Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical method”

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 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Use of Forward Sensititvity Analysis Method to Improve Code Scaling, Applicability, and Uncertainty (CSAU) Methodology

Since the Code Scaling, Applicability, and Uncertainty (CSAU) methodology was proposed about two decades ago, it has been widely used for new reactor designs and existing LWRs power uprates. In spite of these huge successes, CSAU has been criticized for the need of further improvement, focusing on two main issues - lack of objectiveness and high cost. With the effort to develop next generation safety analysis codes, new opportunities appear to take advantage of new numerical methods, better physical models, and modern uncertainty qualification methods. Forward sensitivity analysis (FSA) directly solves the partial differential equations for parameter sensitivities. Moreover, our work shows that time and space steps can be treated as special sensitivity parameters so that numerical errors can be directly compared with physical uncertainties. When the FSA is implemented in a new advanced system analysis code, CSAU could be significantly improved by quantifying numerical errors and allowing a quantitative PIRT (Q-PIRT) to reduce subjective judgement and improving efficiency. This paper will review the issues related to the current CSAU implementations, introduce FSA, show a simple example to perform FSA, and discuss potential improvements on CSAU with FSA. Finally, the general research direction and requirements to use FSA in an advanced system analysis code will be discussed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Adaptive rotating-wave approximation for driven open quantum systems

We present a numerical method to approximate the long-time asymptotic solution $\rho_\infty(t)$ to the Lindblad master equation for an open quantum system under the influence of an external drive. The proposed scheme uses perturbation theory to rank individual drive terms according to their dynamical relevance, and adaptively determines an effective Hamiltonian. In the constructed rotating frame, $\rho_\infty$ is approximated by a time-independent, nonequilibrium steady-state. This steady-state can be computed with much better numerical efficiency than asymptotic long-time evolution of the system in the lab frame. We illustrate the use of this method by simulating recent transmission measurements of the heavy-fluxonium device, for which ordinary time-dependent simulations are severely challenging due to the presence of metastable states with lifetimes of the order of milliseconds.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Progress on Understanding Rayleigh–Taylor Flow and Mixing Using Synergy Between Simulation, Modeling, and Experiment

Simultaneous advances in numerical methods and computing, theoretical techniques, and experimental diagnostics have all led independently to better understanding of Rayleigh–Taylor (RT) instability, turbulence, and mixing. In particular, experiments have provided significant motivation for many simulation and modeling studies, as well as validation data. Numerical simulations have also provided data that is not currently measurable or very difficult to measure accurately in RT unstable flows. Thus, simulations have also motivated new measurements in this class of buoyancy-driven flows. This overview discusses simulation and modeling studies synergistic with experiments and examples of how experiments have motivated simulations and models of RT instability, flow, and mixing. First, a brief summary of measured experimental and calculated simulation quantities, of experimental approaches, and of issues and challenges in the simulation and modeling of RT experiments is presented. Implicit large-eddy, direct numerical, and large-eddy simulations validated using RT experimental data are then discussed. This is followed by a discussion of modeling using analytical, modal, buoyancy–drag, and turbulent transport models of RT mixing experiments. The discussion will focus on three-dimensional RT mixing arising from multimode perturbations. Finally, this focused review concludes with a perspective on future simulation, modeling, and experimental directions for further research. Research in simulation and modeling of RT unstable flows, coupled with experiments, has made significant progress over the past several decades. This overview serves as an opportunity to both discuss progress and to stimulate future research on simulation and modeling of this unique class of hydrodynamically unstable turbulent flows.

42 ENGINEERING↗
DOE OSTI2023

Mean Flow from Phase Averages in the 2D Boussinesq Equations

The atmosphere and ocean are described by highly oscillatory PDEs that challenge both our understanding of their dynamics and their numerical approximation. This paper presents a preliminary numerical study of one type of phase averaging applied to mean flows in the 2D Boussinesq equations that also has application to numerical methods. The phase averaging technique, well-known in dynamical systems theory, relies on a mapping using the exponential operator, and then an averaging over the phase. The exponential operator has connections to the Craya–Herring basis pioneered by Jack Herring to study the fluid dynamics of oscillatory, nonlinear fluid dynamics. In this paper, we perform numerical experiments to study the effect of this averaging technique on the time evolution of the solution. We explore its potential as a definition for mean flows. We also show that, as expected from theory, the phase-averaging method can reduce the magnitude of the time rate of change in the PDEs, making them potentially suitable for time stepping methods.

