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CaTSM: A Pseudo-Spectral Thermodynamically Consistent Model of Compressible Flows

JOURNAL OF ADVANCES IN MODELING EARTH SYSTEMS 2022年第11期14卷 e2022MS003112-e2022MS003112页

作者： Brown, Justin M. Dewar, William Radko, Timour Naval Postgrad Sch Dept Oceanog Monterey CA 93943 USA Florida State Univ Dept Earth Ocean & Atmospher Sci Tallahassee FL USA

We introduce a pseudo-spectral algorithm that includes full compressible dynamics with the intent of simulating near-incompressible fluids, CaTSM (Compressible and Thermodynamically consistent Spectral Model). A semi-implicit scheme is used to model acoustic waves in order to evolve the system efficiently for such fluids. We demonstrate the convergence properties of this numerical code for the case of a shock tube and for Rayleigh-Taylor instability. A linear equation of state is also presented, which relates the specific volume of the fluid linearly to the potential temperature, salinity, and pressure. This permits the results to be easily compared to a Boussinesq framework in order to assess whether the Boussinesq approximation adequately represents the relevant exchange of energy to the problem of interest. One such application is included, that of the development of a single salt finger, and it is shown that the energetic behavior of the system is comparable to the typical canonical development of the problem for oceanographic parameters. However, for more compressible systems, the results change substantially even for low-Mach number flows.

关键词： compressible fluids incompressible fluids numerical algorithm microscale

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An Installation Angle Error Calibration Method in an Ultra-Short Baseline System Based on a Dual Transponder

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POLISH MARITIME RESEARCH 2023年第2期30卷 121-129页

作者： Liu, Baoheng Zhang, Xiaochuan Jia, Shuyang Zou, Sichen Tian, Deyan Da, Lianglong PLA Navy Submarine Acad Qingdao Peoples R China Naval Submarine Acad Qingdao Peoples R China

The installation error of an acoustic transceiver array is one of the important error sources in an ultra-short baseline (USBL) system. In a USBL system with a positioning accuracy of 0.5%, an installation error angle of 1 degrees will lead to a positioning error of 1.7% times the slant distance. In this paper, a dual transponder-based installation angle error calibration method for USBL is proposed. First, the positioning errors induced by various installation angles are deduced and analysed using the linear measurement of seafloor targets. Then, an iterative algorithm is proposed that estimates the rolling alignment error, pitching alignment error, and heading alignment error, in that order. The simulation and experienced results show that, after three iterations, the estimates of the three alignment errors can converge quickly, all of the estimates converge to within 0.001 degrees and the estimated values are very close to the true values. The horizontal positioning error caused by the installation error angle can be reduced by nearly 75%. The method has good effectiveness and robustness, and can greatly improve the positioning accuracy of the USBL system.

关键词： USBL installation angle error misalignment calibration numerical algorithm hydrolocation

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Two-scale Time Homogenization for Isotropic Viscoelastic- Viscoplastic Homogeneous Solids Under Large Numbers of Cycles

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Procedia Engineering 2013年 66卷 598-607页

作者： Sarra Haouala Issam Doghri Université Catholique de Louvain (UCL) Institute of Mechanics Materials and Civil Engineering (IMMC) Bâtiment Euler 4 Avenue G. Lemaître B-1348 Louvain-la-Neuve Belgium

A two-scale time homogenization approach for coupled viscoelastic-viscoplatic (VE-VP) homogeneous solids and structures subjected to large numbers of cycles, is proposed. The main aim is to give a description of the long time behaviour, by calculating the evolution of internal variables within the structure, while reducing the computational overhead. This method consists in decomposing the original VE-VP initial-boundary problem into coupled micro-chronological (fast time scale) and macro-chronological (slow time-scale) problems. The proposed methodology was implemented and studied for J2 VP coupled with VE using fully implicit time integration and a return-mapping algorithm. An illustration of the time homogenization on a simple case is presented and a good agreement with the reference solution is observed.

