SEARCH · Engineering Papers

Results for “BOUNDARY CONDITIONS”

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.

SourceResearch connectionFrom yearThrough year

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

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

NASA NTRS1985

The Control of Float Zone Interfaces by the Use of Selected Boundary Conditions

Since the float zone process involves two solid-melt interfaces, possible gas interfaces, heat and mass transfers, various driving forces and complex heating sources, an analysis of the entire process would be very complex. For an initial investigation, a more feasible approach is to examine each component of the process separately. The three principal components are: (1) the shapes of the melt and solid-melt interfaces, (2) the heat and mass transfers, and (3) the heating and cooling sources. This study combined facets of all three components. The purpose of this effort was to study and compute the surface boundary conditions required to give flat (float zone) FZ solid-melt interfaces. This study was undertaken in two phases. The first phase was to investigate the solid zones surface boundary conditions required for flat solid-melt interfaces when given the melt zone surface boundary conditions. The second phase complemented the first and was to investigate the melt zone surface boundary conditions required for flat solid-melt interfaces if given the solid zones surface boundary conditions. Dual integral transform methods were used in both phases; in addition, the use of various numerical methods for differential equations and linear systems of equations were required.

Foster, L. M.↗

DOE OSTI2021

An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems

In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ 2 ) in the L∞(Ω) norm, which is optimal considering the O(δ 2 ) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Finally, based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ 2 ) convergence.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Maxwell boundary condition and velocity dependent accommodation coefficient

A modification of Maxwell's boundary condition for the Boltzmann equation is developed that allows to incorporate velocity dependent accommodation coefficients into the microscopic description. As a first example, it is suggested to consider the wall-particle interaction as a thermally activated process with three parameters. A simplified averaging procedure leads to jump and slip boundary conditions for hydrodynamics. Coefficients for velocity slip, temperature jump, and thermal transpiration flow are identified and compared with those resulting from the original Maxwell model and the Cercignani-Lampis model. An extension of the model leads to temperature dependent slip and jump coefficients.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1985

Application of radiative boundary conditions to nonhydrostatic primitive equation models

A procedure is presented for applying a radiative boundary condition to the lateral boundary of a limited domain model. The model considered, the Terminal Area Simulation System (TASS), has nonhydrostatic compressible and unsteady governing equations. The primary applications to date have been studies of downbursts, wind shear, thunderstorms and mass fires. A time-splitting integration is used with TASS, with the acoustic terms being integrated separately with a smaller time step. A first-order closure approximation is employed to ensure subgrid turbulence closure. TASS applications for two-dimensional axisymmetric and three-dimensional simulations are described. The radiative boundary conditions were applied in the two-dimensional case to the temperature, pressure and non-normal velocity components. Solutions in both cases avoided runaway circulations and experienced minimal domain-wide mass loss. Also, distorsion was minimized at the boundaries.

Proctor, F. H.↗

DOE OSTI2020

Numerical study of heat transfer enhancement in laminar and turbulent flow in enhanced tubes with uniform and non-uniform thermal boundary conditions

Various types of tube enhancements have been proposed in order to increase heat transfer while minimizing any associated increases in pressure drop. This paper presents a numerical study of two different types of enhanced tubes: the relatively common twisted tape insert tube, and a novel tube with airfoil shaped pins on the inner surface. Each tube is studied in both the laminar and turbulent flow regime. In addition to the typical constant temperature and constant flux boundary conditions, a non-constant heat flux boundary condition is applied on one half of the tube, a situation which may be encountered when absorbing solar radiation. In general, each type of enhanced tube offers a thermal performance factor greater than unity at certain Re. In addition, the non-uniform heat flux boundary condition appears to function similarly as the uniform heat flux boundary condition.

