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 ...
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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 bondi...
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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.
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 i...
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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.
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 ...
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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.
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 ...
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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.
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 ...
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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
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 a...
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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.
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, polynomi...
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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.
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 th...
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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.
In this paper, we consider the accuracy of integration algorithms such as the implicit Euler and the trapezoidal ones, which are largely employed in the time domain circuit analysis. These algorithms require to make h...
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In this paper, we consider the accuracy of integration algorithms such as the implicit Euler and the trapezoidal ones, which are largely employed in the time domain circuit analysis. These algorithms require to make hypotheses on the intersample shape and on the "energy content" of the sampled waveforms. For example, the implicit Euler algorithm supposes functions to be piecewise constant. When these hypotheses are violated, some errors are introduced by the integration process into the solution waveform. We consider the energy of the sampled functions, and through energy balance equations, estimate the accuracy of the integration algorithm. Furthermore, we propose an implicit algorithm to determine an adequate integration time step during numerical time domain analysis, This algorithm is based on a global energy balance equation and not on the conventional estimation of the local truncation error. It avoids the "cut and try" mechanism used in SPICE to determine the time step that satisfies the desired error tolerance.
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