关键词： Time homogenization two-scale modeling viscoelasticity (VE) viscoplasticity (VP) numerical algorithm

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Regret-based budgeted decision rules under severe uncertainty

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INFORMATION SCIENCES 2024年 665卷

作者： Nakharutai, Nawapon Destercke, Sebastien Troffaes, Matthias C. M. Chiang Mai Univ Fac Sci Dept Stat Chiang Mai 50200 Thailand Univ Technol Compiegne Sorbonne Univ CNRS UMR Heudiasyc 7253 F-60200 Compiegne France Univ Durham Dept Math Sci Durham DH1 3LE England

One way to make decisions under uncertainty is to select an optimal option from a possible range of options, by maximizing the expected utilities derived from a probability model. However, under severe uncertainty, identifying precise probabilities is hard. For this reason, imprecise probability models uncertainty through convex sets of probabilities, and considers decision rules that can return multiple options to reflect insufficient information. Many well-founded decision rules have been studied in the past, but none of those standard rules are able to control the number of returned alternatives. This can be a problem for large decision problems, due to the cognitive burden decision makers have to face when presented with a large number of alternatives. Our contribution proposes regret-based ideas to construct new decision rules which return a bounded number of options, where the limit on the number of options is set in advance by the decision maker as an expression of their cognitive limitation. We also study their consistency and numerical behaviour.

关键词： Decision Regret Minimax Maximin Imprecise probability Optimization numerical algorithm

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Effective algorithm for two-dimensional frictional system involving arbitrary impacting boundaries

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2020年第0期167卷 105232-000页

作者： Wang, Xiaosun Zhao, Deng Wu, Shijing Li, Xiaofeng Yuan, Hao Li, Qiaoquan Wuhan Univ Sch Power & Mech Engn Wuhan 430072 Peoples R China

Impacting and friction are always encountered in the mechanical system and make the system experience nonlinearities in both force-position and force-velocity characteristics. In this paper, we propose one effective numerical algorithm for a two-dimensional frictional system involving the impacting by employing the closed form solution to yield the slip responses and extend the closed form solutions for curve length to predict the impacting location and time with high accuracy. By performing the accuracy analysis and robustness analysis through several representative scenarios, we reveal that, (1) the impacting dynamic responses can be predicted through our new algorithm with high accuracy, (2) the accumulative errors of dynamic responses are insensitive to the complex boundary, (3) the new algorithm can keep better robustness when involving repeated impacting.

关键词： numerical algorithm Accuracy analysis Robust analysis Impacting Two-dimensional frictional system

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Free Rocking of a Rigid Block on a Flexible Structure with Non-Smooth Contact Dynamics

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APPLIED SCIENCES-BASEL 2024年第15期14卷 6483页

作者： Mudric, Teo Ceh, Nina Hante, Stefan Arnold, Martin Univ Rijeka Fac Civil Engn Radmile Matejcic 3 Rijeka 51000 Croatia Martin Luther Univ Halle Wittenberg Inst Math Theodor Lieser St 5 D-06120 Halle Halle Germany

When structures are subjected to dynamic loading, such as that caused by an earthquake or working machinery, the rocking behavior of objects located on parts of the loaded structure plays an important role in addressing the protection and stability of non-structural components. In this work, the free rocking of a rigid block on a flexible beam and rigid base was investigated using numerical simulations. To this end, a numerical code based on the non-smooth contact dynamics method was developed for this particular problem, and numerical simulations are compared to experimental tests when a rigid base is considered. The purpose of the study was to investigate the predictive capabilities and limitations of the numerical model and address the effect of introducing beam flexibility on the rocking response. The investigated flexibilities were such that the beam deflection under the static weight of the block remains within the common limit of 1/250 of the beam span. For a rigid base, qualitatively good correlation with the experiments was obtained, and good convergence in terms of the time-step is displayed. With the increase in beam base flexibility, it was observed that the simulation results tend to become more sensitive to mesh density and time-step size. Furthermore, we identify a limited flexibility with respect to which unreliable predictions of the overall free rocking are obtained, which corresponds to the stiffness resulting in the beam deflection under the block weight of beam-span/2500. For stiffnesses higher than that, no significant effect of beam flexibility in comparison to the rigid base was noticed in terms of tilt angle and rocking duration, which indicates the adequacy of a rigid base approximation for beams with low flexibility.

关键词： non-smooth contact dynamics rocking numerical algorithm experimental validation

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Implicit Integration algorithm for Solving Evolution of Microstructural Vectors Based on Eulerian Formulation in Plane Stress Condition

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JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME 2023年第4期90卷 041004-041004页

作者： Lee, Eun-Ho Sungkyunkwan Univ Sch Mech Engn Dept Smart Fab Technol Suwon 16419 Gyeonggi South Korea

