly believed that pore-water storage will always enhance gas transport in fractures during oscillatory flow (e.g., during reversing pressure gradients such as barometric pumping cycles), our simulations indicate that this may not always be the case. Our numerical investigations indicate that scenarios with lower effective diffusion coefficients ( &#x2A85;<!-- <≈ --> 10 &#x2212;<!-- - --> 5 &#xA0;m 2 / s ) and lower dissolution coefficients (i.e., the dissolution diffusion coefficient) ( &#x2A85;<!-- <≈ --> 10 &#x2212;<!-- - --> 11 &#xA0;m 2 / s ) will result in enhanced gas transport. Other combinations of gaseous diffusion and dissolution coefficients result in delayed gas transport or insignificant effect on gas transport. Based on these results, and given the fact that the free-air diffusion coefficients for many gases are slightly above 10 &#x2212;<!-- - --> 5 &#xA0;m 2 / s (near the boundary of enhanced/non-enhanced gas transport), tortuosity would have to be significant for gas transport enhancement to occur. Similarly, if we consider the free-water diffusion coefficient of gases (around 10 &#x2212;<!-- - --> 9 &#xA0;m 2 / s for many gases of interest) to be a maximum bound for the effective dissolution coefficients (i.e., the rate of diffusion into the water away from the air/water interface will limit the dissolution rate), the effective dissolution coefficient would have to be at least 2 orders of magnitude less for enhanced gas transport to occur. Otherwise, pore-water storage will delay or have negligible effect on the gas transport. The results also indicate that the assumption of instantaneous equilibrium, often invoked in numerical codes for dissolution processes (i.e., dissolution coefficient is effectively infinite), will fail to accurately capture important details of soluble gas transport. Finally, the implication of our results is that gas breakthrough times in fractured rock during oscillatory flow may be highly dependent on the effective gaseous diffusion and dissolution coefficients.

58 GEOSCIENCES↗

Transport of absolute angular momentum in quasi-axisymmetric equatorial jet streams

It is well known that prograde equatorial jet stresses cannot occur in an axisymmetric inviscid fluid, owing to the constraints of local angular momentum conservation. For a viscous fluid, the constraints of mass conservation prevent the formation of any local maximum of absolute angular momentum (m) without a means of transferring m against its gradient (delta m) in the meridional plane. The circumstances under which m can be diffused up-gradient by normal molecular viscosity are derived, and illustrated with reference to numerical simulations of axisymmetric flows in a cylindrical annulus. Viscosity is shown to act so as to tend to expel m from the interior outwards from the rotation axis. Such an effect can produce local super-rotation even in a mechanically isolated fluid. The tendency of viscosity to result in the expulsion of m is shown to be analogous in certain respects to a vorticity-mixing hypothesis for the effects of non-axisymmetric eddies of the zonally-averaged flow. It is shown how the advective and diffusive transport of m by non-axisymmetric eddies can be represented by the Transformed Eulerian Mean meridional circulation and the Eliassen-Palm (EP) flux of Andrews and McIntyre respectively, in the zonal mean. Constraints on the form and direction of the EP flux in an advective/diffusive flow for such eddies are derived, by analogy with similar constraints on the diffusive flux of m due to viscosity.

Read, P. L.↗

Pitch angle diffusion in the Jovian magnetodisc

Using a linear approximation to the field variation and a mathematical technique for distorting the orbit integration into the complex gyrophase plane, a formula is derived for the nonadiabatic change in magnetic moment. This change varies as the cosine of the particle gyrophase at the equator, so that if a particle traverses the equator several times with different values of this gyrophase, it suffers randomly correlated values for the nonadiabatic change in magnetic moment. The algebraic formula for this nonadiabatic change is found to be in excellent agreement with previous numerical computations. The phase space density, averaged over several bounce periods, is found to satisfy a diffusion equation in pitch angle. The diffusion coefficient is dependent on particle energy, pitch angle, and the field line along which the particles are moving.

Birmingham, T. J.↗

High-Throughput Study of Diffusion and Phase Transformation Kinetics of Magnesium-Based Systems for Automotive Cast Magnesium Alloys

The objective of the proposed study is to establish a scientific foundation on kinetic modeling of diffusion, phase precipitation, and casting/solidification, in order to accelerate the design and optimization of cast magnesium (Mg) alloys for weight reduction of U.S. automotive fleet. The team has performed the following tasks: 1) study diffusion kinetics of various Mg-containing binary systems using high-throughput diffusion multiples to establish reliable diffusivity and mobility databases for the Mg-aluminum (Al)-zinc (Zn)-tin (Sn)-calcium (Ca)-strontium (Sr)-manganese (Mn) systems; 2) study the precipitation kinetics (nucleation, growth and coarsening) using both innovative dual-anneal diffusion multiples and cast model alloys to provide large amounts of kinetic data (including interfacial energy) and microstructure atlases to enable implementation of the Kampmann-Wagner numerical model to simulate phase transformation kinetics of non-spherical/non-cuboidal precipitates in Mg alloys; 3) implement a micromodel to take into account back diffusion in the solid phase in order to predict microstructure and microsegregation in multicomponent Mg alloys during dendritic solidification especially under high pressure die-casting (HPDC) conditions; and, 4) widely disseminate the data, knowledge and information using the Materials Genome Initiative infrastructure (http://www.mgidata.org) as well as publications and digital data sharing to enable researchers to identify new pathways/routes to better cast Mg alloys.

