SEARCH · Search NASA
Results for “Boundary condition”
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.
Validity condition for the local sheath impedance boundary condition and a nonlocal generalization
ICRF sheaths can cause unwanted interactions of high-power RF waves with material surfaces in magnetic fusion devices. In previous work, a local RF sheath impedance boundary condition (BC) was derived for use in ICRF codes together with a microscale (i.e., Debye or sheath width scale) model for obtaining the sheath impedance used in that BC. This local RF sheath BC matches the normal component of current and electrostatic potential across the sheath-plasma interface. Collapsing the matching conditions at the sheath-plasma interface to a BC depends on the assumption of scale separation, which can be violated when conditions along the local radius of curvature of the surface vary sufficiently rapidly. The validity condition is explored in this contribution, with special attention to the case where the magnetic field approaches being tangent to the surface. When the local sheath BC no longer applies, a non-local sheath BC is developed under the assumption of a more relaxed scale separation assumption. It is shown that the non-local sheath BC reduces to the previous local sheath BC under appropriate conditions. Furthermore, a surface-integrated sheath admittance parameter describes the 2D physics in the new BC.
Chiral propulsion: The method of effective boundary conditions
We propose to apply an “effective boundary condition” method to the problem of chiral propulsion. For the case of a rotating helix moving through a fluid at a low Reynolds number, the method amounts to replacing the original helix (in the limit of small pitch) by a cylinder, but with a special kind of partial slip boundary conditions replacing the non-slip boundary conditions on the original helix. These boundary conditions are constructed to reproduce far-field velocities of the original problem and are defined by a few parameters (slipping lengths) that can be extracted from a problem in planar rather than cylindrical geometry. We derive the chiral propulsion coefficients for spirals, helicoids, helically modulated cylinders and some of their generalizations using the introduced method. In the case of spirals, we compare our results with the ones derived by Lighthill and find a very good agreement. Here, the proposed method is general and can be applied to any helical shape in the limit of a small pitch. Furthermore, we have established that for a broad class of helical surfaces the dependence of the chiral propulsion on the helical angle θ is universal, x ~ cos θ sin 2θ with the maximal propulsion achieved at the universal angle θ m = tan –1 (1/√2) ≈ 35.26°.
Stochastic boundary condition effects on supersonic leading edge blowing
The present manuscript studies the robustness of leading edge blowing for active control of the upstream bow shock and overall aerothermal characteristics of a supersonic airfoil subject to variability in the injection conditions. The injection boundary conditions were considered stochastic and their randomness was propagated to the flow topology and aerothermal quantities of interest by means of non-intrusive Polynomial Chaos Expansions. The evaluations needed to build these expansions were carried out via steady two-dimensional Reynolds-Averaged Navier Stokes simulations. Two different injection port sizes were considered, with the smallest promoting a Coanda effect that gives rise to non-symmetric flow topologies. The uncertain boundary conditions lead to significant variations in the flow topology, particularly at the injection exit and the bow shock position, with variations of up to 75% of the nominal value. Here this study identifies the key operating conditions to ensure the optimal application of leading-edge injection for active control of supersonic airfoils.
Considering computational speed vs. accuracy: Choosing appropriate mesoscale RVE boundary conditions
Modeling a material’s microstructure using continuum theories allows for inspection of the relationship between coarse scale and fine scale behaviors. Computational limits generally require selection of a sub-volume from a bulk sample in order to directly model the microstructure. Boundary conditions are applied to the sub-volume to mimic the excluded bulk material. Appropriate selection of boundary conditions helps effectively determine the appropriate spatial scale required of the sub-volume. Applicable boundary conditions include direct displacement, periodic, and uniform traction. While direct displacement and periodic boundary conditions are commonly used, uniform traction boundary conditions have seen limited use due to rigid body stability issues in simulations of compression or shear deformation. A new application of uniform traction boundary conditions was developed through linear constraint equations, similar to approaches employed by direct displacement and periodic boundary conditions, to quench rigid body motions with minimal interference of the relative deformation of the model. These boundary conditions were tested by compressing several synthetically generated periodic microstructures using the finite element method. Evaluating the effective stiffness along the compression axis, the direct displacement boundary condition produced the stiffest response, whereas the uniform traction boundary condition produced the most compliant. Periodic boundary conditions produced the same response for all volumes analyzed and both the direct displacement and uniform traction boundary conditions trended toward the periodic response as the domain volume increased. Computational performance was also evaluated for each boundary condition using implicit and explicit solvers. Direct displacement boundary conditions presented the lowest computational cost of all of the boundary conditions followed by periodic then uniform traction. The computational expense of periodic and uniform traction boundary conditions limited the viable spatial scale and mesh resolutions able to be simulated. Selection of appropriate boundary conditions for specific uses need to be a balance between allowable computational expense and accuracy of the method. Techniques for evaluating which boundary conditions to use are discussed.