This paper presents a mathematical formulation and implicit numerical algorithm for solving the integral of a three-dimensional momentum balance based on the inelastic evolution of microstructural vectors for thin plates in Eulerian formulation. A recent theoretical discussion (Lee and Rubin, 2020, Modeling Anisotropic Inelastic Effects in Sheet Metal Forming Using Microstructural Vectors-Part I: Theory, Int. J. Plast., 134, p. 102783. 10.1016/***.2020.102783) showed that Eulerian constitutive equation based on micro structural vectors for thin plates has the advantage of capturing the anisotropic behavior of the material axis with insensitivity to the randomness of the reference configuration. However, all the discussions were theoretically conducted only at a local material point in homogeneous deformation conditions, which do not require consideration of the momentum balance with flexible velocity gradients in a three-dimensional volume. For usability, numerical algorithms are needed to solve evolution of the microstructural vectors in the three-dimensional space. This paper presents the first numerical algorithm to solve the inelastic evolution of microstructural vectors in the Eulerian formulation. A generalized material coordinated system is matched to the microstructural vectors in a three-dimensional space by considering the Eulerian constitutive equations insensitive to the superposed rigid body motions (SRBM). numerical algorithms were then introduced to implicitly solve the nonlinear momentum balance, evolution of the microstructural vectors, and tangent modulus. The formula and numerical algorithms were validated by predicting the tension tests when the principal loading angle varied from the reference axis. The results show that the proposed numerical algorithm can describe the evolution of the microstructure based on the Eulerian formulation.

关键词： eulerian formulation momentum balance microstructural vectors inelastic deformation material axes numerical algorithm computational mechanics mechanical properties of materials plasticity

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Angular Values of Nonautonomous and Random Linear Dynamical Systems: Part I-Fundamentals

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SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 2022年第2期21卷 1245-1286页

作者： Beyn, Wolf-Juergen Froyland, Gary Huels, Thorsten Bielefeld Univ Dept Math D-33501 Bielefeld Germany Univ New South Wales Sch Math & Stat Sydney NSW 2052 Australia

We introduce the notion of angular values for deterministic linear difference equations and random linear cocycles. We measure the principal angles between subspaces of fixed dimension as they evolve under nonautonomous or random linear dynamics. The focus is on long-term averages of these principal angles, which we call angular values: we demonstrate relationships between different types of angular values and prove their existence for random dynamical systems. For one-dimensional subspaces in two-dimensional systems our angular values agree with the classical theory of rotation numbers for orientation-preserving circle homeomorphisms if the matrix has positive determinant and does not rotate vectors by more than pi/2. Because our notion of angular values ignores orientation by looking at subspaces rather than vectors, our results apply to dynamical systems of any dimension and to subspaces of arbitrary dimension. The second part of the paper delves deeper into the theory of the autonomous case. We explore the relation to (generalized) eigenspaces, provide some explicit formulas for angular values, and set up a general numerical algorithm for computing angular values via Schur decompositions.

关键词： nonautonomous dynamical systems random dynamical systems angular value ergodic average principal angles of subspaces numerical algorithm

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Application of power-law formalism method to equilibrium computation of vapor growth epitaxy

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JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 1999年第4期32卷 506-513页

作者： Hasegawa, T Takatani, H Yoshimura, J Shizuoka Univ Fac Engn Dept Syst Engn Hamamatsu Shizuoka 4328561 Japan

Modeling and numerical solutions of vapor phase epitaxy are limited because of convergence ability and a large number of iterations. To overcome these limitations, for the first time two Newton-like methods have been applied to models of vapor phase epitaxy for GaAs and InxGa1-xP: The Newton-Raphson method (NRM) and the power-law formalism method (PLFM). We compare the performances of the two methods In terms of the ability of convergence and the iteration numbers. The results indicate that PLFM is always significantly superior to NRM. All calculations by PLFM successfully converge from a rough estimated initial values for equilibrium partial pressures, where NRM can not. These results suggest that the Limitation in the numerical calculations of the vapor growth epitaxy can be widely extended by the application of PLFM.

关键词： vapor phase epitaxy thermodynamic analysis numerical algorithm power-law formalism convergence performances

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Nonaxisymmetric vibrations of ellipsoidal shells under nonstationary distributed loads

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INTERNATIONAL APPLIED MECHANICS 2008年第9期44卷 1015-1024页

作者： Meish, V. F. Maiborodina, N. V. Natl Acad Sci Ukraine S P Timoshenko Inst Mech Kiev Ukraine Natl Agr Univ Kiev Ukraine

Problems of forced nonaxisymmetric vibrations of ellipsoidal shells under nonstationary loads are formulated. A numerical algorithm to solve them is developed. The solutions obtained are analyzed.

关键词： ellipsoidal shell nonstationary load forced nonaxisymmetric vibrations numerical algorithm

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