36 MATERIALS SCIENCE↗

A high-order adaptive algorithm for multispecies gaseous flows on mapped domains

We report a fourth-order accurate finite-volume method is developed and verified for solving strongly nonlinear, time-dependent, compressible, thermally perfect, and multispecies gaseous flows on mapped grids that are adaptively refined in space and time. The algorithm introduces a new scheme for numerical flux calculations in order to cope with the nonlinear, spatially and temporally varying thermodynamic and transport properties of the gaseous mixture. The fourth-order numerical error convergence and solution accuracy are verified using Couette flow, species mass diffusion bubble, and vortex convection and diffusion problem. The thermally perfect, multispecies functionality is validated using a one-dimensional shock tube and two-dimensional shock box problem. Results are obtained for the Mach reflection problem where a strong shock propagates in the multispecies gaseous flow along a ramp and are compared to the solution of the shock propagation in a single species, calorically perfect, gaseous flow over the same ramp. The validated algorithm is then applied to simulate a relatively complex flow configuration to examine the secondary flow mixing due to the double air jets along with the main inlet where a premixed fuel mixture flows in. Future investigations will focus on three-dimensional configurations.

42 ENGINEERING↗

Learning subgrid-scale models with neural ordinary differential equations

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary differential equations (NODEs). Solving systems with fine temporal and spatial grid scales is an ongoing computational challenge, and closure models are generally difficult to tune. Machine learning approaches have increased the accuracy and efficiency of computational fluid dynamics solvers. In this approach neural networks are used to learn the coarse- to fine-grid map, which can be viewed as subgrid-scale parameterization. We propose a strategy that uses the NODE and partial knowledge to learn the source dynamics at a continuous level. Our method inherits the advantages of NODEs and can be used to parameterize subgrid scales, approximate coupling operators, and improve the efficiency of low-order solvers. Numerical results with the two-scale Lorenz 96 ODE, the convection-diffusion PDE, and the viscous Burgers' PDE are used to illustrate this approach.

97 MATHEMATICS AND COMPUTING↗

Asymptotic-preserving semi-implicit finite volume scheme for extended magnetohydrodynamics

A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such that it allows the algorithm to retain the use of ideal MHD Riemann solvers and the constrained transport method to preserve divergence-free magnetic fields. Incorporation of electron inertia and displacement current introduces additional numerical stiffness which motivates a semi-implicit FV scheme that re-formulates the XMHD model as a relaxation system. The equations are then advanced in time using an explicit 2nd-order Runge–Kutta scheme with operator splitting applied to the implicit source term updates at each sub-stage. For additional numerical stability, a density-dependent slope limiter is implemented to increase flux diffusivity at low density regions where non-ideal effects become significant. The algorithm is subsequently implemented in a scalable adaptive mesh refinement (AMR) framework. As the new algorithm retains many aspects of the ideal MHD formulations, it asymptotes naturally to the ideal MHD limit. Moreover, it shows promising results at the resistive and Hall MHD limits. This is verified against reference test problems for ideal, resistive and Hall MHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Calculation of Last Closed Drift Shells for the 2013 GEM Radiation Belt Challenge Events

Radiation belt behavior is often analyzed in terms of adiabatic invariants, of which the third roughly characterizes the radial distance of particle drift shells. The outermost, or last closed drift shell, can be an important boundary for numerical modeling, especially for drift-averaged treatments such as three-dimensional diffusion codes. In this work, we discuss calculation of the last closed drift shell, using the widely used International Radiation Belt Environment Modeling (IRBEM) Library, the LanlGeoMag code, and a guiding center code named AFRL-Shell, in conjunction with a variety of current magnetic field models. Furthermore, we present results for the four events in 2013, comprising the radiation belt challenge organized by the Quantitative Assessment of Radiation Belt Modeling focus group of the Geospace Environment Modeling (GEM) program.

79 ASTRONOMY AND ASTROPHYSICS↗

A Unified Analytical Model for Pressure Solution With Fully Coupled Diffusion and Reaction

Abstract Geophysical models for pressure solution are typically developed for diffusion‐controlled or reaction‐controlled scenarios. We present a unified analytical model that considers fully coupled diffusion and reaction during pressure solution. The model recovers the diffusion‐controlled and reaction‐controlled models in the literature as specific limiting cases. When diffusion and reaction exhibit comparable influences, we validate the proposed model against independent numerical simulations. The proposed model is then employed in interpreting experimental measurements, demonstrating a better agreement compared to previous interpretations.