Wingate, Beth A.↗
DOE OSTI2012

A Description of the Full Particle Orbit Following SPIRAL Code for Simulating Fast-ion Experiments in Tokamaks

The numerical methods used in the full particle-orbit following SPIRAL code are described and a number of physics studies performed with the code are presented to illustrate its capabilities. The SPIRAL code is a test-particle code and is a powerful numerical tool to interpret and plan fast-ion experiments in Tokamaks. Gyro-orbit effects are important for fast ions in low-field machines such as NSTX and to a lesser extent in DIII-D. A number of physics studies are interlaced between the description of the code to illustrate its capabilities. Results on heat loads generated by a localized error-field on the DIII-D wall are compared to measurements. The enhanced Triton losses caused by the same localized error-field are calculated and compared to measured neutron signals. MHD activity such as tearing modes and Toroidicity-induced Alfven Eigenmodes (TAEs) have a profound effect on the fast-ion content of Tokamak plasmas and SPIRAL can calculate the effects of MHD activity on the confined and lost fast-ion population as illustrated for a burst of TAE activity in NSTX. The interaction between Ion Cyclotron Range of Frequency (ICRF) heating and fast ions depends solely on the gyro-motion of the fast ions and is captured exactly in the SPIRAL code. A calculation of ICRF absorption on beam ions in ITER is presented. The effects of high harmonic fast wave heating on the beam-ion slowing-down distribution in NSTX is also studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

General Relativistic Implicit Monte Carlo Radiation-hydrodynamics

Abstract We report on a new capability added to our general relativistic radiation-magnetohydrodynamics code, Cosmos++ : an implicit Monte Carlo (IMC) treatment for radiation transport. The method is based on a Fleck-type implicit discretization of the radiation-hydrodynamics equations, but generalized for both Newtonian and relativistic regimes. A multiple reference frame approach is used to geodesically transport photon packets (and solve the hydrodynamics equations) in the coordinate frame, while radiation–matter interactions are handled either in the fluid or electron frames then communicated via Lorentz boosts and orthonormal tetrad bases attached to the fluid. We describe a method for constructing estimators of radiation moments using path-weighting that generalizes to arbitrary coordinate systems in flat or curved spacetime. Absorption, emission, scattering, and relativistic Comptonization are among the matter interactions considered in this report. We discuss our formulations and numerical methods, and validate our models against a suite of radiation and coupled radiation-hydrodynamics test problems in both flat and curved spacetimes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Efficient and robust relaxation procedures for multi-component mixtures including phase transition

We consider a thermodynamic consistent multi-component model in multi-dimensions that is a generalization of the classical two-phase flow model of Baer and Nunziato. The exchange of mass, momentum and energy between the phases is described by additional source terms. Typically these terms are handled by relaxation procedures. Available relaxation procedures suffer from efficiency and robustness resulting in very costly computations that in general only allow for one-dimensional computations. Therefore we focus on the development of new efficient and robust numerical methods for relaxation processes. We derive exact procedures to determine mechanical and thermal equilibrium states. Further we introduce a novel iterative method to treat the mass transfer for a three component mixture. All new procedures can be extended to an arbitrary number of inert ideal gases. We prove existence, uniqueness and physical admissibility of the resulting states and convergence of our new procedures. Efficiency and robustness of the procedures are verified by means of numerical computations in one and two space dimensions. - Highlights: • We develop novel relaxation procedures for a generalized, thermodynamically consistent Baer–Nunziato type model. • Exact procedures for mechanical and thermal relaxation procedures avoid artificial parameters. • Existence, uniqueness and physical admissibility of the equilibrium states are proven for special mixtures. • A novel iterative method for mass transfer is introduced for a three component mixture providing a unique and admissible equilibrium state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Level 2 Milestone: Develop and Incorporate Novel Code Verification of Fundamental Equations in Gemma and Set Up Appropriate Tests

For computational physics simulations, code verification plays a major role in establishing the credibility of the results by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, surface integral equations, such as the method-of-moments implementations of the electric-, magnetic-, and combinedfield integral equations, are frequently used to solve Maxwell’s equations on the surfaces of electromagnetic scatterers. These electromagnetic surface integral equations yield many code-verification challenges due to the various sources of numerical error and their possible interactions. In this report, we provide approaches to separately measure the numerical errors arising from these different error sources. We demonstrate the effectiveness of these approaches in Gemma.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2012

