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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions

The time-dependent, 3D incompressible Navier-Stokes equations in (1) boundary layers, the semiinfinite domain, and (2) mixing layers or wakes, the fully infinite domain, are respectively solved by two numerical methods which employ rapidly decaying spectral basis functions to approximate the vertical dependence of the solutions. These functions are then combined with one, for method (1), and two, for method (2), slowly decaying 'extra functions' for each wave vector. Each extra function can exactly represent the solution's irrotational component at large distances. The two methods have been applied to extensive direct-numerical simulation of transition and turbulence.

Spalart, Philippe R.↗
NASA NTRS2013

Numerical Modeling of Ablation Heat Transfer

A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

Ewing, Mark E.↗
DOE OSTI2024

Green's function methods for multiphysics simulations (Final Report)

Green's functions are important tools for analyzing mathematical properties of partial differential equations (PDEs), and for numerically solving PDEs, especially when equations for the same operator but with multiple right hand sides need to be solved simultaneously. This proposal aims at developing efficient and accurate numerical methods for computing Green's functions, which can be used to tackle a challenging question in multiphysics simulation of DOE-mission science problems: how to couple quantum physics with classical physics. The key mathematical difficulty is properly formulate a "boundary condition" for the region described by quantum physics, and conventional approaches often model such boundary conditions in an empirical way. The proposed Green's function methods use the Dirichlet-to-Neumann map to formulate a boundary condition that is non-empirical and can couple the quantum and classical regions in an in principle exact way. The key ingredient of the new methods is to construct the Dirichlet-to-Neumann map in an efficient, accurate and versatile manner. The new methods have provably low complexity and are ideally suited for massively parallel and emerging many-core computational systems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2

Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.

Engquist, B. E.↗
NASA NTRS1977

Displacement incrementation in non-linear structural analysis by the self-correcting method

The prediction of nonlinear structural behavior by the finite element method wherein buckling does not occur has received considerable attention and, with it, reasonable success has been achieved. However, the post-buckling problem has been less actively pursued probably because of the inherent numerical difficulties encountered. This note reviews very briefly the numerical methods currently being used for pre- and post-buckling analysis and presents a self-correcting approach based on load and displacement incrementation which is shown to be efficient, reliable, and easy to program. Numerical solutions are presented which demonstrate the effectiveness of the method.

Haisler, W. E.↗
NASA NTRS1983

Formulation and solution of rotary-wing aeroelastic stability and response problems

The state of the art in the formulation and solution of rotary-wing aeroelastic stability and response problems is reviewed in detail. The approximations used in the structural, inertia and aerodynamic operators are discussed. The important role of geometric nonlinearities, due to moderate deflections, and aerodynamic stall in the aeroelastic stability and response problem are identified. It is also shown that geometric nonlinearities are of primary importance in aeroelastic stability calculations, and have a more limited, though important, role in response calculations. Next, formulation of coupled rotor/fuselage problems is described, for both air and ground resonance type problems. Both topics, the isolated blade problem and the coupled rotor/fuselage problem, are treated for both hover and forward flight. Solution of aeroelastic stability and response problems proceeds in two stages. First, the spatial dependence is eliminated by using Galerkin's method, or by using the finite element method. Next the nonlinear, or linear, ordinary differential equation with periodic coefficients have to be solved for stability or response. Efficient numerical methods for accomplishing these objectives are presented in a comprehensive manner. The paper contains a number of illustrative numerical results which are intended to clarify various aspects of the modeling process and serve as representative results for both aeroelastic stability and response calculations for a variety of blade and rotor configurations.

Friedmann, P. P.↗
DOE OSTI2017

Mathematical Simulation of the Migration of Radionuclides in a Soil Medium Under Nonisothermal Conditions with Account for Catalytic Microparticles and Nonlinear Processes

The problem of mathematical simulation of the vertical migration of radionuclides in a catalytic porous medium under nonisothermal conditions is considered. A numerical solution of the corresponding one-dimensional nonlinear boundary-value problem is obtained by the finite difference method. Numerical experiments are carried out and their analysis is made.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II

Here, in this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I

In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In conclusion, these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Eddy Current Probe Parameters Identification Using a Genetic Algorithm and Simultaneous Perturbation Stochastic Approximation

This study tries to identify the coil parameters using numerical methods. The eddy current testing (ECT) is used for evaluation of a crack with the aid of numerical simulations by utilizing the identification of these parameters. In this study, a comparison of the performance of the GA and SPSA algorithms to identify the parameter values of the coil sensors are presented. So, the optimization probe geometry is introduced in the simulation with Three-dimensional finite element simulations (FLUX finite element code) were conducted to obtain eddy current signals resulting from a crack in a plate made of aluminium. The simulation results are compared with experimental measurements for the defect present in a plate.