Sandlin, Matthew J.↗

DOE OSTI2024

Numerical study of heat transfer enhancement in laminar and turbulent flow in enhanced tubes with uniform and non-uniform thermal boundary conditions

Sandlin, M↗

DOE OSTI2014

On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition

We consider an elliptic operator in a multidimensional domain with frequently changing boundary conditions in the case when the homogenized operator contains the Dirichlet boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain estimates for the rate of convergence. A complete asymptotic expansion is constructed for the resolvent when it acts on sufficiently smooth functions. Bibliography: 41 titles.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1994

Boundary Conditions for Jet Flow Computations

Ongoing activities are focused on capturing the sound source in a supersonic jet through careful large eddy simulation (LES). One issue that is addressed is the effect of the boundary conditions, both inflow and outflow, on the predicted flow fluctuations, which represent the sound source. In this study, we examine the accuracy of several boundary conditions to determine their suitability for computations of time-dependent flows. Various boundary conditions are used to compute the flow field of a laminar axisymmetric jet excited at the inflow by a disturbance given by the corresponding eigenfunction of the linearized stability equations. We solve the full time dependent Navier-Stokes equations by a high order numerical scheme. For very small excitations, the computed growth of the modes closely corresponds to that predicted by the linear theory. We then vary the excitation level to see the effect of the boundary conditions in the nonlinear flow regime.

Hayder, M. E.↗

DOE OSTI2016

Thermodynamically admissible boundary conditions for the regularized 13 moment equations

A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump, and thermal creep coefficients with linearized Boltzmann solutions for Maxwell’s accommodation model for different values of the accommodation coefficient. For this, the linearized R13 equations are solved for viscous slip, thermal creep, and temperature jump problems and the results are compared to the solutions of the linearized Boltzmann equation. The influence of different collision models (hard-sphere, Bhatnagar–Gross–Krook, and Maxwell molecules) and accommodation coefficients on the phenomenological coefficients is studied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2005

A Robust Absorbing Boundary Condition for Compressible Flows

An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper by the author. The absorbing NRBC technique is based on a first principle of non reflecting, which contains the essential physics that a plane wave solution of the Euler equations remains intact across the boundary. The technique is theoretically shown to work for a large class of finite volume approaches. When combined with the hyperbolic conservation laws, the NRBC is simple, robust and truly multi-dimensional; no additional implementation is needed except the prescribed physical boundary conditions. Several numerical examples in multi-dimensional spaces using two different finite volume schemes are illustrated to demonstrate its robustness in practical computations. Limitations and remedies of the technique are also discussed.

Loh, Ching Y.↗

NASA NTRS1995

A far-field non-reflecting boundary condition for two-dimensional wake flows

Far-field boundary conditions for external flow problems have been developed based upon long-wave perturbations of linearized flow equations about a steady state far field solution. The boundary improves convergence to steady state in single-grid temporal integration schemes using both regular-time-stepping and local-time-stepping. The far-field boundary may be near the trailing edge of the body which significantly reduces the number of grid points, and therefore the computational time, in the numerical calculation. In addition the solution produced is smoother in the far-field than when using extrapolation conditions. The boundary condition maintains the convergence rate to steady state in schemes utilizing multigrid acceleration.

Danowitz, Jeffrey S.↗

NASA NTRS1981

Stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations

Implicit, noniterative, finite difference schemes were recently developed by several authors for multidimensional systems of nonlinear hyperbolic partial differential equations. When applied to linear model equations with periodic boundary conditions those schemes are unconditionally stable (A-stable). As applied in practice the algorithms often face a severe time step restriction. A major source of the difficulty is the treatment of the numerical boundary conditions. One conjecture was that unconditional stability requires implicit numerical boundary conditions. An apparent counter example was the space time extrapolation considered by Gustafsson, Kreiss, and Sunstrom. Spatial (implicit) and space time (explicit) extrapolation using normal mode analysis for a finite and infinite number of spatial mesh intervals are examined. The results indicate that for unconditional stability with a finite number of spatial mesh intervals, the numerical boundary conditions must be implicit.