Testing horizontal momentum boundary conditions in MPAS-Ocean
A rising concern within E3SM’s MPAS-Ocean is the implementation of boundary conditions. Currently, MPAS-Ocean utilizes a no-slip boundary condition, meaning that the velocity of fluid at the boundaries is zero; however, the model should should satisfy both no-slip and free-slip boundary conditions given the correct parameters. This study focuses on testing these boundary conditions in depth, determining the accuracy of the current implementation. To accomplish this, we focus on two test cases: the barotropic gyre and barotropic channel. By manipulating parameters and comparing the numerical to corresponding analytical solutions (when available), we show that MPAS-Ocean’s ability to satisfy both boundary conditions is promising.
Effects of Horizontal Resolution, Domain Size, Boundary Conditions, and Surface Heterogeneity on Coarse LES of a Convective Boundary Layer
Atmospheric properties in a convective boundary layer vary over a wide range of spatial scales and are commonly studied using large-eddy simulations (LES) in various configurations. We examine how the boundary layer depth and distribution of variability across scales are affected by LES grid spacing, domain size, inhomogeneity of surface properties, and external forcing. Two different setups of the Weather Research and Forecasting (WRF) model are analyzed. A semi-idealized configuration uses a periodic domain, flat surface, prescribed homogeneous surface heat fluxes, and horizontally uniform profiles of large-scale advective tendencies. A nested LES setup employs a larger domain and realistic initial and boundary conditions, including an interactive land surface model with representative topography and vegetation and soil types. Subdomains of identical size are analyzed for all simulations. Characteristic structure sizes are quantified using the variability scales L 50 and L 95 , defined such that features smaller than that contain 50% and 95% of the total variance, respectively. Progressive increase in L 50 from vertical velocity to temperature and moisture structures is systematically reproduced in all simulation configurations. This dependence of L 50 on the considered variable complicates the development of scale-aware parameterizations for models with grid spacing in the “terra incognita”. In simulations using a larger domain with heterogeneous surface properties, the development of internal mesoscale patterns significantly affects variance distributions inside analyzed subdomains. Sizes of boundary layer structures also strongly depend on the LES grid spacing and, in case of heterogeneous surface and topography, on location of the subdomain inside a larger computational domain.
Extended FFT-based micromechanical formulation to consider general non-periodic boundary conditions
Here, this paper presents a new approach for applying non-periodic boundary conditions in the context of FFT-based methods to solve micromechanical problems in heterogeneous solids. The domain of the original problem is extended to satisfy the periodicity requirements at the boundary of the extended domain. The velocity constraint on the boundary of the original domain is replaced by a corresponding constraint on the velocity gradient in the extended volume, and a two-level augmented Lagrangian method is used to enforce the constraint. The proposed method is implemented as an extension of the large-strain elasto-viscoplastic FFT-based (LS-EVPFFT) model of Zecevic et al. (2022). The proposed method is verified in the cases of fully imposed velocity boundary conditions and mixed velocity/traction-free boundary conditions. The accuracy and convergence of the method are studied next, followed by applications to bending and indentation of polycrystals that illustrate the extended capabilities of the proposed formulation.
A phase-shift-periodic parallel boundary condition for low-magnetic-shear scenarios
Abstract We formulate a generalized periodic boundary condition as a limit of the standard twist-and-shift parallel boundary condition that is suitable for simulations of plasmas with low magnetic shear. This is done by applying a phase shift in the binormal direction when crossing the parallel boundary. While this phase shift can be set to zero without loss of generality in the local flux-tube limit when employing the twist-and-shift boundary condition, we show that this is not the most general case when employing periodic parallel boundaries, and may not even be the most desirable. A non-zero phase shift can be used to avoid the convective cells that plague simulations of the three-dimensional Hasegawa–Wakatani system, and is shown to have measurable effects in periodic low-magnetic-shear gyrokinetic simulations. We propose a numerical program where a sampling of periodic simulations at random pseudo-irrational flux surfaces are used to determine physical observables in a statistical sense. This approach can serve as an alternative to applying the twist-and-shift boundary condition to low-magnetic-shear scenarios, which, while more straightforward, can be computationally demanding.
Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries
Here, we propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the variational formulation is appropriately modified to enforce free-slip wall boundary conditions, without perturbing the structure of the function spaces used to represent the solution, with a considerable simplification with respect to traditional approaches. Total energy is conserved and the resulting mass matrices are constant in time. The robustness and accuracy of the proposed method are validated with an extensive set of tests involving nontrivial curved boundaries.
Boundary conditions for extremal black holes from 2d gravity
We devise new boundary conditions for the near-horizon geometries of extremal BTZ and Kerr black holes, as well as for the ultra-cold limit of the Kerr-de Sitter black hole. These boundary conditions are obtained as the higher-dimensional uplift of recently proposed boundary conditions in two-dimensional gravity. Their asymptotic symmetries consist in the semi-direct product of a Virasoro and a current algebra, of which we determine the central extensions.
