Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Implicit”

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.

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

At least 1,639 records · Page 91
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A sub-pore model for multi-scale reaction–diffusion problems in porous media

Applications of reaction–diffusion systems in porous media pose a challenging problem for computational modeling approaches due to their multi-physics and multi-scale nature. The length scales usually span 3–4 orders of magnitude while physical phenomena involved include heat and mass transfer processes, and surface reactions. In this paper, a novel methodology that accounts for all the length scales and physical phenomena involved in a single framework is described. A length scale based dual approach is proposed – the larger pore channels (macro-pores) are resolved using conventional numerical techniques and a novel ‘sub-pore’ model is used to account for the unresolved pore channels (sub-pores) and the important physics therein. The porous network in the sub-pore system is composed of a fractal-like hierarchical system of straight cylindrical pores. Simplified governing equations for mass and energy transport are solved within the sub-pore system along with a reaction kinetics model to account for surface adsorption. An implicit coupling strategy is used to couple the macro-pore and the sub-pore systems so as to ensure conservation. The developed methodology is then applied to a few test cases and it is established that the proposed framework is necessary for problems where the adsorption time scale is much smaller than (diffusion-limited) or comparable to the diffusion time scale. Furthermore, it is also demonstrated that the framework can be potentially used to model the network of porous channels in its entirety thus significantly reducing computational costs.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Fluid dynamic and thermal performance of a slotted cylinder at low Reynolds number

The fluid dynamic and thermal performance of a circular cylinder with a slot parallel to the flow is numerically investigated. The study utilized the semi-implicit finite volume multi-material algorithm MPM-ICE, a component of the Uintah framework. The normalized slot width s/D ranges from 0.1 - 0.3, introducing an additional heat transfer surface area between ~ 10 and ~ 50%, and a mass reduction between ~ 13 and ~ 38% in the cylinder. We assumed two-dimensional incompressible flow and simulated a Reynolds number Re D between 100 and 1000. The slotted cylinders are found to have a total drag force reduction up to ~ 45%, compared to a solid cylinder despite the additional viscous drag force in the slot. Convection heat transfer is enhanced up to ~ 70%. Further, the slotted cylinder performance index, defined as the ratio of the heat rate to the drag force, increases up to maximum of ~ 3, indicating better overall thermal fluid performance. An entropy analysis showed the best performance index occurs at the highest Re D . Correlations for drag coefficient and Nusselt number are proposed along with an entropy optimization method.

42 ENGINEERING↗
DOE OSTI2020

Experimental verification of a crystal plasticity-based simulation framework for predicting microstructure and geometric shape changes: Application to bending and Taylor impact testing of Zr

This paper is concerned with experimental verification of a recently developed multi-scale simulation framework for plastic deformation of metallic materials from quasi-static to impact deformation conditions. The framework is a visco-plastic self-consistent (VPSC) polycrystalline model embedded in an implicit finite element method (FE-VPSC) to provide a microstructure-sensitive constitutive response at each material point. Each material point of the FEM model is a polycrystalline aggregate with crystallographic deformation mechanisms operating at the single crystal scale with their evolving activity based on a dislocation density-based hardening law and texture. Four beams and three cylinders machined in different orientations from a textured plate of high-purity zirconium are tested quasi-statically in 4-point bending and at speeds of 100 m/s, 170 m/s and 243 m/s during Taylor impact tests, respectively. The variation in dimensional changes resulting from different sample orientations in the plate with respect to loading directions is measured for each sample. Moreover, texture and twinning characterization is performed using electron backscattered diffraction (EBSD). The deformation processes and underlying evolution of microstructure are successfully simulated using the FE-VPSC framework. In doing so, the model parameters are optimized and validated across a broad range of strain rates and temperatures. Simulation results in terms of geometrical changes and microstructural evolution are compared with the experimental measurements. The model predicts anisotropic material flow resulting from the hard-to-deform crystallographic directions, the development of gradients in texture and twinning through the geometries, tension–compression asymmetry, as well as the extent of plasticity under impact.

