A numerical solution of the Navier-Stokes equations using the finite element technique

The finite element discretisation technique is used to effect a solution of the Navier- Stokes equations. Two methods of formulation are presented, and a comparison of the effeciency of the methods, associated with the solution of particular problems, is made. The first uses velocity and pressure as field variables and the second stream function and vorticity. It appears that, for contained flow problems the first formulation has some advantages over previous approaches using the finite elemental method[1,2].     

High resolution finite volume computations on unstructured grids using solution dependent weighted least squares gradients

An improved high resolution finite volume method based on linear and quadratic variable reconstructions using solution dependent weighted least squares (SDWLS) gradients has been presented here. An extended stencil consisting of vertex-based neighbours of a cell is used in the higher order reconstructions for inviscid flux computations. A QR algorithm with Householder transformation is used to solve the weighted least squares problem. In case of Navier–Stokes equations, viscous fluxes are discretized in a central differencing manner based on the Coirier’s diamond path. A few inviscid and viscous test cases are solved in order to demonstrate the efficacy of the present method. Progressive improvements in solution accuracy are observed with the increase in the order of variable reconstructions. In most cases, results of quadratic reconstruction show significant improvements over that of linear reconstruction.     

Numerical solution of 3D elastostatic inclusion problems using the volume integral equation method

A volume integral equation technique developed by Lee and Mal (J. Appl. Mech. Trans. ASME 64 (1997) 23) has been extended to investigate three-dimensional stress problems with multiple inclusions of various shapes. Based on the volume integral formulation, displacement continuity and traction equilibrium along the interfaces between the matrix and the inclusions are automatically satisfied. While the embedding matrix is represented by an integral formulation, only the inclusion parts are discretized into finite elements (isoparametric quadratic 10-node tetrahedral or 20-node hexahedral elements are used in the present study). A number of numerical examples are given to show the accuracy and effectiveness of the proposed method.     

An analysis of and a comparison between the discontinuous Galerkin and the spectral finite volume methods

The discontinuous Galerkin method has been developed and applied extensively to solve hyperbolic conservation laws in recent years. More recently Wang et al. developed a class of discontinuous Petrov–Galerkin method, termed spectral (finite) volume method [J. Comput. Phys. 78 (2002) 210; J. Comput. Phys. 179 (2002) 665; J. Sci. Comput. 20 (2004) 137]. In this paper we perform a Fourier type analysis on both methods when solving linear one-dimensional conservation laws. A comparison between the two methods is given in terms of accuracy, stability, and convergence. Numerical experiments are performed to validate this analysis and comparison.     

Numerical simulation of low-Reynolds number flows past rectangular cylinders based on adaptive finite element and finite volume methods

The flow past rectangular cylinders has been investigated by two different numerical techniques, an adaptive finite-element (AFEM) and a finite-volume method (FVM). A square and a rectangular cylinder with width-to-height equal to 5 are taken into account. 2D computations have been performed for different Reynolds numbers in order to consider different flow regimes, i.e. the stationary, the periodic and the turbulent flow. The comparison between the two methods regarded both the reliability of the computed solutions and the overall resulting efficiency of the methods. Velocity profiles and integral parameters such as Strouhal number, drag coefficient and recirculation length have been compared. A good agreement between the adaptive FEM and the FVM computations, as well as with the available literature results, has been found. The computational effort has been evaluated in terms of used degrees of freedom in space and time and human resources employed to reach the mesh and timestep-length independence of the solutions. Relevant outcomes of this work are the cross validation of an adaptive FE method and a popular open source FV code.     

Numerical solution of some initial optimal control problems using the reproducing kernel Hilbert space technique

ABSTRACT

In this paper, we present a general technique for solving a class of linear/nonlinear optimal control problems. In fact, an analytical solution of the state variable is represented in the form of a series in a reproducing kernel Hilbert space. Sometimes with the aid of this series form, we can also present the optimal control variable in a series form. An iterative method is given to obtain the approximate optimal control and state variables and the cost functional is numerically obtained. Convergence analysis of the method is also provided. Several numerical examples are tested to demonstrate the applicability and efficiency of the method.     

Mechanics of bipedal and quadrupedal locomotion on dry and wet granular media

The effectiveness of exploration robots is contingent upon their capability and efficiency to locomote on contorted and multifaceted terrains. Traditional wheeled robots do not suffice at overcoming such terrains and complications they introduce. The proposed work explores the performance of WhegRunner, a whegged (i.e., wheel-legged) robotic platform used to examine the mechanics of running on granular media at different saturation levels. In particular, the effect of bipedal/quadrupedal gait, saturation level, stride length, and stride frequency on robot's forward body velocity and cost of transport (COT) was studied. To increment nominal stride length, the robot was fitted with different number of spoked whegs from 3 to 7. In addition, eight evenly spaced motor speeds ranging from 2.33 to 7.43 Hz were used to observe the effect of stride frequency. Similar trends were observed between the two gaits, with the quadrupedal gait showing better overall performance. On dry sand, wider strides were attained at reduced motor speeds with lower spoked whegs. However, on wet sand (15% and 30% saturation), wider strides were achieved with higher motor speeds and lower spoked whegs. As a result, lower spoked whegs accomplished higher body forward velocity and lower COT as saturation increased. The acquired knowledge elucidates underexplored mechanics of locomotion on granular media at different saturation levels. The WhegRunner can be used as a platform to obtain a greater insight on how to develop more proficient exploration robots, ones which can face complex and deformable terrains and mediums.     

