Freestream and vortex preservation properties of high-order WENO and WCNS on curvilinear grids

Freestream and vortex preservation properties of a weighted essentially nonoscillatory scheme (WENO) and a weighted compact nonlinear scheme (WCNS) on curvilinear grids are investigated. While the numerical technique used for the compact difference scheme can be applied to WCNS, applying it to WENO is difficult. This difference is caused by difference in the formulation of numerical fluxes. WENO computed in the generalized coordinate system does not work well for either freestream or vortex preservation, whereas WENO computed in the Cartesian coordinate system works well for both freestream and vortex preservation, but its resolution is lower than that of WCNS. In addition, WENO in the Cartesian coordinate system costs three times as much as WENO or WCNS in the generalized coordinate system. Therefore, WENO in the Cartesian coordinate system is not suitable for solving Euler equations on a curvilinear grid. On the other hand, WCNS computed in the generalized coordinate system works well for freestream and vortex preservation when used with the numerical technique proposed for the compact difference scheme. The results show that WCNS with this numerical technique can be used for an arbitrary grid system. In this paper, the excellent freestream and vortex preservation properties of WCNS when used with the numerical technique, compared with those of WENO, are shown for the first time.     

Study of the equation for the Abrikosov vortex pinning on a linear defect in a superconducting wafer

An equation for an Abrikosov vortex bound state on a linear defect in a superconducting thin film in the presence of transport current is studied. A theoretical analysis of the corresponding boundary problem has been carried out and an estimate of the density of the critical current resulting in the vortex string depinning is obtained. The shape of an elastic vortex string is calculated. The instability threshold of the vortex-bound state due to the increase in the current, which results in the vortex string depinning, is found using numerical modeling. The results agree qualitatively with the data of the experiments carried out on high-temperature superconductors.     

Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity

Since direct numerical simulations of buoyancy driven flows cannot be computed at high Rayleigh numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the non-linearity: the convective term is altered to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yielded a novel class of regularizations [Comput Fluids 2008;37:887] that restrain the convective production of smaller and smaller scales of motion in an unconditionally stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. In the present work, a criterion to determine dynamically the regularization parameter (local filter length) is proposed: it is based on the requirement that the vortex stretching must stop at the scale set by the grid. Therefore, the proposed method constitutes a parameter-free turbulence model. The resulting regularization method is tested for a 3D natural convection flow in an air-filled (Pr = 0.71) differentially heated cavity of height aspect ratio 4. Direct comparison with DNS results at Rayleigh number 6.4 × 10⁸ ? Ra ? 10¹¹ shows fairly good agreement even for very coarse grids. Finally, the robustness of the method is tested by performing simulations with Ra up to 10¹⁷. A 2/7 scaling law of Nusselt number has been obtained for the investigated range of Ra.     

The Method of Difference Potentials for the Helmholtz Equation Using Compact High Order Schemes

The method of difference potentials was originally proposed by Ryaben??kii and can be interpreted as a generalized discrete version of the method of Calderon??s operators in the theory of partial differential equations. It has a number of important advantages; it easily handles curvilinear boundaries, variable coefficients, and non-standard boundary conditions while keeping the complexity at the level of a finite-difference scheme on a regular structured grid. The method of difference potentials assembles the overall solution of the original boundary value problem by repeatedly solving an auxiliary problem. This auxiliary problem allows a considerable degree of flexibility in its formulation and can be chosen so that it is very efficient to solve. Compact finite difference schemes enable high order accuracy on small stencils at virtually no extra cost. The scheme attains consistency only on the solutions of the differential equation rather than on a wider class of sufficiently smooth functions. Unlike standard high order schemes, compact approximations require no additional boundary conditions beyond those needed for the differential equation itself. However, they exploit two stencils??one applies to the left-hand side of the equation and the other applies to the right-hand side of the equation. We shall show how to properly define and compute the difference potentials and boundary projections for compact schemes. The combination of the method of difference potentials and compact schemes yields an inexpensive numerical procedure that offers high order accuracy for non-conforming smooth curvilinear boundaries on regular grids. We demonstrate the capabilities of the resulting method by solving the inhomogeneous Helmholtz equation with a variable wavenumber with high order (4 and 6) accuracy on Cartesian grids for non-conforming boundaries such as circles and ellipses.     

