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A simplified axisymmetric lattice Boltzmann method for incompressible swirling and rotating flows

PHYSICS OF FLUIDS 2019年第2期31卷 023605-023605页

作者： Chen, Z. Shu, C. Zhang, L. Q. Natl Univ Singapore Dept Mech Engn 10 Kent Ridge Crescent Singapore 119260 Singapore Natl Univ Singapore Temasek Labs 5A Engn Dr 1 Singapore 117411 Singapore

A simplified axisymmetric lattice Boltzmann method (SALBM) is developed in this paper for effective simulation of incompressible swirling and rotating flows. This model explores an alternative approach of reconstructing an axisymmetric model within the lattice Boltzmann (LB) framework. Essentially, SALBM reconstructs solutions to the macroscopic governing equations recovered from the axisymmetric LB equation through the Chapman-Enskog expansion analysis. Two variations of schemes, which bear different orders of temporal accuracy and are, respectively, suitable for the steady and the unsteady axisymmetric flow problems, can be evolved from SALBM. The proposed schemes reflect direct evolution of macroscopic variables instead of distribution functions, which could reduce the cost in virtual memory. Meanwhile, analytical interpretation of physical boundary conditions is available in SALBM which avoids tedious transformations as required in conventional LB models. numerical tests further reveal that SALBM performs better than the existing axisymmetric LB models in numerical stability. These merits endow the present SALBM with advantages over previous models and forge its prospect in engineering applications. Published under license by AIP Publishing.

关键词： Kinetic theory Laminar flows Particle distribution functions numerical algorithms Lattice Boltzmann methods

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Rate and Collision Probability of Tethers and Sails Against Debris or Spacecraft

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2019年第6期42卷 1330-1342页

作者： Garcia-Pelayo, Ricardo Gonzalo, Juan Luis Bombardelli, Claudio Tech Univ Madrid Dept Appl Phys ETSIAE Plaza Cardenal Cisneros 3 Madrid 28040 Spain Polytech Univ Milan Dept Aerosp Sci & Technol Via Giuseppe LA Masa 34 I-20156 Milan Italy

The work done on probability of collision between spherical objects in orbit is extended here to the case of one spherical object and one circular or rectangular object. The former is a model for spacecraft or debris, whereas the latter is a model for a sail or a tether. Two kinds of computations are done. The first kind is the computation of the collision rate when the flux of one object (typically debris) with respect to the other object is known. This information is important when planning a mission. The second kind is the computation of the collision probability for a particular pair of objects whose probability density functions of the positions are known. This information is necessary to decide whether an evasive maneuver will be performed or not.

关键词： Spacecrafts Probability Density Functions Satellites International Space Station Electrodynamic Tether European Space Agency numerical Integration Aspect Ratio numerical algorithms Orbital Period

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Modeling dynamic fragmentation of tempered glass

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ENGINEERING FRACTURE MECHANICS 2023年第1期289卷

作者： Stewart, Ross J. Prakash, Naveen Corning Inc Mfg Technol & Engn Div Corning NY 14831 USA

Understanding why a strengthened glass article will fragment, and to what extent, has long been incomplete. This work addresses this gap for glass plates with parabolic residual stress profiles;this can include tempered glass as well as deep chemically strengthened profiles. Various thicknesses of glass are studied to give credibility to a parameter that defines the onset of fragmentation susceptibility (frangibility limit) and an equation that predicts the number of fragments per sheet area. This equation can then be used to fit experimental data, thus allowing for back calculating the frangibility limit and dynamic toughness. This is beneficial since neither of these values is easily measurable. Future work will seek to understand how differently shaped stress profiles fit into this theoretical framework.

关键词： numerical algorithms Dynamic fracture Crack branching and bifurcation Glass material Residual stress

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Closed-Form Solution for Secondary Perturbation Displacement in Finite-Element-Implemented Koiter's Theory

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AIAA JOURNAL 2020年第4期58卷 1785-1795页

作者： Yan, Jiayi Li, Shuguang Univ Nottingham Fac Engn Nottingham NG7 2RD England Univ Nottingham Fac Engn Aerosp Composites Nottingham NG7 2RD England Zhuzhou China Railway Rolling Corp Ltd Times Elect UK Innovat Ctr 2650 Kings CourtBirmingham Business Pk Solihull B37 7YE W Midlands England

The finite-element-implemented Koiter's initial postbuckling analysis has not managed to convince commercial finite element code developers to incorporate it into their codes to benefit structural designers and analysts. Three key obstacles have been identified. With two of them being resolved recently, the present paper addressed the remaining one, namely, the efficient solution of the second-order perturbation equation. A closed-form solution is obtained, which is more computationally efficient than any approach adopted in the past. The closed-form solution is obtained mathematically rigorously, and in the meantime it is computational efficient. The approach applies also to problems where buckling is of multiple modes. The solution procedure established in this paper has been verified and demonstrated through a structural application.

