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numerical-SIMULATION OF TRANSIENT INVISCID SHOCK-TUBE FLOWS

AIAA JOURNAL 1987年第2期25卷 245-251页

作者： YANG, JY LOMBARD, CK BERSHADER, D PEDA CORP PALO ALTO CA USA STANFORD UNIV DEPT AERONAUT & ASTRONAUT STANFORD CA 94305 USA

Time-dependent upwind high resolution schemes for solving the Euler equations were developed and applied to simulate one- and two-dimensional transient inviscid gas flows in a shock tube. Using obstacles of different geometries, a series of calculations were carried out to investigate the transient complex shock wave diffraction phenomena. Shock wave and object interaction with shock Mach numbers ranging from 2-20 were simulated. Comparison with analytical and available experimental results indicate good agreement. Display of detailed flow structures including multiple Mach shocks, sliplines, and vortex are also given. © 1987 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Rotor Aerodynamics numerical Simulation Shock Wave Propagation Primitive Variable Vortices numerical algorithms Transonic Flow Solid Propellant Rocket Gas Dynamics Specific Heat

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numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1998年第2期46卷 187-218页

作者： Gao, HJ Klein, P Stanford Univ Div Mech & Computat Stanford CA 94305 USA

A virtual internal bond (VIE) model with randomized cohesive interactions between material particles is proposed as an integration of continuum models with cohesive surfaces and atomistic models with interatomic bonding. This approach differs from an atomistic model in thai a phenomenological "cohesive force law" is assumed to act between "material particles" which are not necessarily atoms;it also differs from a cohesive surface model in that, rather than imposing a cohesive law along a prescribed set of discrete surfaces, a randomized network of cohesive bonds is statistically incorporated into the constitutive law of the material via the Cauchy-Born rule, i.e., by equating the strain energy function on the continuum level to the potential energy stored in the cohesive bonds due to an imposed deformation. This work is motivated by the notion that materials exhibit multiscale cohesive behaviors ranging from interatomic bonding to macroscopic ductile failure. It is shown that the linear elastic behavior of the VIE model is isotropic and obeys the Cauchy relation;the instantaneous elastic properties under equibiaxial stretching are transversely isotropic, with all the in-plane components of the material tangent moduli vanishing at the cohesive stress limit;the instantaneous properties under equitriaxial stretching are isotropic with a finite strain modulus. We demonstrate through two preliminary numerical examples that the VIE model can be applied in direct simulation of crack growth without a presumed fracture criterion. The prospect of this type of approach in numerical simulations of fracture seems to be highly promising. (C) 1995 Elsevier Science Ltd. All rights reserved.

关键词： crack branching and bifurcation crack propagation and arrest constitutive behavior principles finite strain numerical algorithms

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An efficient approach for numerical treatment of some inequalities in solid mechanics on examples of Kuhn-Tucker and Signorini-Fichera conditions

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2014年第1期63卷 432-450页

作者： Kindrachuk, Vitaliy M. Galanov, Boris A. BAM Fed Inst Mat Res & Testing D-12205 Berlin Germany Frantzevich Inst Problems Mat Sci UA-252142 Kiev Ukraine

A computationally efficient solution scheme is presented for the mechanical problems whose formulations include the Kuhn-Tucker or Signorini-Fichera conditions. It is proposed to reformulate these problems replacing inequalities in these conditions by equations with respect to new unknowns. The solutions of the modified problems have simple physical meanings and determine uniquely the unknowns of the original problems. The approach avoids application of multi-valued operators (inclusions or inequalities) in formulation of the problems. Hence, the modified formulations are suitable for numerical analysis using established powerful mathematical methods and corresponding solvers developed for solving systems of non-linear equations. To demonstrate the advantages of the proposed approach, it is applied for solving problems in two different areas: constitutive modeling of single-crystal plasticity and mixed boundary value problems of elastic contact mechanics with free boundaries. The original formulations of these problems contain respectively the Kuhn-Tucker and Signorini-Fichera conditions. A problem of the former area is integrated using an implicit integration scheme based on the return-mapping algorithm. The derived integration scheme is free of any update procedure for identification of active slip systems. A problem of the latter area is reduced to solution of non-linear integral boundary equations (NBIEs). numerical examples demonstrate stability and efficiency of the solution procedures and reflect the mathematical similarities between the both non-linear problems. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Kuhn-Tucker and Signorini-Fichera conditions numerical algorithms Crystal plasticity Constitutive behavior Contact mechanics

