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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.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

On High-Order/Low-Order and Micro-Macro Methods for Implicit Time-Stepping of the BGK Model

In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the Bhatnagar–Gross–Krook (BGK) equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. Furthermore, the accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near equilibrium.

BGK model↗
DOE OSTI2024

ABC -Auxetics: An Implicit Design Approach for Negative Poisson's Ratio Materials

A novel methodology is introduced for designing auxetic (negative Poisson's ratio) structures based on topological principles and is demonstrated by investigating a new class of auxetics based on two-dimensional (2D) textile weave patterns. Conventional methodology for designing auxetic materials typically involves determining a single deformable block (a unit cell) of material whose shape results in auxetic behavior. Consequently, patterning such a unit cell in a 2D (or 3D) domain results in a larger structure that exhibits overall auxetic behavior. Such an approach naturally relies on some prior intuition and experience regarding which unit cells may be auxetic. Second, tuning the properties of the resulting structures is typically limited to parametric variations of the geometry of a specific type of unit cell. Thus, most of the currently known auxetic structures belong to a selected few classes of unit cell geometries that are explicitly defined in accordance with a specified topological (i.e., grid structure). Herein, a new class of auxetic structures is demonstrated that, while periodic, can be generated implicitly, i.e., without reference to a specific unit cell design. The approach leverages weave-based parameters (A–B–C), resulting in a rich design space for auxetics that is previously unexplored.

36 MATERIALS SCIENCE↗
DOE OSTI2011

On Implicit Active Constraints in Linear Semi-Infinite Programs with Unbounded Coefficients

The concept of implicit active constraints at a given point provides useful local information about the solution set of linear semi-infinite systems and about the optimal set in linear semi-infinite programming provided the set of gradient vectors of the constraints is bounded, commonly under the additional assumption that there exists some strong Slater point. This paper shows that the mentioned global boundedness condition can be replaced by a weaker local condition (LUB) based on locally active constraints (active in a ball of small radius whose center is some nominal point), providing geometric information about the solution set and Karush-Kuhn-Tucker type conditions for the optimal solution to be strongly unique. The maintaining of the latter property under sufficiently small perturbations of all the data is also analyzed, giving a characterization of its stability with respect to these perturbations in terms of the strong Slater condition, the so-called Extended-Nuernberger condition, and the LUB condition.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

On implicit abstract neutral nonlinear differential equations

In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

A Membrane Model from Implicit Elasticity Theory. Application to Visceral Pleura

A Fungean solid is derived for membranous materials as a body defined by isotropic response functions whose mathematical structure is that of a Hookean solid where the elastic constants are replaced by functions of state derived from an implicit, thermodynamic, internal energy function. The theory utilizes Biot’s (Lond Edinb Dublin Philos Mag J Sci 27:468–489, 1939) definitions for stress and strain that, in one-dimension, are the stress/strain measures adopted by Fung (Am J Physiol 28:1532–1544, 1967) when he postulated what is now known as Fung’s law. Our Fungean membrane model is parameterized against a biaxial data set acquired from a porcine pleural membrane subjected to three, sequential, proportional, planar extensions. These data support an isotropic/deviatoric split in the stress and strain-rate hypothesized by our theory. These data also demonstrate that the material response is highly nonlinear but, otherwise, mechanically isotropic. These data are described reasonably well by our otherwise simple, four-parameter, material model.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Application of the p-Adic Topology on ℤ to the Problem of Finding Solutions in Integers of an Implicit Linear Difference Equation

We study solutions in integers of an implicit linear inhomogeneous first order difference equation bx{sub n+1} = ax{sub n} + f{sub n}. Based on the p-adic topology on the ring of integers, we obtain a criterion for the existence of solutions and show that for a = 1 a typical (in the natural topological sense) equation has no integer solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equations at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Mass-conserving implicit–explicit methods for coupled compressible Navier–Stokes equations

Earth system models are composed of coupled components that separately model systems such as the global atmosphere, ocean, and land surface. While these components are well developed, coupling them in a single system can be a significant challenge. Computational efficiency, accuracy, and stability are principal concerns. In this study we focus on these issues. In particular, implicit–explicit (IMEX) tight and loose coupling strategies are explored for handling different time scales. For a simplified model for the air–sea interaction problem, we consider coupled compressible Navier–Stokes equations with an interface condition. Under the rigid-lid assumption, horizontal momentum and heat flux are exchanged through the interface. Several numerical experiments are presented to demonstrate the stability of the coupling schemes. Here, we show both numerically and theoretically that our IMEX coupling methods are mass conservative for a coupled compressible Navier–Stokes system with the rigid-lid condition