On nonlocal problems with Neumann boundary conditions: scaling and convergence for nonlocal operators and solutions
Formulations of Neumann-type boundary conditions for boundary value problems in the nonlocal framework are beset with difficulties, some related to the choice of a proper scaling. Here we identify a space-dependent scaling for a nonlocal Neumann operator, for which we prove linear in δ (δ being the radius for the support for the kernel) convergence of the Neumann operator and $\mathcal{O}$(δ 2 ) convergence of solutions to their classical counterparts. The pointwise-like convergence of the nonlocal normal operator is cast as a new type of two-scale operator-point convergence, which we call condensated convergence . The results hold for general integrable kernels, a setting which is favored in numerical simulations. We support this analysis with numerical convergence studies using a piecewise linear discontinuous Galerkin discretization and show an $\mathcal{O}$(δ 2 ) rate of convergence of solutions, also exhibiting an $\mathcal{O}$(h 2 ) convergence, where h is the mesh size.
Computational Characterization and Boundary Condition Models of a Jet Interaction Fluidic Oscillator
Fluidically oscillating jet actuators that generate sweeping jets when supplied with a pressurized fluid have been used to mitigate separation and reduce drag in a range of flow control applications. Their implementation in future flight vehicles would require fundamental understanding and accurate predictive techniques of the physics of their internal flow and jet formation. The present investigations focus on high-fidelity, time-accurate simulations to characterize the flow physics of the actuator in quiescent conditions. An important element of the present simulations is to demonstrate the ability of the computational fluid dynamics (CFD) solver to predict the jet characteristics and provide a basis for the development of improved boundary conditions (BC) without entirely resolving the geometrical features of the fluidic device. The CFD-predicted oscillation frequencies of the engendered jets were found to be in excellent agreement with experiments, even on two-dimensional meshes. The study revealed that three-dimensional simulations are required to capture some of the flow features of the sweeping jet such as the double peak in time-averaged velocity distributions downstream of the actuator’s orifice that were measured in experiments. Furthermore, several approaches for modeling the actuator were implemented and assessed in quiescent conditions. The evaluation of a boundary condition at the device throat, based on the phase-averaged flow variables, provides the basis for devising surface-based boundary conditions. The influence and necessity of including turbulent characteristics as part of the boundary conditions have also been identified.
Quantum properties of non-Dirichlet boundary conditions in gravity
The Euclidean path integral for gravity is enriched by the addition of boundaries, which provide useful probes of thermodynamic properties. Common boundary conditions include Dirichlet conditions on the boundary induced metric; microcanonical conditions, which refers to fixing some components of the Brown-York boundary stress tensor; and conformal conditions, in which the conformal structure of the induced metric and the trace of the extrinsic curvature are fixed. Boundaries also present interesting problems of consistency. The Dirichlet problem is known, under various (and generally different) conditions, to be inconsistent with perturbative quantization of graviton fluctuations, to exhibit thermodynamic instability, or to require infinite fine-tuning in the presence of matter fluctuations. We extend some of these results to other boundary conditions. We find that similarly to the Dirichlet problem, the graviton fluctuation operator is not elliptic with microcanonical boundaries, and the nonelliptic modes correspond to “boundary-moving diffeomorphisms.” However, we argue that microcanonical factorization of path integrals—essentially, the insertion of microcanonical constraints on two-sided surfaces in the bulk—is not affected by the same issues of ellipticity. We also show that for a variety of matter field boundary conditions, matter fluctuations renormalize the gravitational bulk and boundary terms differently, so that the classical microcanonical or conformal variational problems are not preserved unless an infinite fine-tuning is performed.
Impact of inland boundary conditions on seawater intrusion modeling in stratified coastal aquifers under sea-level rise
This study systematically examines the impact of inland boundary conditions on seawater intrusion modeling in general stratified coastal aquifers under sea-level rise (SLR). We derived analytical solutions for seawater wedge toe positions in stratified aquifers with general head boundary (GHB) conditions and compiled solutions for constant head boundary (CHB), constant flux boundary (CFB), and GHB conditions in both homogeneous and stratified aquifers. Additionally, we introduced the concept of equivalent boundary conditions and developed equations to ensure consistent steady-state toe positions across different boundary types. Unlike previous studies focusing on specific layering configurations, we conducted a comprehensive sensitivity analysis of seawater intrusion in general stratified aquifers using transmissivity centroid elevation (TCE). Our results show that SLR generally exacerbates seawater intrusion, with unconfined aquifers exhibiting higher sensitivity across all boundary conditions. Among boundary types, CHB conditions were the most sensitive to SLR, CFB the least, and GHB showed an intermediate response depending on its distance from the model boundary. Furthermore, seawater intrusion increases with the TCE of the stratified aquifer under SLR, suggesting that high-permeability or preferential flow layers near the surface amplify the impact of SLR. These findings emphasize the importance of selecting appropriate boundary conditions when evaluating SLR-driven seawater intrusion in stratified coastal aquifers.
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.
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.
Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations
Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. Here in this work, we describe a discretization of viscous terms in the compressible Navier-Stokes equations which enables a simple and explicit imposition of entropy stable no-slip and reflective (symmetry) wall boundary conditions for discontinuous Galerkin (DG) discretizations. Specifically, we derive methods for imposing adiabatic no-slip and reflective (symmetry) boundary conditions for modal entropy stable DG formulations which preserve a semi-discrete entropy inequality. Numerical results confirm the robustness and accuracy of the proposed approaches.