42 ENGINEERING↗
DOE OSTI2022

A correction procedure for self-induced velocity of a finite-sized particle in two-way coupled Euler–Lagrange simulations

The importance of incorporating a correction to undo the self-induced perturbation velocity of a particle, when its size becomes comparable to the Eulerian grid, in a two-way coupled Euler–Lagrange (EL) simulation is now well appreciated. The present work improves upon the prior correction procedures in a few important ways. First, the past correction procedures have been scalar-based with the assumption that the quasi-steady force is the source of self-induced velocity perturbation. Here we generalize to a vector correction procedure and thereby the directions of feedback force and relative velocity can be different. This allows the correction procedure to be used even in the presence of added-mass, history, and lift forces. Second, the effect of a nearby wall has been systematically included in the correction procedure. The correction procedure depends on fundamental Oseen solutions of streamwise and transverse regularized feedback forces. We present a Fourier transform-based analytical approach to obtaining these regularized Oseen solutions. We also present a step-by-step numerical procedure for obtaining the Oseen solutions in any EL code. With the analytical or numerical Oseen functions, the correction procedure can be easily implemented in any EL code. Iterations are required in solving the implicit correction equations and it is demonstrated that the correction procedure converges rapidly within three or four iterations. In conclusion, a simple empirical approach is also presented to account for unsteady effects in the correction procedure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Crystal plasticity modeling of strain-induced martensitic transformations to predict strain rate and temperature sensitive behavior of 304 L steels: Applications to tension, compression, torsion, and impact

This paper advances crystallographically-based Olson-Cohen (direct γ → α’) and deformation mechanism (indirect γ→ε→α’) phase transformation models for predicting strain-induced austenite to martensite transformation. Here, the advanced transformation models enable predictions of not only strain-path sensitive, but also of strain-rate and temperature sensitive deformation of polycrystalline stainless steels (SSs). The deformation of constituent grains in SSs is modeled as a combination of anisotropic elasticity, crystallographic slip, and phase transformation, while the hardening is based on the evolution of dislocation density and explicit shifts in phase fractions. Such grain-scale deformation is implemented within the meso-scale elasto-plastic self-consistent (EPSC) homogenization model, which is coupled with the implicit finite element (FE) method to provide a constitutive response at each FE integration point for solving boundary value problems at the macro-scale. Parameters pertaining to the hardening and transformation models within FEEPSC are calibrated and validated on a suite of data including flow curves and phase fractions for monotonic compression, tension, and torsion as a function of strain-rate and temperature for wrought and additively manufactured (AM) SS304L. To illustrate the potential and accuracy of the integrated multi-level FE-EPSC simulation framework, geometry, mechanical response, phase fractions, and texture evolution are simulated during gas-gun impact deformation of a cylinder and quasi-static tension of a notched specimen made of AM SS304L. Details of the simulation framework, comparison between experimental and simulation results, and insights from the results are presented and discussed.

304L steels↗
DOE OSTI2022

Peridynamics and surrogate modeling of pressure-driven well stimulation

In this work we use the peridynamics theory of solid mechanics to simulate fracture in an annular rock domain subject to an in-situ stress and create surrogate models that predict the area of the resulting cracks. Peridynamics is a non-local formulation of continuum mechanics that naturally accommodates material discontinuities. Furthermore, unlike other fracture modeling techniques there is no need to provide information about the crack path. We utilize the peridynamics code Peridigm and take a two-stage approach to fracture modeling. First an implicit solve is performed to compute the in-situ stress state. We then execute an explicit solve where a pressure loading designed to emulate fluid-driven hydraulic fracture is applied at the borehole and transmitted to the pre-stressed rock. We present results from polynomial and single and multi-level Gaussian process surrogate models constructed from a sampling study of the peridynamics model. The surrogates predict crack area given a measure of the in-situ stress anisotropy and rise time and amplitude of the pressure loading. These surrogates take a minuscule fraction of peridynamics model's running time to evaluate and are a step towards enabling advanced optimization and uncertainty quantification workflows that require many model evaluations.