Wang, Ziyan [Energy Geosciences Division Lawrence ↗

Rapid growth of anthropogenic organic nanoparticles greatly alters cloud life cycle in the Amazon rainforest

Aerosol-cloud interactions remain uncertain in assessing climate change. While anthropogenic activities produce copious aerosol nanoparticles smaller than 10 nanometers, they are too small to act as efficient cloud condensation nuclei (CCN). The mechanisms responsible for particle growth to CCN-relevant sizes are poorly understood. Here, we present aircraft observations of rapid growth of anthropogenic nanoparticles downwind of an isolated metropolis in the Amazon rainforest. Model analysis reveals that the sustained particle growth to CCN sizes is predominantly caused by particle-phase diffusion-limited partitioning of semivolatile oxidation products of biogenic hydrocarbons. Cloud-resolving numerical simulations show that the enhanced CCN concentrations in the urban plume substantially alter the formation of shallow convective clouds, suppress precipitation, and enhance the transition to deep convective clouds. The proposed nanoparticle growth mechanism, expressly enabled by the abundantly formed semivolatile organics, suggests an appreciable impact of anthropogenic aerosols on cloud life cycle in previously unpolluted forests of the world.

54 ENVIRONMENTAL SCIENCES↗

GP-BayesOpInf

SAND2025-01851O GP-BayesOpInf is a software tool that uses algorithms to combine Gaussian process regression, principal component analysis, and linear Bayesian inference to produce a probabilistic reduced-order model for time-dependent systems. Numerical examples include the compressible Euler equations for an ideal gas, a heat diffusion process with a nonlinear reaction term, and a set of ordinary differential equations describing a compartmental model in epidemiology. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗

Diffusion Bonded Hydrogen Pre-Cooler Pressure Testing

Diffusion bonded heat exchangers, also known as printed circuit heat exchangers (PCHEs), have numerous benefits over traditional shell and tube heat exchangers including high pressure containment, a compact size with 1000 to 5000 m 2 of surface area per unit volume, and lower costs. One emerging application is in hydrogen vehicle fueling stations as a hydrogen pre-cooler (H2PC™) where the hydrogen is cooled at pressures up to 900 bar. These pre-coolers must be able to withstand pressure cycling over 10 5 cycles during the fueling station lifetime without degradation of their pressure vessel integrity that could result in hydrogen leakage.

08 HYDROGEN↗

Thermal analysis of Bridgman-Stockbarger growth

A thermal analysis of a cylindrical HgCdTe sample in a Bridgman-Stockbarger crystal growth configuration was conducted with emphasis on the thermal profile, interface shape and position, and the thermal gradients at the liquid-solid interface. Alloys of HgTe and CdTe with compositions approximating 20 percent CdTe, 80 percent HgTe were used. This composition results in a bandgap suited for the detection of 10.6 micron CO2 radiation. The sensitivity of the sample thermal characteristics to important growth parameters, such as thermal diffusivities, thermal conductivities, furnace temperature profile, ampoule dimensions, and growth velocity was assessed. Numerical techniques and associated computational models necessary to analyze the heat transfer process within the sample and the Bridgman-Stockbarger boundary conditions were developed. This thermal analysis mode was programmed in FORTRAN V, and is currently operational on the MSFC Univac 1100 system.

Knopf, F. W.↗

Numerical solution of the problem of flame propagation by the use of the random element method

A numerical, grid-free algorithm is presented for one-dimensional reaction-diffusion model of laminar flame propagation in premixed gases. It is based on the random element method we developed for the analysis of diffusional processes. The effect of combustion is taken into account by applying the principle of fractional steps to separate the process of diffusion, modeled by the random walk of computational elements, from the exothermic effects of chemical reaction, monitoring their strength. The validity of the algorithm is demonstrated by application to flame propagation problems for which exact solutions exist. The flame speed evaluated by its use oscillates around the exact value at a relatively small amplitude, while the temperature and species concentration profiles are self-correcting in their convergence to the exact solution. A satisfactory resolution is obtained by the use of quite a small number of computational elements which automatically adjust their distribution of fit sharp gradients.

Ghoniem, A. F.↗

Effect of free stream turbulence on flow separation

An analysis is presented to study the influence of free stream turbulence on separation in the case of crossflow over a circular cylinder. An eddy diffusivity model has been formulated and the governing momentum equation has been solved numerically. A correlation parameter has been suggested to correlate the angle of separation. It has been found that the angle of separation increases with increasing free stream turbulence intensity.

Gorla, R. S. R.↗