Identification of dry and wet soil conditions using TRMM/TMI brightness temperatures and potential for drought monitoring

In this study we present a methodology for monitoring drought conditions directly from microwave brightness temperature observations. Tropical Rainfall Measurement Mission (TRMM)/TRMM Microwave Imager (TMI) 10.7 GHz brightness temperatures were analysed along with TRMM merged rainfall products during June–August for 4 years to depict the spatial and temporal extent of dry and wet soil conditions. Comparison of brightness temperature anomalies with rainfall anomalies clearly shows the contrasting features of drought year 2002 and normal monsoon year 2001.     

Implementation of an element-by-element solution algorithm for the finite element method on a coarse-grained parallel computer

An element-by-element solution algorithm for systems of equations arising in applying the finite element method in solid mechanics was implemented on the loosely coupled array of processors (lCAP) parallel computer located at IBM Kingston. The element-by-element algorithm has previously been shown to be advantageous over direct solution algorithms for large problems on sequential computers. It also has the advantage that it can be implemented in parallel on machines such as the lCAP in a relatively straightforward manner. The results show that solution speedup efficiencies of approximately 95% can be readily achieved with this method, with no indication that the speed-up efficiency drops off as more processors are added. The implementation used is applicable to other coarse-grained parallel architectures in addition to the lCAP computer.     

基于GPS直接求解姿态矩阵算法的精度分析研究

利用GPS对载体的姿态进行测量是其应用的一个较新领域,直接求解姿态矩阵进行姿态角解算是一种直接有效的方法,但是解算精度受周跳、基线长度及卫星几何分布等因素的影响.在对直接求解姿态矩阵算法的解算过程进行深入分析的基础上,定量分析了周跳、基线长度等关键因素对测姿精度的影响,并通过计算机仿真对精度分析结果进行验证.开展的研究...     

Numerical analysis of pre- and post-critical response of elastic continua at finite strains

Based on the method of finite-elements, and the exact formulation of finite and incremental elasticity, the paper presents techniques for the numerical analysis of the pre- and post-critical behavior of elastic continua which are subjected to conservative loads and which undergo large deformations with finite strains. A combined incremental and iterative scheme is used in such a manner that convergence to the equilibrium state is attained at each state of loading, independently of the inaccuracy which may be involved in the characterization of the preceding state. The initial undeformed configuration of the elastic continuum is divided into a finite number of tetrahedra, and a linear variation of the displacement field within each tetrahedron is assumed. The first and second variations of the total potential energy at each loading stage are then developed in the form of a finite number of equations which characterize the response (the total response from the undeformed state, as well as the incremental one) and stability of the continuum. At each loading stage a pseudo-eigenvalue problem is formulated, by means of which an estimate can be made of the increment of load required to reach the critical state. The results are illustrated by means of two examples for compressible rubber-like materials for which a computer program has been developed. The first example demonstrates a snap-through instability, while the second example demonstrates a bifurcation-type instability. A formution for incompressible materials in plane strain is also presented.     

Calculating modes of quantum wire and dot systems using a finite differencing technique

In this paper the Schrödinger equation of both a quantum wire and a quantum dot are solved using a finite difference approach. It is demonstrated that the method is valid for the simple case of an infinitely deep quantum wire, where the solutions obtained are within 0.25 meV of the analytical solutions. The method is then used to calculate the eigenenergies of a triangular wire with finite barriers. The eigenenergies of the more complex case of a pyramidal quantum dot were then calculated using this method. The method is compared to an eigenvalue method in terms of memory usage, time requirements and the numerical solutions. It is shown that this method has the advantages of being relatively fast, usable with any wire geometry and any potential profile. In addition, the demand on computer memory varies linearly with the size of the system under investigation.     

Image segmentation using multilevel thresholding based on type II fuzzy entropy and marine predators algorithm

Multimedia Tools and Applications - The digital image segmentation is an open problem that is growing day by day and is attracting the attention of researchers from last few years. Image resolution...     