42 ENGINEERING↗
DOE OSTI2017

PIC simulations of wave-particle interactions with an initial electron velocity distribution from a kinetic ring current model

Whistler wave-particle interactions play an important role in the Earth inner magnetospheric dynamics and have been the subject of numerous investigations. By running a global kinetic ring current model (RAM-SCB) in a storm event occurred on Oct 23–24 2002, we obtain the ring current electron distribution at a selected location at MLT of 9 and L of 6 where the electron distribution is composed of a warm population in the form of a partial ring in the velocity space (with energy around 15 keV) in addition to a cool population with a Maxwellian-like distribution. The warm population is likely from the injected plasma sheet electrons during substorm injections that supply fresh source to the inner magnetosphere. These electron distributions are then used as input in an implicit particle-in-cell code (iPIC3D) to study whistler-wave generation and the subsequent wave-particle interactions. Here, we find that whistler waves are excited and propagate in the quasi-parallel direction along the background magnetic field. Several different wave modes are instantaneously generated with different growth rates and frequencies. The wave mode at the maximum growth rate has a frequency around 0.62ω ce , which corresponds to a parallel resonant energy of 2.5 keV. Linear theory analysis of wave growth is in excellent agreement with the simulation results. These waves grow initially due to the injected warm electrons and are later damped due to cyclotron absorption by electrons whose energy is close to the resonant energy and can effectively attenuate waves. The warm electron population overall experiences net energy loss and anisotropy drop while moving along the diffusion surfaces towards regions of lower phase space density, while the cool electron population undergoes heating when the waves grow, suggesting the cross-population interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Site heterogeneity and broad surface-binding isotherms in modern catalysis: Building intuition beyond the Sabatier principle

Learning the science of heterogeneous catalysis and electrocatalysis always starts with the simple case of a flat, uniform surface with an ideal adsorbate. It has of course been recognized for a century that real catalysts are more complicated. For the increasingly complex catalysts of the 21st century, this Perspective argues that surface heterogeneity and non-ideal binding isotherms are central features, and their implications need to be incorporated in current thinking. A variety of systems are described herein where catalyst complexity leads to broad, non-Langmuirian surface isotherms for the binding of hydrogen atoms – and this occurs even for ideal, flat Pt(111) surfaces. Modern catalysis employs nanoscale materials whose surfaces have substantial step, edge, corner, impurity, and other defect sites, and they increasingly have both metallic and non-metallic elements M n X m , including metal oxides, chalcogenides, pnictides, carbides, doped carbons, etc. The surfaces of such catalysts are often not crystal facets of the bulk phase underneath, and they typically have a variety of potential active sites. Catalytic surfaces in operando are often non-stoichiometric, amorphous, dynamic, and impure, and often vary from one part of the surface to another. Understanding of the issues that arise at such nanoscale, multi-element catalysts is just beginning to emerge. Yet these catalysts are widely discussed using Brønsted/Bell-Evans-Polanyi (BEP) relations, volcano plots, Tafel slopes, the Butler-Volmer equation, and other linear free energy relations (LFERs), which all depend on the implicit assumption that the active sites are “similar” and that surface adsorption is close to ideal. These assumptions underly the ubiquitous intuition based on the Sabatier Principle, that the fastest catalysis will occur when key intermediates have free energies of adsorption that are not too strong nor too weak. Current catalysis research often aims to minimize the complexity of non-ideal isotherms through experimental and computational design (e.g., the use of single crystal surfaces), and these studies are the foundation of the field. In contrast, this Perspective argues that the heterogeneity of binding sites and binding energies is an inherent strength of these catalysts. Here, this diversity makes many nanoscale catalysts inherently a high-throughput screen wrapped in a tiny package. Only by making the heterogeneity part of the foundation of catalysis models, sorting the types of active sites and dissecting non-ideal binding isotherms, will modern catalysis learn to harness the inherent diversity of real catalysts. Controlling and exploiting diversity rather than avoiding it will help to optimize complex modern catalysts and catalytic conditions.

