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91.
    
This paper applies the technique of successive approximation to the nonlinear theory of elastic materials with voids, as developed by Nunziato and Cowin [2]. The complete set of equations for the first and second order approximation is derived. The torsion problem within the second‐order theory is studied. It is shown that the solution can be expressed in terms of solutions of some two‐dimensional problems. The theory is applied to study the torsion of a circular cylinder. It is shown that an infinitesimal twist produces a second‐order volume fraction field which is proportional to the square of the amount of torsion.  相似文献   
92.
    
We study the existence and uniqueness of solution for a class of equations of the form ∑mi=0aiy( i) (t) + ∫abϕ(α) y(α) (t) dα= h(t) , where y(α)(t) is the Riemann Liouville fractional derivative, in the space of tempered distributions. Such equations arise in the distributed derivatives models of linear viscoelasticity.  相似文献   
93.
    
System analysis and optimization of combustion engines and engine components are increasingly supported by digital simulations. In the simulation process of combustion engines multi physics simulations are used. As an example, in the simulation of a crank drive the mechanical subsystem is coupled to a hydrodynamic subsystem. As far as the modeling of the mechanical subsystems is concerned, elastic multibody systems are frequently used. During the simulation many equations must be solved simultaneously, the hydrodynamic equations as well as the equations of motion of each body in the elastic multibody system. Since the discretization of the elastic bodies, e.g with the help of the finite element method, introduces a large number of elastic degrees of freedom, an efficient simulation of the system becomes difficult. The linear model reduction of the elastic degrees of freedom is a key step for using flexible bodies in multibody systems and turning simulations more efficient from a computational point of view. In recent years, a variety of new reduction methods alongside the traditional techniques were developed in applied mathematics. Some of these methods are reviewed and compared for reducing the equations of motion of an elastic body used in multibody systems. The special focus of this work is on balanced truncation model order reduction, which is a singular value based reduction technique using the Gramian matrices of the system. We investigate a version of this method that is adapted to the structure of a special class of second order dynamical systems which is important for the particular application discussed here. The simulation of a crank drive with a flexible crankshaft is taken as technically relevant example. The results are compared to other methods like Krylov approaches or modal reduction.  相似文献   
94.
    
We consider an initial‐boundary value problem for a fully nonlinear coupled parabolic system with nonlinear boundary conditions modeling hygro‐thermal behavior of concrete at high temperatures. We prove a global existence of a weak solution to this system on any physically relevant time interval. The main result is proved by an approximation procedure. This consists in proving the existence of solutions to mollified problems using the Leray‐Schauder theorem, for which a priori estimates are obtained. The limit then provides a weak solution for the original problem. A practical example illustrates a performance of the model for a problem of a concrete segment exposed to transient heating according to three different fire scenarios. Here, the focus is on the short‐term pore pressure build up, which can lead to explosive spalling of concrete and catastrophic failures of concrete structures.  相似文献   
95.
    
This paper presents a new high‐order approach to the numerical solution of the incompressible Stokes and Navier–Stokes equations. The class of schemes developed is based upon a velocity–pressure–pressure gradient formulation, which allows: (i) high‐order finite difference stencils to be applied on non‐staggered grids; (ii) high‐order pressure gradient approximations to be made using standard Padé schemes, and (iii) a variety of boundary conditions to be incorporated in a natural manner. Results are presented in detail for a selection of two‐dimensional steady‐state test problems, using the fourth‐order scheme to demonstrate the accuracy and the robustness of the proposed methods. Furthermore, extensions to higher orders and time‐dependent problems are illustrated, whereas the extension to three‐dimensional problems is also discussed. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   
96.
    
An empirical investigation is made of AMG solver performance for the fully coupled set of Navier–Stokes equations. The investigation focuses on two different FV discretizations for the standard driven cavity test problem. One is a collocated vertex‐based discretization; the other is a cell‐centred staggered‐grid discretization. Both employ otherwise identical orthogonal Cartesian meshes. It is found that if mixed‐order interpolation is used in the construction of the Galerkin coarse‐grid approximation (CGA), a close‐to‐optimum mesh‐independent scaling of the AMG convergence is observed with similar convergence rates for both discretizations. If, on the other hand, an equal‐order interpolation is used, convergence rates are mesh‐dependent but the scaling differs in each case. For the collocated‐grid case, it depends both on the mesh size, h (or bandwidth Qh?1) and on the total number of grids, G, whereas for the staggered‐grid case it depends only on Q. Comparing the two characteristics reveals that the Q‐dependent parts are very similar; it is only in the G‐dependent convergence for the collocated‐grid case that they differ. This takes the form of stepped reductions in the AMG convergence rate (implying step reductions in the quality of the Galerkin CGA that correlate exactly with step increases in G). These findings reinforce previous evidence that, for optimum mesh‐independent performance, mixed‐order interpolations should be used in forming Galerkin CGAs for coupled Navier–Stokes problems. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   
97.
    
The effect of variable viscosity on the peristaltic motion of MHD third‐order fluid in a channel is studied using slip condition. The series solution for stream function, longitudinal velocity and pressure gradient are first derived and then discussed in detail. The pressure rise and frictional forces are monitored through numerical integration. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   
98.
    
Four‐dimensional variational data assimilation in meteorology and oceanography suffers from the presence of local minima in the cost function. These local minima arise when the system under study is strongly nonlinear. The number of local minima further dramatically increases with the length of the assimilation period and often renders the solution to the problem intractable. Global optimization methods are therefore needed to resolve this problem. However, the huge computational burden makes the application of these sophisticated techniques unfeasible for large variational data assimilation systems. In this study, a Simulated Annealing (SA) algorithm, complemented with an order‐reduction of the control vector, is used to tackle this problem. SA is a very powerful tool of combinatorial minimization in the presence of several local minima at the cost of increasing the execution time. Order‐reduction is then used to reduce the dimension of the search space in order to speed up the convergence rate of the SA algorithm. This is achieved through a proper orthogonal decomposition. The new approach was implemented with a realistic eddy‐permitting configuration of the Massachusetts Institute of Technology general circulation model (MITgcm) of the tropical Pacific Ocean. Numerical results indicate that the reduced‐order SA approach was able to efficiently reduce the cost function with a reasonable number of function evaluations. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   
99.
在对室内液化石油气泄漏流动过程进行量级估算分析的基础上,提出了一种预测室内泄漏液化石油气浓度分布的简化方法. 并结合一次居民室内液化气爆炸事故,讨论了此方法在实际应用中的简易可行性.  相似文献   
100.
    
Three-dimensional dynamic gas–liquid flow simulations that accurately track the phase interface are numerically challenging. This article presents a numerical study of the performance of the level-set phase–interface tracking method when combined with extremely high order (7th to 11th) weighted essentially non-oscillatory (WENO) advection schemes for gas–liquid free surface flows. Comparisons between simulation results and prior benchmark results suggest that such a combination of methods can be satisfactorily applied to the level-set and Navier-Stokes equations for free surface flow simulations when volume conservation is enforced at every time step, and minor numerical oscillations are suppressed through use of an artificial viscosity term. In particular, simulations of solid body rotation, the unsteady flow following an ideal dam break, tank sloshing, and the rise of a single bubble all agree with analytical or experimental results to within ± 3.12% when the level-set method is combined with an 11th order WENO scheme. Furthermore, use of an 11th order WENO advection scheme actually has a computational cost advantage because, for the same accuracy, it can be used on a coarser grid when compared with a more-common second-order advection scheme; computational savings of up to 87% are possible.  相似文献   
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