关键词： Prebuckling Deformations Finite Element Modeling Aspect Ratio Airy Stress Function numerical Analysis Poisson's Ratio Plane Stress Structural Stability numerical algorithms Iterative Algorithm

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Developing a new method to represent the low and high angle grain boundaries by using multi-scale modeling of crystal plasticity

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JOURNAL OF ALLOYS AND COMPOUNDS 2023年第1期939卷

作者： Rezaei, M. J. Sedighi, M. Pourbashiri, M. Iran Univ Sci & Technol IUST Sch Mech Engn Tehran Iran Graz Univ Technol Inst Mat Sci Joining & Forming IMAT Graz Austria

The main goal of the research is an investigation on a multi-scale crystal plasticity of a finite element model for polycrystalline material by using a hierarchical computational framework and macro/micro structure analysis. Therefore, several systematic numerical studies on the evolution of the microstructure and texture of pure Aluminum during torsion have been performed to identify crystal misorientation. The framework is integrated into ABAQUS finite element package using Dusseldorf Advanced Materials Simulation Kit (DAMASK) software. Then a Python algorithm was developed to examine the high and low grain boundaries, and the results were compared to experimental data of electron back scattering diffraction (EBSD). The findings showed that the torsion texture of pure Aluminum is completely attributed to dislocation sliding, and it was predictable by crystal plasticity. It was also shown that the Brass component with (phi(1),phi,phi(2)) = (35 degrees, 45 degrees, 0 degrees) appeared in the deformed sample. As a result, it is demonstrated that the multi-scale crystal plasticity simulation can predict the effect of inhomogeneous strain on the deformed texture. (c) 2023 Elsevier B.V. All rights reserved.

关键词： Crystal plasticity Microstructure Grain boundaries numerical algorithms Texture

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Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics

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JOURNAL OF CHEMICAL PHYSICS 2019年第12期151卷 124103-124103页

作者： Korol, Roman Bou-Rabee, Nawaf Miller, Thomas F., III CALTECH Div Chem & Chem Engn Pasadena CA 91125 USA Putgers Univ Camden Dept Math Sci Camden NJ 08102 USA

Path-integral-based molecular dynamics (MD) simulations are widely used for the calculation of numerically exact quantum Boltzmann properties and approximate dynamical quantities. A nearly universal feature of MD numerical integration schemes for equations of motion based on imaginary-time path integrals is the use of harmonic normal modes for the exact evolution of the free ring-polymer positions and momenta. In this work, we demonstrate that this standard practice creates numerical artifacts. In the context of conservative (i.e., microcanonical) equations of motion, it leads to numerical instability. In the context of thermostated (i.e., canonical) equations of motion, it leads to nonergodicity of the sampling. These pathologies are generally proven to arise at integration time steps that depend only on the system temperature and the number of ring-polymer beads, and they are numerically demonstrated for the cases of conventional ring-polymer MD (RPMD) and thermostated RPMD (TRPMD). Furthermore, it is demonstrated that these numerical artifacts are removed via replacement of the exact free ring-polymer evolution with a second-order approximation based on the Cayley transform. The Cayley modification introduced here can immediately be employed with almost every existing integration scheme for path-integral-based MD-including path-integral MD (PIMD), RPMD, TRPMD, and centroid MD-providing strong symplectic stability and ergodicity to the numerical integration, at no penalty in terms of computational cost, algorithmic complexity, or accuracy of the overall MD time step. Furthermore, it is shown that the improved numerical stability of the Cayley modification allows for the use of larger MD time steps. We suspect that the Cayley modification will therefore find useful application in many future path-integral-based MD simulations.

关键词： Pathology Conformal differential geometry Monte Carlo methods numerical integration Path integral molecular dynamics Molecular dynamics numerical algorithms Exponential map

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INVERSE METHOD FOR AIRFOIL DESIGN

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JOURNAL OF AIRCRAFT 1995年第5期32卷 1001-1011页

作者： LIMACHE, AC Universidad National de Cordoba Cordoba 5000 Argentina

This article presents an exact inverse method that generates the airfoil shape, satisfying all fluid dynamic and geometric constraints imposed by prescribing any input velocity distribution (or contour at the hodograph), with the only restriction that it does not take the same vector velocity at two different points of the boundary. The method is supported with a successive conformal mapping technique that can also be used in other problems as the one of grid-generation. The method may be a valuable general tool to obtain optimized designs with excellent performance. It can be extended to generate high-lift airfoils for compressible subsonic flow velocities.