基于I-PSO算法和Simulink的湿式离合器优化设计

为提高湿式离合器的轻便性和可靠性,提出了一种I-PSO算法与MATLAB/Simulink相结合的湿式离合器优化设计新方法。对湿式离合器进行动力学分析,并基于MATLAB/Simulink搭建湿式离合器动力传递的仿真模型。引入模拟退火算法中对粒子进行扰动的思想对改进的粒子群算法再度进行改进,并基于某测试函数验证了算法改进的效果,选择离合器的滑磨功与体积为优化目标。最终联合改进粒子群算法与MATLAB/Simulink中建立的湿式离合器仿真模型对某具体型号湿式离合器进行多目标优化设计。结果表明,改进后的粒子群算法在寻优的速率和精度上有一定效果;优化后的湿式离合器与原设计相比,总目标函数缩小约40.12%,滑磨功减小了约61.8%,优化效果明显。     

1D wave propagation in saturated viscous geomaterials: Improvement and validation of a fractional step Taylor–Galerkin finite element algorithm

This paper tackles the numerical simulation of 1D wave propagation in saturated viscous porous media, and especially in soil-like geomaterials. For this purpose, an improved fractional step Taylor–Galerkin algorithm is first formulated and then validated on the basis of a new analytical solution.The algorithm, based on a stress–velocity–pressure formulation of the hydro-mechanical problem, combines an explicit Taylor–Galerkin method with a fractional time-stepping, while an accurate Runge–Kutta-type integrator is introduced to treat the viscosity of the porous skeleton. The overall algorithm results in an efficient stabilized scheme allowing for linear equal interpolation of field variables, even when the so-called “undrained incompressible limit” is approached.The accuracy and stability of the method are verified with reference to a 1D benchmark problem, concerning the propagation of P waves along a saturated viscoelastic soil stratum. For this problem, a frequency-domain analytical solution is derived, assuming incompressible interstitial fluid and soil grains. The assumption of Maxwell viscoelastic soil skeleton is analytically convenient to preserve the linearity of the problem, while the same rheology of a more realistic elasto-viscoplastic non-linear behaviour is maintained.The performance of the fractional step Taylor–Galerkin algorithm is explored simulating the dynamic response of the stratum to harmonic, impulsive and seismic input excitations. In particular, parametric analyses are performed to confirm the effectiveness of the method in reproducing fully undrained responses, as well as in dealing with weakly viscous materials.     

Modeling of 2D density-dependent flow and transport in porous media using finite volume method

A two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular mesh is developed for modeling density-dependent flow and transport through saturated-unsaturated porous media. The combined flow and transport model can handle a wide range of real-word problems, including the simulation of flow alone, contaminant transport alone, and combined flow and transport. Saltwater intrusion problems and instability caused by denser water on the top were investigated in this paper. Because the fundamental mechanism causing saltwater intrusion most likely is caused by density-induced convection and dispersion, the developed model is used to assess the interplay between density-driven flow and subsurface media through which the saltwater intrusion occurs.The mathematical formulation of the model is comprised of fluid flow and solute transport equations, coupled by fluid density. In the specific case of saltwater intrusion and unstable brine transport problems, this set of governing equation is non-linear and requires iterative methods to solve them simultaneously. Three case studies, which include a wide range of physical conditions, are used for verification of presented model and comparison with previously published solutions from other researchers presents encouraging agreements.     

A fast and efficient image registration algorithm using outlier rejection technique based on subimage

Image registration is a process of overlaying two or more images of the same scene taken at different times, from different viewpoints, and by different sensors. It geometrically aligns two images, the reference and sensed image. In this paper, a fast and efficient image registration algorithm is proposed for IDS (Intruder Detection System). To reduce a calculation time, outlier rejection method based on uniformity, entropy and subimage is used. An edge tapering method is applied to alleviate a boundary effect of a subimage. And it is shown that the proposed algorithm improves the accuracy and calculation time effectively.     

The solution of linear equations on a SIMD computer using a parallel iterative algorithm

Techniques for solving linear equations on a single instruction multiple data (SIMD) computer such as the ICL DAP have so far been confined to simple methods such as the Successive Overrelaxation and Alternating Direction Implicit algorithms. While these techniques are adequate for simple finite difference problems require more complex algorithms. Preconditioned conjugate gradient methods have solved difficult problems successfully on serial machines. This paper describes a preconditioning technique suitable for parallel machines and numerical results obtained from a series of problems of varying degrees of difficulty.     

A robust watermarking algorithm based on QR factorization and DCT using quantization index modulation technique

We propose a robust digital watermarking algorithm for copyright protection.A stable feature is obtained by utilizing QR factorization and discrete cosine transform(DCT) techniques,and a meaningful watermark image is embedded into an image by modifying the stable feature with a quantization index modulation(QIM) method.The combination of QR factorization,DCT,and QIM techniques guarantees the robustness of the algorithm.Furthermore,an embedding location selection method is exploited to select blocks with small modifications as the embedding locations.This can minimize the embedding distortion and greatly improve the imperceptibility of our scheme.Several standard images were tested and the experimental results were compared with those of other published schemes.The results demonstrate that our proposed scheme can achieve not only better imperceptibility,but also stronger robustness against common signal processing operations and lossy compressions,such as filtering,noise addition,scaling,sharpening,rotation,cropping,and JPEG/JPEG2000 compression.