Finite amplitude one-dimensional wave propagation in a thermoelastic half-space

The problem of finite wave propagation in a nonlinearly thermoelastic half-space is considered. The surface of the half-space is subjected to a time-dependent thermal and normal mechanical loading. The solution is obtained by a numerical procedure, which is shown to furnish accurate results, and linear dynamic thermoelastic problems are obtained as special cases. The accuracy of the results is checked by comparison with some known analytical solutions which can be obtained in some special cases of both the linear and the nonlinear problems. In those cases where the solution contains shocks, it is shown that the numerical results satisfy the necessary jumps conditions which need to hold across such discontinuities.     

Some applications of the concept of minimized integrated exponential error for low dispersion and low dissipation

Several techniques to optimize parameters that regulate dispersion and dissipation effects in finite difference schemes have been devised in our previous works. They all use the notion that dissipation neutralizes dispersion. These techniques are the minimized integrated square difference error (MISDE) and the minimized integrated exponential error for low dispersion and low dissipation (MIEELDLD). It is shown in this work based on several numerical schemes tested that the technique of MIEELDLD is more accurate than MISDE to optimize the parameters that regulate dispersion and dissipation effects with the aim of improving the shock‐capturing properties of numerical methods. First, we consider the family of third‐order schemes proposed by Takacs. We use the techniques MISDE and MIEELDLD to optimize two parameters, namely, the cfl number and another variable which also controls dispersion and dissipation. Second, these two techniques are used to optimize a numerical scheme proposed by Gadd. Moreover, we compute the optimal cfl for some multi‐level schemes in 1D. Numerical tests for some of these numerical schemes mentioned above are performed at different cfl numbers and it is shown that the results obtained are dependent on the cfl number chosen. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Finally, we make use of a composite scheme made of corrected Lax–Friedrichs and the two‐step Lax–Friedrichs schemes like the CFLF4 scheme at its optimal cfl number, to solve some problems in 2D, namely: solid body rotation test, acoustics and the circular Riemann problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Thermomagnetic effect with microtemperature in a semiconducting photothermal excitation medium

The main goal of this paper is to focus on the investigation of interaction between a magnetic field and elastic materials with microstructure, whose microelements possess microtemperatures with photothermal excitation. The elastic-photothermal problem in one-dimension is solved by introducing photothermal excitation at the free surface of a semi-infinite semiconducting medium (semiconductor rod). The integral transform technique is used to solve the governing equations of the problem under the effect of the microtemperature field. The analytical expressions for some physical quantities in the physical domain are obtained with the heating boundary surface and free traction. The numerical inversion technique is used to obtain the resulting quantities in the physical domain. The obtained numerical results with some comparisons are discussed and shown graphically.     

Heterogeneous elastic solids: a mixed homogenization-rigidification technique

A homogenization technique for heterogeneous elastic solids made up by a matrix containing inclusions modelled as rigid in the limit, is proposed. It is shown that the approach can cause considerable simplifications with respect to the use of standard homogenization procedures. The case of a masonry panel set across on an opening is analysed by applying the proposed technique and some numerical results are given. They are compared first with those obtained by considering the panel as a heterogeneous body and, in turn, by using standard homogenization.     

A novel numerical algorithm based on Galerkin–Petrov time-discretization method for solving chaotic nonlinear dynamical systems

Nonlinear chaotic systems yield many interesting features related to different physical phenomena and practical applications. These systems are very sensitive to initial conditions at each time-iteration level in a numerical algorithm. In this article, we study the behavior of some nonlinear chaotic systems by a new numerical approach based on the concept of Galerkin–Petrov time-discretization formulation. Computational algorithms are derived to calculate dynamical behavior of nonlinear chaotic systems. Dynamical systems representing weather prediction model and finance model are chosen as test cases for simulation using the derived algorithms. The obtained results are compared with classical RK-4 and RK-5 methods, and an excellent agreement is achieved. The accuracy and convergence of the method are shown by comparing numerically computed results with the exact solution for two test problems derived from another nonlinear dynamical system in two-dimensional space. It is shown that the derived numerical algorithms have a great potential in dealing with the solution of nonlinear chaotic systems and thus can be utilized to delineate different features and characteristics of their solutions.     

A numerical model for the flooding and drying of irregular domains

A numerical technique for the modelling of shallow water flow in one and two dimensions is presented in this work along with the results obtained in different applications involving unsteady flows in complex geometries. A cell‐centred finite volume method based on Roe's approximate Riemann solver across the edges of both structured and unstructured cells is presented. The discretization of the bed slope source terms is done following an upwind approach. In some applications a problem arises when the flow propagates over adverse dry bed slopes, so a special procedure has been introduced to model the advancing front. It is shown that this modification reproduces exactly steady state of still water in configurations with strong variations in bed slope and contour. The applications presented are mainly related with unsteady flow problems. The scheme is capable of handling complex flow domains as will be shown in the simulations corresponding to the test cases that are going to be presented. Comparisons of experimental and numerical results are shown for some of the tests. Copyright © 2002 John Wiley & Sons, Ltd.     