关键词： Airfoil Freestream Velocity Adverse Pressure Gradient Flow Conditions Boundary Layer Analysis numerical algorithms Spline Interpolation Compressibility Inverse Problems

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HEAT TRANSFER OF MHD OLDROYD-B FLUID WITH RAMPED WALL VELOCITY AND TEMPERATURE IN VIEW OF LOCAL AND NONLOCAL DIFFERENTIAL OPERATORS

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FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2022年第5期30卷 2240172-2240172页

作者： Asgir, Maryam Riaz, Muhammad Bilal Jarad, Fahd Govt Coll Univ Dept Math Lahore 54770 Pakistan Lodz Univ Technol Dept Automat Biomech & Mechatron 1-15 Stefanowskiego St PL-90924 Lodz Poland Univ Management & Technol Dept Math Lahore 54770 Pakistan Cankaya Univ Dept Math Ankara Turkey China Med Univ China Med Univ Hosp Dept Med Res Taichung Taiwan

The theoretical study focuses on the examination of the convective flow of Oldroyd-B fluid with ramped wall velocity and temperature. The fluid is confined on an extended, unbounded vertical plate saturated within the permeable medium. To depict the fluid flow, the coupled partial differential equations are settled by using the Caputo (C) and Caputo Fabrizio (CF) differential time derivatives. The mathematical analysis of the fractionalized models of fluid flow is performed by Laplace transform (LT). The complexity of temperature and velocity profile is explored by numerical inversion algorithms of Stehfest and Tzou. The fractionalized solutions of the temperature and velocity profile have been traced out under fractional and other different parameters considered. The physical impacts of associated parameters are elucidated with the assistance of the graph using the software MATHCAD 15. We noticed the significant influence of the fractional parameter (memory effects) and other parameters on the dynamics of the fluid flow. Shear stress at the wall and Nusselt number also are considered. It's brought into notice the fractional-order model (CF) is the best fit in describing the memory effects in comparison to the C model. An analysis of the comparison between the solution of velocity and temperature profile for ramped wall temperature and velocity and constant wall temperature and velocity is also performed.

关键词： Oldroyd-B Fluid Convection MHD Permeable Medium Fractional Calculus Laplace Transform numerical algorithms

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On determination of the complex voltage ratio using the ellipse-fitting algorithm in the case of an ill-conditioned scattering matrix

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MEASUREMENT 2023年第1期216卷

作者： Augustyn, Jerzy Kampik, Marian Musio, Krzysztof Kielce Univ Technol Dept Automatic Control & Comp Sci Kielce Poland Silesian Tech Univ Dept Measurements Elect & Control ul Akad 10 Gliwice 44100 Poland

The article analyzes three modified versions of the standard ellipse fitting algorithm (EFA), which enables the determination of the complex voltage ratio (CVR) for extremely small values of the phase shift angle when the input scattering matrix of sampled data is poorly conditioned. The novelty of the method is in the use of EFA twice for the sequence of samples shifted by the same angle value, but with opposite signs. The results of the numerical simulation tests are confirmed by the results of measurements carried out in the sampling system using the NI PXI 4461 data acquisition module.

关键词： Ellipse fitting Scattering matrix Phase shift Complex voltage ratio numerical algorithms

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DEVELOPMENT OF AN ITERATIVE BOUNDARY-LAYER-TYPE SOLVER FOR AXISYMMETRICAL SEPARATED FLOWS

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AIAA JOURNAL 1986年第8期24卷 1298-1304页

作者： HALIM, AAM GEORGE WASHINGTON UNIV HAMPTONVA

A boundary-layer-type solver is developed for the numerical solution of axisymmetric separated flows. A new, fully implicit coupling scheme for the viscous and inviscid regions is demonstrated. This fully implicit coupling technique is similar to the work of Carter and of Veldman and an extension of an earlier work of Halim and Hafez. A comparison is made for the convergence rate using this new, fully implicit coupling technique and the semi-implicit coupling of Halim and Hafez. numerical results using the fully implicit coupling are obtained for laminar incompressible separated flows, including a boattail and a series of trough geometries. Also, the nearwake flow problem is considered using the present formulation. A clear conclusion of this investigation is that the present scheme, using the fully implicit coupling method, converges at a faster rate than the semi-implicit coupling and the partially parabolized Navier-Stokes procedures. © 1986 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Boundary Layer Equations Incompressible Flow Skin Friction Coefficient Eddy Viscosity Inviscid Flow Equations Navier Stokes Equations Turbulence Models Mach Number numerical algorithms Vorticity

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