42 ENGINEERING↗
DOE OSTI2020

A higher-order finite element reactive transport model for unstructured and fractured grids

Abstract This work presents a new reactive transport framework that combines a powerful geochemistry engine with advanced numerical methods for flow and transport in subsurface fractured porous media. Specifically, the PhreeqcRM interface (developed by the USGS) is used to take advantage of a large library of equilibrium and kinetic aqueous and fluid-rock reactions, which has been validated by numerous experiments and benchmark studies. Fluid flow is modeled by the Mixed Hybrid Finite Element (FE) method, which provides smooth velocity fields even in highly heterogenous formations with discrete fractures. A multilinear Discontinuous Galerkin FE method is used to solve the multicomponent transport problem. This method is locally mass conserving and its second order convergence significantly reduces numerical dispersion. In terms of thermodynamics, the aqueous phase is considered as a compressible fluid and its properties are derived from a Cubic Plus Association (CPA) equation of state. The new simulator is validated against several benchmark problems (involving, e.g., Fickian and Nernst-Planck diffusion, isotope fractionation, advection-dispersion transport, and rock-fluid reactions) before demonstrating the expanded capabilities offered by the underlying FE foundation, such as high computational efficiency, parallelizability, low numerical dispersion, unstructured 3D gridding, and discrete fraction modeling.

58 GEOSCIENCES↗
DOE OSTI2015

A mass conserving level set method for detailed numerical simulation of liquid atomization

An improved mass conserving level set method for detailed numerical simulations of liquid atomization is developed to address the issue of mass loss in the existing level set method. This method introduces a mass remedy procedure based on the local curvature at the interface, and in principle, can ensure the absolute mass conservation of the liquid phase in the computational domain. Three benchmark cases, including Zalesak's disk, a drop deforming in a vortex field, and the binary drop head-on collision, are simulated to validate the present method, and the excellent agreement with exact solutions or experimental results is achieved. It is shown that the present method is able to capture the complex interface with second-order accuracy and negligible additional computational cost. The present method is then applied to study more complex flows, such as a drop impacting on a liquid film and the swirling liquid sheet atomization, which again, demonstrates the advantages of mass conservation and the capability to represent the interface accurately.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Indium tin oxide-free transparent and conductive electrode based on SnO{sub x} | Ag | SnO{sub x} for organic solar cells

A SnO{sub x} | Ag | SnO{sub x} multilayer deposited by E-beam evaporation is proposed as transparent anode for a (poly-3-hexylthiophene):[6,6]-phenyl-C{sub 61}-butyric acid methyl ester (P3HT:PCBM) bulk heterojunction based Organic Solar Cell (OSC). Such multilayers are studied and manufactured with the objective to give to the electrode its best conductivity and transparency in the visible spectral range. A transfer matrix method numerical optimization of the thicknesses of each layer of the electrode is developed to limit the number of test samples which would have been manufactured whether an empirical method was chosen. Optical characterization of the deposited SnO{sub x} and Ag thin films is performed to determine the dispersion of the complex refractive indices which are used as input parameters in the model. A satisfying agreement between numerical and experimental optical properties is found. The bare tri-layer electrodes show low sheet resistance (as low as 6.7 Ω/□) and the whole Glass | SnO{sub x} | Ag | SnO{sub x} structure presents a mean transparency on 400–700 nm spectral band as high as 67%. The multilayer is then numerically studied as anode for a P3HT:PCBM bulk heterojunction based OSC. Intrinsic absorption inside the sole active layer is calculated giving the possibility to perform optical optimization on the intrinsic absorption efficiency inside the active area by considering the media embedding the electrodes. An additional study using the morphology of the silver inserted between both oxide layers as input data is performed with a finite difference time domain 3D-method to improve the accordance between optical measurements and numerical results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Decentralised demand response market model based on reinforcement learning

