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Mathematical solution for doubly-connected regions with contiguous circular boundaries, and treatment of half-plane with one circular hole and plane with two equal holes
Problems involving mesh motion-which should not be mistakenly associated with moving mesh methods, a class of adaptive mesh redistribution techniques-are of critical importance in numerical simulations of the thermal response of melting and ablative materials. Ablation is the process by which material vaporizes or otherwise erodes due to strong heating. Accurate modeling of such materials is of the utmost importance in design of passive thermal protection systems ("heatshields") for spacecraft, the layer of the vehicle that ensures survival of crew and craft during re-entry. In an explicit mesh motion approach, a complete thermal solve is first performed. Afterwards, the thermal response is used to determine surface recession rates. These values are then used to generate boundary conditions for an a posteriori correction designed to update the location of the mesh nodes. Most often, linear elastic or biharmonic equations are used to model this material response, traditionally in a finite element framework so that complex geometries can be simulated. A simple scheme for moving the boundary nodes involves receding along the surface normals. However, for all but the simplest problem geometries, evolution in time following such a scheme will eventually bring the mesh to intersect and "tangle" with itself, inducing failure. This presentation demonstrates a comprehensive and sophisticated scheme that analyzes the local geometry of each node with help from user-provided clues to eliminate the tangle and enable simulations on a wide-class of difficult problem geometries. The method developed is demonstrated for linear elastic equations but is general enough that it may be adapted to other modeling equations. The presentation will explicate the inner workings of the tangle-free mesh motion algorithm for both two and three-dimensional meshes. It will show abstract examples of the method's success, including a verification problem that demonstrates its accuracy and correctness. The focus of the presentation will be on the algorithm; specifics on how the techniques may be used in spacecraft design will be not discussed.
A numerical scheme is developed for computing steady supercritical flow about symmetrical airfoils, applying it to an ellipse for zero angle of attack. An algorithmic description of this new scheme is presented. Application to a symmetrical bicircular arc airfoil is also proposed. The flow field before the shock is region 1. For transonic flow, singularity can be avoided by integrating the resulting ordinary differential equations away from the body. Region 2 contains the shock which will be located by shock fitting techniques. The shock divides region 2 into supersonic and subsonic regions and there is no singularity problem in this case. The Method of Lines is used in this region and it is advantageous to integrate the resulting ordinary differential equation along the body for shock fitting. Coaxial coordinates have to be used for the bicircular arc airfoil so that boundary values on the airfoil body can be taken with one direction of the coaxial coordinates fixed. To avoid taking boundary values at + or - infinity in the coaxial co-ordinary system, approximate analytical representation of the flow field near the tips of the airfoil is proposed.
Here, the range of values of scalar fields in turbulent flows is bounded by their boundary values, for passive scalars, and by a combination of boundary values, reaction rates, phase changes, etc., for active scalars. The current investigation focuses on the local conservation of passive scalar concentration fields and the ability of the large-eddy simulation (LES) method to observe the boundedness of passive scalar concentrations. In practice, as a result of numerical artifacts, this fundamental constraint is often violated with scalars exhibiting unphysical excursions. The present study characterizes passive-scalar excursions in LES of a shear flow and examines methods for diagnosis and assesment of the problem. The analysis of scalar-excursion statistics provides support of the main hypothesis of the current study that unphysical scalar excursions in LES result from dispersive errors of the convection-term discretization where the subgrid-scale model (SGS) provides insufficient dissipation to produce a sufficiently smooth scalar field. In the LES runs three parameters are varied: the discretization of the convection terms, the SGS model, and grid resolution. Unphysical scalar excursions decrease as the order of accuracy of non-dissipative schemes is increased, but the improvement rate decreases with increasing order of accuracy. Two SGS models are examined, the stretched-vortex and a constant-coefficient Smagorinsky. Scalar excursions strongly depend on the SGS model. The excursions are significantly reduced when the characteristic SGS scale is set to double the grid spacing in runs with the stretched-vortex model. The maximum excursion and volume fraction of excursions outside boundary values show opposite trends with respect to resolution. The maximum unphysical excursions increase as resolution increases, whereas the volume fraction decreases. The reason for the increase in the maximum excursion is statistical and traceable to the number of grid points (sample size) which increases with resolution. In contrast, the volume fraction of unphysical excursions decreases with resolution because the SGS models explored perform better at higher grid resolution.