Mayer, James M.↗
DOE OSTI2012

Perfectly matched layers in a divergence preserving ADI scheme for electromagnetics

For numerical simulations of highly relativistic and transversely accelerated charged particles including radiation fast algorithms are needed. While the radiation in particle accelerators has wavelengths in the order of 100 {mu}m the computational domain has dimensions roughly five orders of magnitude larger resulting in very large mesh sizes. The particles are confined to a small area of this domain only. To resolve the smallest scales close to the particles subgrids are envisioned. For reasons of stability the alternating direction implicit (ADI) scheme by Smithe et al. [D.N. Smithe, J.R. Cary, J.A. Carlsson, Divergence preservation in the ADI algorithms for electromagnetics, J. Comput. Phys. 228 (2009) 7289-7299] for Maxwell equations has been adopted. At the boundary of the domain absorbing boundary conditions have to be employed to prevent reflection of the radiation. In this paper we show how the divergence preserving ADI scheme has to be formulated in perfectly matched layers (PML) and compare the performance in several scenarios.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Time dependent Schroedinger equation on arbitrary structured grids: Application to photoionization

A systematic technique for conservatively discretizing the time dependent Schroedinger equation on an arbitrary structured grid is given. Spatial differencing is carried out by finite volumes, and temporal differencing is carried out semi-implicitly. It is shown that the resulting algorithm conserves probability to within a round-off error regardless of the grid geometry. The algorithm is efficient for both serial and parallel computation. The conservative nature of the algorithm, and its phase accuracy, are demonstrated for a bound state, and for a free state in an electromagnetic field. The ionization rate for a hydrogen atom in a strong electromagnetic field is computed, and compared with the rate from tunneling theory. The regime of validity of tunneling theory is clarified.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2012

A finite element/Fourier treatment of the Fokker-Planck equation

A method is proposed for a finite element/Fourier solution of the Fokker-Planck (FP) equation describing Coulomb collisions between particles in a fully ionized, spatially homogeneous plasma. A linearized FP equation is obtained by assuming collisions between test particles and a static background are more important than between the test particles themselves. A full 3D velocity space dependence is maintained using cylindrical coordinates (v{sub Double-Vertical-Line },v{sub Up-Tack },{gamma}). When a magnetic field exists, v{sub Double-Vertical-Line} is aligned with it and {gamma} corresponds to gyroangle. Distribution functions are approximated by a Fourier representation in the azimuthal angle, {gamma}, and by a 2D finite element representation in the parallel and perpendicular directions. The FP equation can be solved in a fully implicit manner allowing large, stable timesteps and simulations that arrive quickly at equilibrium solutions. The results of several test problems are discussed including a calculation of the resistivity of a Lorentz plasma, the heating and cooling of a test particle distribution, the slowing down of a beam of test particles and the acquisition of a perpendicular flow for a non-flowing Maxwellian test distribution. Robust convergence upon refinement of the finite element/Fourier representation is highlighted.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations in optically thick media. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many smaller Monte Carlo steps, thus improving the efficiency of the simulation. In this paper, we present an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold, as optical thickness is typically a decreasing function of frequency. Above this threshold we employ standard Monte Carlo, which results in a hybrid transport-diffusion scheme. With a set of frequency-dependent test problems, we confirm the accuracy and increased efficiency of our new DDMC method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows

The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier-Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Generalized fictitious methods for fluid–structure interactions: Analysis and simulations