A new decentralised demand response (DR) model relying on bi‐directional communications is developed in this study. In this model, each user is considered as an agent that submits its bids according to the consumption urgency and a set of parameters defined by a reinforcement learning algorithm called Q‐learning. The bids are sent to a local DR market, which is responsible for communicating all bids to the wholesale market and the system operator (SO), reporting to the customers after determining the local DR market clearing price. From local markets’ viewpoint, the goal is to maximise social welfare. Four DR levels are considered to evaluate the effect of different DR portions in the cost of the electricity purchase. The outcomes are compared with the ones achieved from a centralised approach (aggregation‐based model) as well as an uncontrolled method. Numerical studies prove that the proposed decentralised model remarkably drops the electricity cost compare to the uncontrolled method, being nearly as optimal as a centralised approach.

Shafie‐Khah, Miadreza↗
DOE OSTI2018

Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures

We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long et al. [Phys. Rev. B 68, 235106 (2003)] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here in this paper, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013)] to obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with S = 1/2, we demonstrate that the proposed procedure is reasonably accurate, even for relatively small systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Evidence for Dissociation and Ionization in Shock Compressed Nitrogen to 800 GPa

Triple bonding in the nitrogen molecule (N 2 ) is among the strongest chemical bonds with a dissociation enthalpy of 9.8 eV/molecule. Nitrogen is therefore an excellent test bed for theoretical and numerical methods aimed at understanding how bonding evolves under the influence of the extreme pressures and temperatures of the warm dense matter regime. Here, we report laser-driven shock experiments on fluid molecular nitrogen up to 800 GPa and 4.0 g/cm 3 . Line-imaging velocimetry measurements and impedance matching method with a quartz reference yield shock equation of state data of initially precompressed nitrogen. Comparison with numerical simulations using path integral Monte Carlo and density functional theory molecular dynamics reveals clear signatures of chemical dissociation and the onset of L-shell ionization. Furthermore, combining data along multiple shock Hugoniot curves starting from densities between 0.76 and 1.29 g/cm 3 , our study documents how pressure and density affect these changes in chemical bonding and provides benchmarks for future theoretical developments in this regime, with applications for planetary interior modeling, high energy density science, and inertial confinement fusion research.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

SU-D-201-04: Study On the Impact of Tumor Shape and Size On Drug Delivery to Pancreatic Tumors

Purpose: Drug delivery to solid tumors can be expressed physically using transport phenomena such as convection and diffusion for the drug of interest within extracellular matrices. We aimed to carefully model these phenomena, and to investigate the effect of tumor shape and size on drug delivery to solid tumors in the pancreas. Methods: In this study, multiple tumor geometries as obtained from clinical PET/CT images were considered. An advanced numerical method was used to simultaneously solve fluid flow and solute transport equations. Data from n=45 pancreatic cancer patients with non-resectable locoregional disease were analyzed, and geometrical information from the tumors including size, shape, and aspect ratios were classified. To investigate effect of tumor shape, tumors with similar size but different shapes were selected and analyzed. Moreover, to investigate effect of tumor size, tumors with similar shapes but different sizes, ranging from 1 to 77 cm{sup 3}, were selected and analyzed. A hypothetical tumor similar to one of the analyzed tumors, but scaled to reduce its size below 0.2 cm{sup 3}, was also analyzed. Results: The results showed relatively similar average drug concentration profiles in tumors with different sizes. Generally, smaller tumors had higher absolute drug concentration. In the hypothetical tumor, with volume less than 0.2 cm{sup 3}, the average drug concentration was 20% higher in comparison to its counterparts. For the various real tumor geometries, however, the maximum difference between average drug concentrations was 10% for the smallest and largest tumors. Moreover, the results demonstrated that for pancreatic tumors the shape is not significant. The negligible difference of drug concentration in different tumor shapes was due to the minimum effect of convection in pancreatic tumors. Conclusion: In tumors with different sizes, smaller tumors have higher drug delivery; however, the impact of tumor shape in the case of pancreatic tumors is not significant.

60 APPLIED LIFE SCIENCES↗