The NASTRAN Thermal Analyzer has been intended to do variance analysis and plot the thermal boundary elements. The objective of the variance analysis addition is to assess the sensitivity of temperature variances resulting from uncertainties inherent in input parameters for heat conduction analysis. The plotting capability provides the ability to check the geometry (location, size and orientation) of the boundary elements of a model in relation to the conduction elements. Variance analysis is the study of uncertainties of the computed results as a function of uncertainties of the input data. To study this problem using NASTRAN, a solution is made for both the expected values of all inputs, plus another solution for each uncertain variable. A variance analysis module subtracts the results to form derivatives, and then can determine the expected deviations of output quantities.
The distribution of grid points for calculating the solution of partial differential equations is chosen so as to include consideration of truncation error, stability, and the resolution of the solution near boundary layers and shocks. It is important to specify the distribution of points along a grid line. The problem of distributing points along a curve is considered. It is assumed that the curve is defined parametrically. The objective is to select a set of parameter values so that the corresponding points on the curves are properly distributed. The distribution is based on some intrinsic property of the curve such as arc length or curvature.
The generalized linear Boltzmann equation is a recently developed framework based on non-classical transport theory for modeling the expected value of particle flux in an arbitrary stochastic medium. Provided with a non-classical cross-section for a given statistical description of a medium, any transport problem in that medium may be solved. Previous work has only considered one-dimensional media without finite boundary conditions and discrete binary mixtures of materials. In this work the solution approach for the GLBE in multidimensional media with finite boundaries is outlined. The discrete ordinates method with an implicit discretization of the pathlength variable is used to leverage sweeping methods for the transport operator. In addition, several convenient approximations for non-classical cross-sections are introduced. The solution approach is verified against random realizations of a Gaussian process medium in a square enclosure.
The laminar steady boundary layer flow of an incompressible MHD Power-law fluid past a continuously moving surface is investigated numerically. The study involves the influence of surface slip and non-uniform heat source/sink on the flow and heat transfer. The governing boundary layer flow equations are transformed into non-dimensional, non-linear coupled ordinary differential equations with the help of suitable similarity transformations. The Galerkin finite element method is implemented to crack the resulting system. The impact of different involved physical parameters is exhibited on the dimensionless velocity profile, temperature distributions and rate of heat transfer in graphical and tabular forms for pseudoplastic and dilatant fluids. The local Nusselt number is found to be the decreasing function of slip parameter, temperature and space-dependent heat sink parameter whereas it increases with increasing values of temperature and space dependent heat source parameter. The problem has important application in attaining the sustainable heat transfer rate for the cooling of fluids, especially in heat exchangers used frequently in chemical industry, in order to increase the trustworthiness of a system, as it removes high heat loads from these systems.
The subsonic doublet-lattice method (DLM) aeroelastic analysis in NASTRAN was successfully applied to produce subsonic flutter boundary data in parameter space for a large delta wing configuration. Computed flow velocity and flutter frequency values as functions of air density ratio, flow Mach number, and reduced frequency are tabulated. The relevance and the meaning of the calculated results are discussed. Several input-deck problems encountered and overcome are cited with the hope that they may be helpful to NASTRAN Rigid Format 45 users.
Steady state radiative transport through homogeneous spherical medium, applying invariance principles of Ambartsumian and Chandrasekhar
We investigate the thermal properties of interacting spin-orbit-coupled bosons with contact interactions in two spatial dimensions. To that end, we implement the complex Langevin method, motivated by the appearance of a sign problem, on a square lattice with periodic boundary conditions. We calculate the density equation of state nonperturbatively in a range of spin-orbit couplings and chemical potentials. In this work, our results show that mean-field solutions tend to underestimate the average density, especially for stronger values of the spin-orbit coupling. Additionally, the finite nature of the simulation volume induces the formation of pseudocondensates. These have been observed to be destroyed by the spin-orbit interactions.