THE BIRTH OF OPEN SEPARATION ON A PROLATE SPHEROID

Results are presented to describe the laminar flow patterns around a prolate spheroid at angles of attack of 1, 2, 3, and 30 degrees and complement those obtained previously at 6 degrees. They were obtained by solving the three-dimensional boundary-layer equations with a combination of standard and characteristic box methods and with a stability criterion to ensure numerical accuracy. Emphasis is placed on the nature of separation which is shown to be coincident with a particular skin friction line on the windward side. The results on the leeward side break down prior to separation but suggest that, in agreement with experiment and contrary to some theoretical claims, the separation is open.     

A high-order characteristics/finite element method for the incompressible Navier-Stokes equations

In this paper we consider a discretization of the incompressible Navier-Stokes equations involving a second-order time scheme based on the characteristics method and a spatial discretization of finite element type. Theoretical and numerical analyses are detailed and we obtain stability results abnd optimal eror estimates on the velocity and pressure under a time step restriction less stringent than the standard Courant-Freidrichs-Levy condition. Finally, some numerical results obtained wiht the code N3S are shown which justify the interest of this scheme and its advantages with respect to an analogous first-order time scheme. © 1997 John Wiley & Sons, Ltd.     

A compact finite difference method for solving Burgers' equation

In this paper, a high‐order accurate compact finite difference method using the Hopf–Cole transformation is introduced for solving one‐dimensional Burgers' equation numerically. The stability and convergence analyses for the proposed method are given, and this method is shown to be unconditionally stable. To demonstrate efficiency, numerical results obtained by the proposed scheme are compared with the exact solutions and the results obtained by some other methods. The proposed method is second‐ and fourth‐order accurate in time and space, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

NUMERICAL INVESTIGATION OF EVOLUTION OF DISTURBANCES IN SUPERSONIC SHARP CONE BOUNDARY LAYERS

The spatial evolution of 2-D disturbances in supersonic sharp cone boundary layers was investigated by direct numerical simulation (DNS) in high order compact difference scheme. The results suggested that, although the normal velocity in the sharp cone boundary layer was not small, the evolution of amplitude and phase for small amplitude disturbances would be well in accordance with the results obtained by the linear stability theory (LST) which supposes the flow was parallel. The evolution of some finite amplitude disturbances was also investigated, and the characteristic of the evolution was shown. Shocklets were also found when the amplitude of disturbances increased over some value.     

Application of the GSMAC-CIP Method to Incompressible Navier-Stokes Equations at High Reynolds Numbers

The conventional shape function for the finite-element method (FEM) is linear, and it is thus inadequate for analyzing numerically complex flows at high Reynolds numbers. In this study, we propose a new scheme, GSMAC-CIP, using the third-order shape function, which requires continuity of the value of the function and its first space derivative in the whole space and is formulated by a finite element method for the cubic interpolated pseudo-particle (CIP) method. We verified the effectiveness of this new scheme by analyzing the forced-driven convection in a square cavity at Re = 1000, 5000 and 10000. The numerical results obtained by the present scheme are compared with those of GSMAC-FEM using coarser meshes, and it is shown that the present scheme is superior to GSMAC-FEM in terms of space accuracy. Moreover, it is shown that the numerical results obtained by the present scheme using fine meshes were in precise agreement with those obtained by Ghia et al.     

A regular boundary element method for fluid flow

The Boundary Element Method is now well established as a valid numerical technique for the solution of field problems, equal to the Finite Element Method in generality and surpassing it in computational efficiency in some cases.¹ In this paper is presented a 'Regular Boundary Element Method' as applied to inviscid laminar fluid flow problems. It involves the formation of a system of regular integral equations obtained by moving the singularity outside the domain of the given problem. It is also shown that non-conforming elements may be used whereby freedoms are not defined at the geometric nodes under the boundary element discretization. A linear element is developed here; higher order variants could easily be defined. Satisfactory numerical results have been obtained using the proposed regular method with both conventional (continuous across the boundary) and non-conforming boundary elements for two-dimensional inviscid laminar fluid flow problems having regular and singular solutions.     

Hopf bifurcation in general Brusselator system with diffusion

The general Brusselator system is considered under homogeneous Neumann boundary conditions. The existence results of the Hopf bifurcation to the ordinary differential equation (ODE) and partial differential equation (PDE) models are obtained. By the center manifold theory and the normal form method, the bifurcation direction and stability of periodic solutions are established. Moreover, some numerical simulations are shown to support the analytical results. At the same time, the positive steady-state solutions and spatially inhomogeneous periodic solutions are graphically shown to supplement the analytical results.     