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numerical OPTIMAL HARVESTING FOR AN AGE-DEPENDENT PREY-PREDATOR SYSTEM

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numerical FUNCTIONAL ANALYSIS AND OPTIMIZATION 2012年第6期33卷 661-679页

作者： Stefanescu, Razvan Dimitriu, Gabriel Florida State Univ Dept Comp Sci Tallahassee FL 32306 USA Gr T Popa Univ Med & Pharm Dept Math & Comp Sci Iasi Romania

In this article, we develop a numerical study of an optimal harvesting problem for age-dependent prey-predator system. Here, the rates of growth and decay as well as the interaction effect between species are assumed to be depending on age, time and space. Existence, uniqueness, and necessary conditions for the optimal control are assured in case of a small final time T. The discrete parabolic nonlinear dynamical systems are obtained by using a finite difference semi-implicit scheme. Then a numerical algorithm is developed to approximate the optimal harvesting effort and the optimal harvest. Results of the numerical tests are given.

关键词： Age structured population dynamics Optimal harvesting Optimality conditions numerical algorithms Finite difference methods

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Experience in numerical Hydrodynamic Simulation of Long River Reaches

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WATER RESOURCES 2023年第4期50卷 465-481页

作者： Belikov, V. V. Aleksyuk, A. I. Borisova, N. M. Vasil'eva, E. S. Glotko, A. V. Russian Acad Sci Water Problems Inst Moscow 119333 Russia Moscow State Univ Civil Engn Moscow 129337 Russia

The article formulates the main requirements to numerical algorithms for hydrodynamic 2D-modeling of long and very long river segments with lengths of up to several thousand kilometers. The main feature is the use of adaptive unstructured mesh along with algorithms that give correct values of water surface elevations on coarse mesh, taking into account abrupt changes of bed elevations. A hydrodynamic model of a segment of the Amur R. with a total length of >3 thous. km is presented, which is based on a numerical solution of two-dimensional shallow-water equations (Saint-Venant) by a new high-accuracy algorithm, taking into account road and protection structures in the floodplain. The stages of model construction and verification are described, and the results of calculations for an extraordinary flood in 2013 and a high flood in 2020 are given. Water levels (with estimates of their errors) and the rates of water discharge at gages are given along with flow fields and the inundation zones of floodplain areas.

关键词： numerical algorithms very long river segments Riemann problem model of long river segment inundation flooded zone Amur R

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Event and Apparent Horizon Finders for 3+1 numerical Relativity

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LIVING REVIEWS IN RELATIVITY 2007年第1期10卷 1页

作者： Thornburg, Jonathan Univ Southampton Sch Math Southampton SO17 1BJ Hants England Max Planck Inst Gravitat Phys Albert Einstein Inst D-14476 Potsdam Germany

Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numeric ally-computed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event horizon of an asymptotic ally-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time: it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part) of spacetime has been numerically computed. There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate. In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is) found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS) in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Theta. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE) for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most "apparent horizon" finders actually find MOTSs. There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well

关键词： .slice spacetimes Black Holes numerical algorithms null geodesics numerical relativity event horizons future-pointing apparent horizons Horizon Finders Finders for numerical

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numerical-SIMULATION OF SHOCK-BOX INTERACTION USING AN ADAPTIVE FINITE-ELEMENT SCHEME

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AIAA JOURNAL 1994年第4期32卷 682-692页

作者： BAUM, JD LOHNER, R GEORGE WASHINGTON UNIV SCH ENGN & APPL SCI WASHINGTON DC 20052 USA

A transient, two-dimensional, finite element shock-capturing scheme on unstructured grids was applied to the study of a shock interacting with a box suspended above a rigid elevated surface. The area between the box and the surface was partially blocked by the box support beams, resulting in complex shock diffraction processes. The results demonstrate the capability of the developed adaptive refinement/coarsening algorithm to properly adapt to weak shocks, expansions, and contact discontinuities, and highlight the resulting excellent resolution of the captured flow features. In addition to interesting shock diffraction and propagation phenomena, the results demonstrate the capability of the new code to capture, and define in great detail, vortex sheets shed from sharp corners. We show that the baroclinic effect, an inviscid process, controls the shedding phenomenon during the diffraction phase. Hence, the Eulerian model is able to correctly predict this process.