Beam, R. M.↗

NASA NTRS1982

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

Source record↗

NASA NTRS1984

A rule for selecting analytical boundary conditions for the conservative quasi-one-dimensional nozzle flow equations

For the one-dimensional nozzle flow equations, the number of analytical boundary conditions that may be applied corresponds to the number of exterior characteristics reaching the boundary points. Since the slopes of the characteristics are the characteristic speeds u, u+c, and u-c, one concludes that two analytical boundary conditions are required at a subsonic inflow boundary and one at a subsonic outflow boundary. However, using this guideline alone can lead to nonunique solutions in subsonic cases. This paper presents a rule for selecting analytical boundary conditions for the dependent variables which will yield unique solutions if they exist.

Wornom, S. F.↗

DOE OSTI2016

ALmost EXact boundary conditions for transient Schrödinger–Poisson system

For the Schrödinger–Poisson system, we propose an ALmost EXact (ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank–Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. [1], yet at a much reduced complexity. Primary peaks in wave function profile appear as a consequence of quantum resonance, and should be considered in selecting the cut-off wave number for numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Assessing boundary condition and parametric uncertainty in numerical-weather-prediction-modeled, long-term offshore wind speed through machine learning and analog ensemble

To accurately plan and manage wind power plants, not only does the time-varying wind resource at the site of interest need to be assessed but also the uncertainty connected to this estimate. Numerical weather prediction (NWP) models at the mesoscale represent a valuable way to characterize the wind resource offshore, given the challenges connected with measuring hub-height wind speed. The boundary condition and parametric uncertainty associated with modeled wind speed is often estimated by running a model ensemble. However, creating an NWP ensemble of long-term wind resource data over a large region represents a computational challenge. Here, we propose two approaches to temporally extrapolate wind speed boundary condition and parametric uncertainty using a more convenient setup in which a mesoscale ensemble is run over a short-term period (1 year), and only a single model covers the desired long-term period (20 year). We quantify hub-height wind speed boundary condition and parametric uncertainty from the short-term model ensemble as its normalized across-ensemble standard deviation. Then, we develop and apply a gradient-boosting model and an analog ensemble approach to temporally extrapolate such uncertainty to the full 20-year period, for which only a single model run is available. As a test case, we consider offshore wind resource characterization in the California Outer Continental Shelf. Both of the proposed approaches provide accurate estimates of the long-term wind speed boundary condition and parametric uncertainty across the region (R 2 >0.75), with the gradient-boosting model slightly outperforming the analog ensemble in terms of bias and centered root-mean-square error. At the three offshore wind energy lease areas in the region, we find a long-term median hourly uncertainty between 10 % and 14 % of the mean hub-height wind speed values. Finally, we assess the physical variability in the uncertainty estimates. In general, we find that the wind speed uncertainty increases closer to land. Also, neutral conditions have smaller uncertainty than the stable and unstable cases, and the modeled wind speed in winter has less boundary condition and parametric sensitivity than summer.

17 WIND ENERGY↗

DOE OSTI2015

A boundary condition to the Khokhlov-Zabolotskaya equation for modeling strongly focused nonlinear ultrasound fields

An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.

42 ENGINEERING↗

NASA NTRS1997

A Smoothed Boundary Condition for Reducing Nonphysical Field Effects

In this paper, we examine the problem associated with abruptly mixing boundary conditions in the context of a two-dimensional semiconductor device simulator. Explicitly, this paper addresses the transition between an ohmic-type Dirichlet condition and a passivated Neumann boundary. In the traditional setting, the details or the transition between the two boundary types are not addressed and an abrupt transition is assumed. Subsequently, the calculated observables (most notably the potential) exhibit discontinuous derivatives near the surface at the point where the boundary type switches. This paper proposes an alternative condition which models the progression between the two boundary types through the use of a finite length, smoothed boundary whereby the numerical discontinuities are eliminated. The physical and mathematical basis for this smoothed boundary condition is discussed and examples of the technique's implementation given. It is found that the proposed boundary condition is numerically efficient and can be implemented in pre-existing device simulators with relative ease.

Smith, Arlynn W.↗