42 ENGINEERING↗
DOE OSTI2022

$\mathrm{IH}$-$\mathrm{GAN}$: A conditional generative model for implicit surface-based inverse design of cellular structures

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignoring the effects of unit cell geometry on properties, or considers the geometry–property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from properties to geometries. Here we further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (R 2 -scores between target properties and properties of generated unit cells >98%) and 2) improve the optimized structural performance over the conventional variable-density single-type structure. In the minimum compliance example, our IH-GAN generated structure achieves a 79.7% reduction in concentrated stress and an extra 3.03% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 86.4% and 79.6% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending.

42 ENGINEERING↗
DOE OSTI2010

A Semi-Implicit Lattice Method for Simulating Flow

We propose a new semi-implicit lattice numerical method for modeling fluid flow that depends only on local primitive variable information (density, pressure, velocity) and not on relaxed upstream distribution function values. This method has the potential for reducing parallel communication and permitting larger time steps compared to the lattice Boltzmann method. The lid-driven cavity is modeled to demonstrate the accuracy of the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Asymptotic analysis of the spatial discretization of radiation absorption and re-emission in Implicit Monte Carlo

We perform an asymptotic analysis of the spatial discretization of radiation absorption and re-emission in Implicit Monte Carlo (IMC), a Monte Carlo technique for simulating nonlinear radiative transfer. Specifically, we examine the approximation of absorption and re-emission by a spatially continuous artificial-scattering process and either a piecewise-constant or piecewise-linear emission source within each spatial cell. We consider three asymptotic scalings representing (i) a time step that resolves the mean-free time, (ii) a Courant limit on the time-step size, and (iii) a fixed time step that does not depend on any asymptotic scaling. For the piecewise-constant approximation, we show that only the third scaling results in a valid discretization of the proper diffusion equation, which implies that IMC may generate inaccurate solutions with optically large spatial cells if time steps are refined. However, we also demonstrate that, for a certain class of problems, the piecewise-linear approximation yields an appropriate discretized diffusion equation under all three scalings. We therefore expect IMC to produce accurate solutions for a wider range of time-step sizes when the piecewise-linear instead of piecewise-constant discretization is employed. We demonstrate the validity of our analysis with a set of numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Implicit and explicit schemes for mass consistency preservation in hybrid particle/finite-volume algorithms for turbulent reactive flows

This work addresses the issue of particle mass consistency in Large Eddy Simulation/Probability Density Function (LES/PDF) methods for turbulent reactive flows. Numerical schemes for the implicit and explicit enforcement of particle mass consistency (PMC) are introduced, and their performance is examined in a representative LES/PDF application, namely the Sandia–Sydney Bluff-Body flame HM1. A new combination of interpolation schemes for velocity and scalar fields is found to better satisfy PMC than multilinear and fourth-order Lagrangian interpolation. A second-order accurate time-stepping scheme for stochastic differential equations (SDE) is found to improve PMC relative to Euler time stepping, which is the first time that a second-order scheme is found to be beneficial, when compared to a first-order scheme, in an LES/PDF application. An explicit corrective velocity scheme for PMC enforcement is introduced, and its parameters optimized to enforce a specified PMC criterion with minimal corrective velocity magnitudes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Compressible, multiphase semi-implicit method with moment of fluid interface representation

A unified method for simulating multiphase flows using an exactly mass, momentum, and energy conserving Cell-Integrated Semi-Lagrangian advection algorithm is presented. The deforming material boundaries are represented using the moment-of-fluid method. Our new algorithm uses a semi-implicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection method in the limit of infinite sound speed. The asymptotically preserving attribute makes the new method applicable to compressible and incompressible flows including stiff materials; enabling large time steps characteristic of incompressible flow algorithms rather than the small time steps required by explicit methods. Moreover, shocks are captured and material discontinuities are tracked, without the aid of any approximate or exact Riemann solvers. As a result, wimulations of underwater explosions and fluid jetting in one, two, and three dimensions are presented which illustrate the effectiveness of the new algorithm at efficiently computing multiphase flows containing shock waves and material discontinuities with large “impedance mismatch.”