关键词： Flux Corrected Transport Finite Element Scheme Vortex Dynamics Unstructured Grid Stagnation Pressure Mach Number Shock Wave Propagation Transonic Flow numerical algorithms Kinematic Viscosity

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A Low-Complexity Parallelizable numerical Algorithm for Sparse Semidefinite Programming

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2018年第4期5卷 1898-1909页

作者： Madani, Ramtin Kalbat, Abdulrahman Lavaei, Javad Univ Texas Arlington Dept Elect Engn Arlington TX 76019 USA United Arab Emirates Univ Dept Elect Engn Abu Dhabi 15551 U Arab Emirates Univ Calif Berkeley Dept Ind Engn & Operat Res Berkeley CA 94720 USA Tsinghua Berkeley Shenzhen Inst Berkeley CA 94704 USA

In the past two decades, the semidefinite programming (SDP) technique has been proven to be extremely successful in the convexification of hard optimization problems appearing in graph theory, control theory, polynomial optimization theory, and many areas in engineering. In particular, major power optimization problems, such as optimal power flow, state estimation, and unit commitment, can be formulated or well approximated as SDPs. However, the inability to efficiently solve large-scale SDPs is an impediment to the deployment of such formulations in practice. Motivated by the significant role of SDPs in revolutionizing the decision-making process for real-world systems, this paper designs a low-complexity numerical algorithm for solving sparse SDPs, using the alternating direction method of multipliers and the notion of tree decomposition in graph theory. The iterations of the designed algorithm are highly parallelizable and enjoy closed-form solutions, whose most expensive computation amounts to eigenvalue decompositions over certain submatrices of the SDP matrix. The proposed algorithm is a general-purpose parallelizable SDP solver for sparse SDPs, and its performance is demonstrated on the SDP relaxation of the optimal power flow problem for real-world benchmark systems with more than 13 600 nodes.

关键词： Large-scale optimization numerical algorithms power systems semidefinite programming tree decomposition

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Rheological viscoplastic models of asphalt concrete and rate-dependent numerical implement

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INTERNATIONAL JOURNAL OF PLASTICITY 2016年 81卷 209-230页

作者： Cheng, Jianlian Qian, Xudong Zhao, Tieshuan Changan Univ Highway Maintenance Equipment Natl Engn Lab Key Lab Rd Construct Technol & Equipment Minist EducSch Construct Machinery 322 Mailbox Xian 710064 Shaanxi Peoples R China Natl Univ Singapore Dept Civil & Environm Engn Singapore 117576 Singapore

Based on the generalized plastic theory, a viscoplastic constitutive model is derived from Perzyna's theory of viscoplasticity and is used to model the ratcheting behavior exhibited by the mix. The evolution of the permanent strain with number of loading cycles is also captured. The loading surface is considered for the viscoplastic model of asphalt concrete (AC) according to Vermeer loading surface. A non-associate flow rule for the plasticity model as well as an evolution equation for hardening parameters is given. The viscoplastic component captures the rate-dependent behavior. The developed viscoplastic model takes into account the anisotropy in AC. Inherent anisotropy is introduced through the fabric tensor and considered by the preferred orientation of non-spherical particles. The developed damage model is incorporated in the viscoplastic model to capture the permanent deformation of AC. numerical implementation and algorithm aspects of the multidimensional elastic-viscoplastic-damage model are presented. A robust integration algorithm for the nonlinear differential equations is carried out, which equations are solved by prediction-corrector method. Model results are compared to experimental observation. For the permanent deformation, results of the RSST-CH and Triaxial experimental are used to calibrate the model and test its prediction of different stress levels. RSST-CH is also modeled as a boundary value problem to assess the capability of the model to predict rutting in the pavement. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Fracture mechanisms Rate-dependent material Viscoplastic material numerical algorithms Asphalt concrete

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numerical Analysis of Liquid-Solid Adsorption Model

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MATHEMATICAL MODELLING AND ANALYSIS 2019年第4期24卷 598-616页

作者： Leonaviciene, Terese Ciegis, Raimondas Baltrenaite, Edita Chemerys, Valeriia Vilnius Gediminas Tech Univ Sauletekio Al 11 LT-10223 Vilnius Lithuania

In this paper, the numerical algorithms for solution of pore volume and surface diffusion model of adsorption systems are constructed and investigated. The approximation of PDEs is done by using the finite volume method for space derivatives and ODE15s solvers for numerical integration in time. The analysis of adaptive in time integration algorithms is presented. The main aim of this work is to analyze the sensitivity of the solution with respect to the main parameters of the mathematical model. Such a control analysis is done for a linearized and normalized mathematical model. The obtained results are compared with simulations done for a full nonlinear mathematical model.

关键词： numerical algorithms finite volume method adsorption models sensitivity analysis

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