Numerical and Experimental Investigations of Polyurethane Foam for Use as Cask Impact Limiter in Accidental Drop Scenarios - 12099

Rigid, closed-cell polyurethane foams are frequently used as cask impact limiters in nuclear materials and hazardous waste transport due to their high energy-absorption potential. When assessing the cask integrity in accidental scenarios based on numerical simulations, a description of the foam damping properties is required for different strain rates and for a wide temperature range with respect to waste heat generation in conjunction with critical operating and environmental conditions. Implementation and adaption of a respective finite element material model strongly relies on an appropriate experimental data base. Even though extensive impact experiments were conducted e.g. in Sandia National Laboratories, Savannah River National Laboratory and by Rolls Royce plc, not all relevant factors were taken into account. Hence, BAM who is in charge of the mechanical evaluation of such packages within the approval procedure in Germany, incorporated systematic test series into a comprehensive research project aimed to develop numerical methods for a couple of damping materials. In a first step, displacement driven compression tests have been performed on confined, cubic specimens at five loading rates ranging from 0.02 mm/s to 3 m/s at temperatures between +90 deg. C and -40 deg. C. Materials include two different polyurethane foam types called FR3718 and FR3730 having densities of 280 kg/m{sup 3} and 488 kg/m{sup 3} from the product line-up of General Plastics Manufacturing Company. Their data was used to adapt an advanced plasticity model allowing for reliably simulating cellular materials under multi-axial compression states. Therefore, an automated parameter identification procedure had been established by combining an artificial neural network with local optimization techniques. Currently, the selected numerical material input values are validated and optimized by means of more complex loading configurations with the prospect of establishing methods applicable to impact limiters under severe accidental conditions. The reference data base is provided by experiments, where weights between 212 kg and 1200 kg have been dropped from heights between 1.25 m and 7 m on confined 10 cm cubic foam specimens. By presenting the deviations between experimental values and the corresponding output of finite element simulations, the potentials and restrictions of the resulting models are highlighted. Systematic compression tests on polyurethane foams had been performed at BAM test site within the framework of a research project on impact limiters for handling casks for radioactive waste. The experimental results had been used to adapt numerical models for simulating the behaviour of different foam types at different temperatures. The loading speed, however, turned out to have a major influence on their flow curves that can not be captured by simple strain-rate dependent multipliers. Especially for guided drop tests that come close to real accidental scenarios there is a significant gap between experimental and numerical results even when applying such advanced material models. Hence, the extensive data base is currently deployed for expanding the standard algorithms to include adequate dynamic hardening factors. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2015

On the numerical treatment of dissipative particle dynamics and related systems

We review and compare numerical methods that simultaneously control temperature while preserving the momentum, a family of particle simulation methods commonly used for the modelling of complex fluids and polymers. The class of methods considered includes dissipative particle dynamics (DPD) as well as extended stochastic-dynamics models incorporating a generalized pairwise thermostat scheme in which stochastic forces are eliminated and the coefficient of dissipation is treated as an additional auxiliary variable subject to a feedback (kinetic energy) control mechanism. In the latter case, we consider the addition of a coupling of the auxiliary variable, as in the Nosé–Hoover–Langevin (NHL) method, with stochastic dynamics to ensure ergodicity, and find that the convergence of ensemble averages is substantially improved. To this end, splitting methods are developed and studied in terms of their thermodynamic accuracy, two-point correlation functions, and convergence. In terms of computational efficiency as measured by the ratio of thermodynamic accuracy to CPU time, we report significant advantages in simulation for the pairwise NHL method compared to popular alternative schemes (up to an 80% improvement), without degradation of convergence rate. The momentum-conserving thermostat technique described here provides a consistent hydrodynamic model in the low-friction regime, but it will also be of use in both equilibrium and nonequilibrium molecular simulation applications owing to its efficiency and simple numerical implementation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M and C 2013

The Mathematics and Computation Division of the American Nuclear (ANS) and the Idaho Section of the ANS hosted the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M and C 2013). This proceedings contains over 250 full papers with topics ranging from reactor physics; radiation transport; materials science; nuclear fuels; core performance and optimization; reactor systems and safety; fluid dynamics; medical applications; analytical and numerical methods; algorithms for advanced architectures; and validation verification, and uncertainty quantification.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