应力三轴度的有限元计算修正

对某高强度钢制成的光滑圆棒和缺口圆棒进行了系列准静态拉伸实验,采用ABAQUS对每个试 件进行了数值模拟,得到了该材料的真实应力应变曲线,拟合出了J-C本构模型和失效模型的部分材料常数。 最后,对该高强度钢制成的平板进行了撞击实验,并用得到的J-C模型对平板撞击实验进行了数值模拟,计算 结果与实验结果吻合很好,证明利用数值模拟并修正应力三轴度的方法是可行的。     

Consequences of the Maxwell relation for anti-plane shear deformations of an elastic solid

Previous numerical work has predicted chaotic distributions of phases in certain deformations of an elastic solid whose stress-strain relation in simple shear is nonmonotone. The present work provides an interpretation of these results making use of elastic stability considerations. For a specific material, a conformal mapping technique is shown to generate the totality of all deformations satisfying the Maxwell relation. It is shown that some boundary value problems have no solutions which obey the Maxwell relation. Such problems may have associated with them an infinite sequence of deformations (corresponding to a minimizing sequence in variational calculus) which satisfies the Maxwell relation in the sense of a limit. The properties of such sequences are examined in detail, and it is shown that the chaotic numerical solutions may be interpreted as terms in this sequence.     

An adaptive algorithm of precise integration for transient analysis

This paper presents an improved precise integration algorithm for transient analysis of heat transfer and some other problems. The original precise integration method is improved by means of the inverse accuracy analysis so that the parameterN, which has been taken as a constant and an independent parameter without consideration of the problems in the original method, can be generated automatically by the algorithm itself. Thus, the improved algorithm is adaptive and the accuracy of the algorithm is not dependent on the length of the time step in the integration process. It is shown that the numerical results obtained by the method proposed are more accurate than those obtained by the conventional time integration methods such as the difference method and others. Four examples are given to demonstrate the validity, accuracy and efficiency of the new method. Project supported by the National Natural Science Foundation of China (No. 19872016, 19872017), the National Key Basic Research Special Foundation (G1999032805) and the Foundation for University Key Teachers by the Ministry of Education of China.     

预折纹管在低速冲击载荷作用下的能量吸收

为了降低结构的初始载荷、增加有效塑性变形面积,进而提高其吸能效率,研究一种以新型的预折纹管,在普通管的管壁上引入特别设计的折角。基于有限元软件ABAQUS/EXPLICIT的数值分析验证了预折纹在低速冲击载荷作用下可以引导预期的大变形模式,预折纹管的这种大变形模式相较于普通方管的对称变形模式有更低峰值载荷和更高的平均载荷。通过低速落锤实验获得了与有限元模拟结果相似的载荷-位移曲线和变形模式,验证了数值结果的可信性和预折纹方管的高效吸能特点。     

气压对压力容器前壁超高速撞击损伤的影响

充气压力容器在超高速撞击下的典型损伤包括穿孔及其边缘的裂纹失稳破坏,会导致气体泄漏或爆炸,内压对容器前壁损伤的影响仍不明确。以不同内压的球形铝合金充气压力容器为研究对象,开展了球形铝合金弹丸超高速撞击实验和数值模拟计算,分析了内充气体压强对前壁穿孔形貌特征、穿孔直径、孔边环向应力等的影响规律和影响机理,讨论了气体冲击波的传播行为及影响前壁穿孔边缘裂纹失稳破坏的机制。结果表明:前壁穿孔边缘内翻边形貌与内压相关,内压越高,弯折程度越轻;穿孔直径与内充气体压强正相关,但气体对孔径的影响远小于容器壁厚及撞击速度的影响;穿孔边缘使裂纹失稳破坏的环向拉应力不仅受到后壁反射冲击波的影响,也与容器壁内应力波的传播有关,与内压成正比。     

Some useful hybrid approaches for predicting aerodynamic noise

In recent years, several numerical studies have shown the feasibility of Direct Noise Computation (DNC) where the turbulent flow and the radiated acoustic field are obtained simultaneously by solving the compressible Navier–Stokes equations. The acoustic radiation obtained by DNC can be used as reference solution to investigate hybrid methods in which the sound field is usually calculated as a by-product of the flow field obtained by a more conventional Navier–Stokes solver. A hybrid approach is indeed of practical interest when only the non-acoustic part of the aerodynamic field is available. In this review, some acoustic analogies or hybrid approaches are revisited in the light of CAA. To cite this article: C. Bailly et al., C. R. Mecanique 333 (2005).