We present a new fictitious pressure method for fluid–structure interaction (FSI) problems in incompressible flow by generalizing the fictitious mass and damping methods we published previously in [1]. The fictitious pressure method involves modification of the fluid solver whereas the fictitious mass and damping methods modify the structure solver. We analyze all fictitious methods for simplified problems and obtain explicit expressions for the optimal reduction factor (convergence rate index) at the FSI interface [2]. This analysis also demonstrates an apparent similarity of fictitious methods to the FSI approach based on Robin boundary conditions, which have been found to be very effective in FSI problems. We implement all methods, including the semi-implicit Robin based coupling method, in the context of spectral element discretization, which is more sensitive to temporal instabilities than low-order methods. However, the methods we present here are simple and general, and hence applicable to FSI based on any other spatial discretization. In numerical tests, we verify the selection of optimal values for the fictitious parameters for simplified problems and for vortex-induced vibrations (VIV) even at zero mass ratio (“for-ever-resonance”). We also develop an empirical a posteriori analysis for complex geometries and apply it to 3D patient-specific flexible brain arteries with aneurysms for very large deformations. We demonstrate that the fictitious pressure method enhances stability and convergence, and is comparable or better in most cases to the Robin approach or the other fictitious methods.

Computer Science↗
DOE OSTI2013

Higher-order compositional modeling of three-phase flow in 3D fractured porous media based on cross-flow equilibrium

Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a compositional numerical simulator for three-phase flow in fractured media has not appeared in the literature, to the best of our knowledge. In this work, we present a three-phase fully compositional simulator for fractured media, based on higher-order finite element methods. To achieve computational efficiency, we invoke the cross-flow equilibrium (CFE) concept between discrete fractures and a small neighborhood in the matrix blocks. We adopt the mixed hybrid finite element (MHFE) method to approximate convective Darcy fluxes and the pressure equation. This approach is the most natural choice for flow in fractured media. The mass balance equations are discretized by the discontinuous Galerkin (DG) method, which is perhaps the most efficient approach to capture physical discontinuities in phase properties at the matrix-fracture interfaces and at phase boundaries. In this work, we account for gravity and Fickian diffusion. The modeling of capillary effects is discussed in a separate paper. We present the mathematical framework, using the implicit-pressure-explicit-composition (IMPEC) scheme, which facilitates rigorous thermodynamic stability analyses and the computation of phase behavior effects to account for transfer of species between the phases. A deceptively simple CFL condition is implemented to improve numerical stability and accuracy. We provide six numerical examples at both small and larger scales and in two and three dimensions, to demonstrate powerful features of the formulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach can be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

On the continuity of mean total normal stress in geometrical multiscale cardiovascular problems

In this work an iterative strategy to implicitly couple dimensionally-heterogeneous blood flow models accounting for the continuity of mean total normal stress at interface boundaries is developed. Conservation of mean total normal stress in the coupling of heterogeneous models is mandatory to satisfy energetic consistency between them. Nevertheless, existing methodologies are based on modifications of the Navier–Stokes variational formulation, which are undesired when dealing with fluid–structure interaction or black box codes. The proposed methodology makes possible to couple one-dimensional and three-dimensional fluid–structure interaction models, enforcing the continuity of mean total normal stress while just imposing flow rate data or even the classical Neumann boundary data to the models. This is accomplished by modifying an existing iterative algorithm, which is also able to account for the continuity of the vessel area, when required. Comparisons are performed to assess differences in the convergence properties of the algorithms when considering the continuity of mean normal stress and the continuity of mean total normal stress for a wide range of flow regimes. Finally, examples in the physiological regime are shown to evaluate the importance, or not, of considering the continuity of mean total normal stress in hemodynamics simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models

The unified gas kinetic scheme (UGKS) of K. Xu et al. (2010) [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knudsen) regime, we prove that UGKS is still asymptotic preserving (AP) in this regime, but for the free transport regime as well. Moreover, this scheme is modified to include a time implicit discretization of the limit diffusion equation, and to correctly capture the solution in case of boundary layers. Contrary to many AP schemes, this method is based on a standard finite volume approach, it does neither use any decomposition of the solution, nor staggered grids. Several numerical tests demonstrate the properties of the scheme.

97 MATHEMATICS AND COMPUTING↗