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Efficient implicit LES method for the simulation of turbulent cavitating flows

We present a numerical method for efficient large-eddy simulation of compressible liquid flows with cavitation based on an implicit subgrid-scale model. Phase change and subgrid-scale interface structures are modeled by a homogeneous mixture model that assumes local thermodynamic equilibrium. Unlike previous approaches, emphasis is placed on operating on a small stencil (at most four cells). The truncation error of the discretization is designed to function as a physically consistent subgrid-scale model for turbulence. We formulate a sensor functional that detects shock waves or pseudo-phase boundaries within the homogeneous mixture model for localizing numerical dissipation. In smooth regions of the flow field, a formally non-dissipative central discretization scheme is used in combination with a regularization term to model the effect of unresolved subgrid scales. The new method is validated by computing standard single- and two-phase test-cases. Comparison of results for a turbulent cavitating mixing layer obtained with the new method demonstrates its suitability for the target applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

One-dimensional Lagrangian implicit hydrodynamic algorithm for Inertial Confinement Fusion applications

A new one-dimensional hydrodynamic algorithm, specifically developed for Inertial Confinement Fusion (ICF) applications, is presented. The scheme uses a fully conservative Lagrangian formulation in planar, cylindrical, and spherically symmetric geometries, and supports arbitrary equations of state with separate ion and electron components. Fluid equations are discretized on a staggered grid and stabilized by means of an artificial viscosity formulation. The space discretized equations are advanced in time using an implicit algorithm. The method includes several numerical parameters that can be adjusted locally. In regions with low Courant–Friedrichs–Lewy (CFL) number, where stability is not an issue, they can be adjusted to optimize the accuracy. In typical problems, the truncation error can be reduced by a factor between 2 to 10 in comparison with conventional explicit algorithms. On the other hand, in regions with high CFL numbers, the parameters can be set to guarantee unconditional stability. The method can be integrated into complex ICF codes. This is demonstrated through several examples covering a wide range of situations: from thermonuclear ignition physics, where alpha particles are managed as an additional species, to low intensity laser–matter interaction, where liquid–vapor phase transitions occur.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Memory-optimized shift operator alternating direction implicit finite difference time domain method for plasma

Through introducing the alternating direction implicit (ADI) technique and the memory-optimized algorithm to the shift operator (SO) finite difference time domain (FDTD) method, the memory-optimized SO-ADI FDTD for nonmagnetized collisional plasma is proposed and the corresponding formulae of the proposed method for programming are deduced. In order to further the computational efficiency, the iteration method rather than Gauss elimination method is employed to solve the equation set in the derivation of the formulae. Complicated transformations and convolutions are avoided in the proposed method compared with the Z transforms (ZT) ADI FDTD method and the piecewise linear JE recursive convolution (PLJERC) ADI FDTD method. The numerical dispersion of the SO-ADI FDTD method with different plasma frequencies and electron collision frequencies is analyzed and the appropriate ratio of grid size to the minimum wavelength is given. The accuracy of the proposed method is validated by the reflection coefficient test on a nonmagnetized collisional plasma sheet. The testing results show that the proposed method is advantageous for improving computational efficiency and saving computer memory. The reflection coefficient of a perfect electric conductor (PEC) sheet covered by multilayer plasma and the RCS of the objects coated by plasma are calculated by the proposed method and the simulation results are analyzed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

An adaptive, implicit, conservative, 1D-2V multi-species Vlasov–Fokker–Planck multi-scale solver in planar geometry

We consider a 1D-2V Vlasov–Fokker–Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we extend the conservative adaptive velocity-space discretization scheme proposed in [Taitano et al., J. Comput. Phys., 318, 391–420, (2016)] to a spatially inhomogeneous system. Here in this approach, we normalize the velocity-space coordinate to a temporally and spatially varying local characteristic speed per species. We explicitly consider the resulting inertial terms in the Vlasov equation, and derive a discrete formulation that conserves mass, momentum, and energy up to a prescribed nonlinear tolerance upon convergence. Our conservation strategy employs nonlinear constraints to enforce these properties discretely for both the Vlasov operator and the Fokker–Planck collision operator. Numerical examples of varying degrees of complexity, including shock-wave propagation, demonstrate the favorable efficiency and accuracy properties of the scheme.

1D2V↗