The wrong diurnal cycle of precipitation is a common weakness of current global climate models (GCMs). To improve the simulation of the diurnal cycle of precipitation and understand what physical processes control it, we test a convective trigger function described in Xie et al. (2019) with additional optimizations in the NCAR Community Atmosphere Model version 5 (CAM5). The revised trigger function consists of three modifications: 1) replacing the Convective Available Potential Energy (CAPE) trigger with a dynamic CAPE (dCAPE) trigger, 2) allowing convection to originate above the top of planetary boundary layer (i.e., the unrestricted air parcel launch level - ULL), and 3) optimizing the entrainment rate and threshold value of the dynamic CAPE generation rate for convection onset based on observations. Results from 1°-resolution simulations show that the revised trigger can alleviate the long-standing GCM problem of too early maximum precipitation during the day and missing the nocturnal precipitation peak that is observed in many regions, including the U.S. southern Great Plains (SGP). The revised trigger also improves the simulation of the propagation of precipitation systems downstream of the Rockies and the Amazon region. A further composite analysis over the SGP unravels the mechanisms through which the revised trigger affects convection. Additional sensitivity tests show that both the peak time and the amplitude of the diurnal cycle of precipitation are sensitive to the entrainment rate and dCAPE threshold values.
An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.
The detectability of urban land cover types is explored using digitally processed Seasat SAR imagery of the Denver, Colorado area. Test sites within the metropolitan area were selected to include a cross section of Anderson, et. al. Level II land cover classes and cover types representative of the urban area growth stages. Using the Image 100 interactive processing system each test site was level sliced in an attempt to define specific reflectance boundaries for each cover type and to determine the spectral and spatial characteristics of homogeneous response regions. The rural-urban fringe boundary was readily definable, but a precise Level I and Level II land cover classification was not possible. High density housing could be separated from low density housing and from parks, but reflectance values were often look angle dependent. Confusion between some water and vegetation responses also posed problems.
The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.
Energy of a high harmonic standing wave tends to be distributed equally over the whole wave even in a stratified medium where the wave's peak amplitude can be much larger near the upper boundary than the lower one. This fact is generalized to the many diverse physical problems which solve second-order differential equations of Sturm-Liouville type. For any such solution y(z) whose sign fluctuates along the z-axis, quantities are found which have the same value between any two neighboring zeros of y. One of the equidistributed quantities for an oscillating fluid sphere is similar to kinetic energy but is identical only in limiting cases. The acoustic midpoint of a cavity can be a unique place where some nonlinear perturbations have extra strength. This may apply to the puzzling solar phenomenon called supergranulation.
Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction, and are characterized by a complex valued frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic scattering of geometric bodies treated with acoustic liners. This work considers using either an impedance boundary condition or admittance boundary condition to allow acoustic scattering problems to be modeled with geometries consisting of both un-lined and lined surfaces; admittance is defined to be the inverse of impedance. Three different acoustic liner models will be discussed: the Extended Helmholtz Resonator Model, the Three-Parameter Impedance Model, and a Broadband Model. In the Extended Helmholtz Resonator Model and Three-Parameter Impedance Model, the liner impedance is specified at a single frequency; the Broadband Model allows for the investigation of multiple frequencies simultaneously. The impedance and admittance boundary conditions for each model will be derived and coupled with a time-domain boundary integral equation. The scattering solution will be obtained iteratively using spatial and temporal basis functions. Stability will be demonstrated through eigenvalue analysis. Moreover, fast algorithms and high performance computing are considered to both assess and reduce the computational cost of the simulation.
Along with nodal calculation, accurate pin-wise calculations with parallel computational platforms have been recently developed as alternative tools to nodal methods to maximize core performance and minimize uncertainties used in reactor safety analysis. Therefore, it is necessary to have a method for accurately reconstructing intra-pin information comparable to whole-core transport calculation while being significantly more computationally efficient. In this study, a method to reconstruct intra-pin information (intra-pin reconstruction) is proposed. This method is based on combining the local intra-pin form function with the global homogeneous distribution. The form functions are generated from a single pin calculation with reflective boundary conditions using Serpent 2, a Monte Carlo neutron transport code. The global homogeneous flux was reconstructed using the analytical solution of the diffusion equation due to its superior accuracy and speed compared to other methods. The study here is limited to a two-dimensional two-group problem of rectangular geometric fuel pin element. The pin-wise boundary constraints (BCs) and reference intra-pin power used for reconstruction and comparison were obtained from the Serpent 2 reference calculation. From our study, it is indicated that maximum relative error (MRE) between reconstructed and reference values is within 5%. In addition, a sensitivity study was also performed to assess the feasibility of the method when the proposed method is coupled with a pin-wise calculation. (authors)