RELAP-7 Beta Release: Summary of Capabilities

RELAP-7 is a nuclear systems safety analysis code being developed at the Idaho National Laboratory (INL). Building upon the decades of software development at the INL, we began the development of RELAP-7 in 2011 to support the Risk Informed Safety Margins Characterization (RISMC) Pathway. As part of this development, the first lines of RELAP-7 code were committed to the software revision control repository on November 7th, 2011. The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical methods, and physical models in order to provide capabilities needed for the RISMC methodology and to support nuclear power safety analysis. RELAP-7 is built using the INL’s modern scientific software development framework, MOOSE (Multi-physics Object Oriented Simulation Environment). MOOSE provides improved numerical calculations (including higher-order integration in both space and time, yielding converged second-order accuracy). The RELAP-7 code structure is based on multiple physical component models such as pipes, junctions, pumps, etc. Each component can have options for different fluid models such as single- and two-phase flow. This component-based and physics-based software architecture allows RELAP-7 to adopt different physical models for different applications. A relatively new two-phase hydrodynamic model, termed the ''7-Equation model'' for two phasic pressures, velocities, energies, and volumetric fraction, is incorporated into RELAP-7 for liquid-gas (water-steam) flows. This new model allows second-order integration because it is well-posed, which will reduce the numerical error associated with traditional systems analysis codes. In this paper, we provide a RELAP-7 capability list describing analysis features, range of applicability, and reactor components that will be available for the December 15th, 2014 beta release of the software.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

Investigation of different magnetic field configurations using an electrical, modular Zeeman slower

We present a method of constructing an automatically reconfigurable, modular, electronic Zeeman slower, which is remotely controlled. This setup is used to investigate the ability of different magnetic field profiles to slow thermal atoms to the capture velocity of a magneto-optical-trap. We show that a simple numerical optimization process yields better results than the commonly used approach for deciding on the appropriate field and comes close to the optimum field, found by utilizing a fast feedback loop which uses a genetic algorithm. Our new numerical method is easily adaptable to a variety of existing slower designs and may be beneficial where feedback is unavailable.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Effective conductivity of the rectangular and hexagonal tessellations in the plane

The effective conductivity of the two-dimensional periodic polygonal tessellations in the plane is determined using the perturbation theory and numerically. A diagram technique in perturbation theory for the effective conductivity of the tesselations in the plane is established using oblique coordinates. Calculations for the three color hexagonal tesselation have been carried out. A numerical method is developed for obtaining effective conductivity with high accuracy both when the perturbation theory is applicable and when the conductivities of the tessellation components are substantially different. For small differences between the conductivities of the components, the approach of the perturbation theory agrees with the numerical results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A semi-Lagrangian transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows

For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier–Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle–particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

The lattice Boltzmann method for isothermal micro-gaseous flow and its application in shale gas flow: A review

The lattice Boltzmann method (LBM) has experienced tremendous advances and been well accepted as a popular method for simulating various fluid flow problems in porous media. With the introduction of an effective relaxation time and slip boundary conditions, the LBM has been successfully extended to solve micro-gaseous transport phenomena. As a result, the LBM has the potential to become an effective numerical method for gas flow in shale matrix in slip flow and transition flow regimes. Additionally, it is very difficult to experimentally determine the permeability of extremely low permeable media like shale. An extensive review on a number of slip boundary conditions and Knudsen layer treatments used in LB models for micro-gaseous flow is carried out. Furthermore, potential applications of the LBM in flow simulation in shale gas reservoirs on pore scale and representative elementary volume (REV) scale are evaluated and summarized. Finally, our review indicates that the LBM is capable of capturing gas flow in continuum to slip flow regimes which cover significant proportion of the pores in shale gas reservoirs and identifies opportunities for future research.

02 PETROLEUM↗
DOE OSTI2011

A posteriori error analysis for a cut cell finite volume method

We study the solution of a diffusive process in a domain where the diffusion coefficient changes discontinuously across a curved interface. We consider discretizations that use regularly-shaped meshes, so that the interface “cuts” through the cells (elements or volumes) without respecting the regular geometry of the mesh. Consequently, the discontinuity in the diffusion coefficients has a strong impact on the accuracy and convergence of the numerical method. This motivates the derivation of computational error estimates that yield accurate estimates for specified quantities of interest. For this purpose, we adapt the well-known adjoint based a posteriori error analysis technique used for finite element methods. In order to employ this method, we describe a systematic approach to discretizing a cut-cell problem that handles complex geometry in the interface in a natural fashion yet reduces to the well-known Ghost Fluid Method in simple cases. We test the accuracy of the estimates in a series of examples.

97 MATHEMATICS AND COMPUTING↗