Cabaret scheme for two-dimensional incompressible fluid in terms of the stream function-vorticity variables

In the present work, the Cabaret method is generalized to the case of two-dimensional incompressible fluid in terms of the stream function-vorticity variables. Using the example of the solitary vortex problem, the high quality of the obtained algorithm in terms of its dissipative and dispersion properties is demonstrated. In the problem about decaying homogeneous isotropic turbulence, the slopes of the energy spectra for all grids (16 × 16, 32 × 32, 64 × 64, 128 × 128) are (−3) up to the highest harmonics, which coincides with Batchelor’s theory.     

Lattice Boltzmann simulation of lid-driven swirling flow in confined cylindrical cavity

Lid-driven swirling flow in a confined cylindrical cavity is investigated using lattice Boltzmann equation (LBE) method. The steady, 3-dimensional flow is examined at different aspect (height-to-radius) ratios and Reynolds numbers. The LBE simulations are carried out using the multiple-relaxation-time method. The LBE simulation results are compared with the results of a finite volume solution of Navier-Stokes equations and with published experimental data. Numerical results are presented for cylindrical cavities with two aspect ratios of 1.5 and 2.5, and three Reynolds numbers of 990, 1010 and 1290. Effects of the aspect ratio and Reynolds number on the size, position and breakdown of the central recirculation bubble, together with the flow pattern in the cavity, are determined. Detailed topological features of the flow, such as, (1) structure and breakdown of the vortex along the axis, (2) azimuthal component of vorticity, and (3) circulation strength of flow about the axis are investigated and compared with previous findings from experiments and theory.The predicted results from LBE simulations are consistent with experiments and theory. Steady results reveal the occurrence of a breakdown bubble in agreement with the regime diagram due to Escudier. The vortex breakdown around a region may be characterized by a change in sign of the azimuthal vorticity near such locations. Investigations are carried out on the characteristics of angular momentum when the vortex breakdown occurs. The theoretical criterion for vortex breakdown to occur, as proposed by Brown and Lopez is verified using the numerical data obtained from the simulations.     

基于具有自适应分段损失函数支持向量机的产品销售预测模型

针对产品销售时序包含噪声的数据特征, 提出一种基于自适应分段损失函数的支持向量机模型(AS??-SVM). AS??-SVM 为每个样本点赋一个单独的不敏感损失值, 以此降低模型对包含较大噪声的样本点的依赖性, 并从理论上证明了该方法可增强模型部分的泛化性能. 将AS??-SVM 与??-SVM 共同应用于处理一个数值算例和一个汽车销售预测实例中, 仿真实验结果表明, AS??-SVM 是有效可行的, 可获得比??-SVM 更精确的预测结果.

     

E型碳化硅压力传感器的优化设计

描述了一种性能优越的SiC压力传感器的理论和仿真运用基于小扰度的解析模型计算出了这种传感器的应变分布.根据应变分布规律优化设计了传感器的力敏电阻.利用ANSYS软件分析了该传感器的一些重要特性.与传统的传感器(圆膜传感器)相比,量程为500 kPa的该传感器表现出优异的灵敏度(24.8 μV/V.kPa)和非线性度小于0.08%.仿真结果与测量结果基本一致.     

A program to generate a basis set adaptive radial quadrature grid for density functional theory

We present an automatic quadrature routine (AQR) which generates an atomic basis set adaptive radial quadrature grid for the numerical evaluation of molecular integrands in density functional theory. Unlike the popular radial grids that are tuned to a particular class of integrands and rely on a fixed selection of points, our grid adapts itself automatically to the atomic shell structure of any radial integrand and determines the best number of quadrature points that provides user specified accuracy. We evaluate the performance of our radial grid on various tight, diffuse, and noble gas atom radial integrands. We conclude that the radial quadrature grid generated by our AQR is generally comparable to and sometimes better than the best ranked popular radial grids in efficiency and reliability.     

Lattice Boltzmann Model Based on the Rebuilding-Divergency Method for the Laplace Equation and the Poisson Equation

In this paper, a new lattice Boltzmann model based on the rebuilding-divergency method for the Poisson equation is proposed. In order to translate the Poisson equation into a conservation law equation, the source term and diffusion term are changed into divergence forms. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales and several higher-order moments of equilibrium distribution functions are obtained. Thus, by rebuilding the divergence of the source and diffusion terms, the Laplace equation and the Poisson equation with the second accuracy of the truncation errors are recovered. In the numerical examples, we compare the numerical results of this scheme with those obtained by other classical method for the Green-Taylor vortex flow, numerical results agree well with the classical ones.     

Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian grids

This paper describes a new numerical procedure, based on point collocation, integrated multiquadric functions and Cartesian grids, for the discretisation of the stream-function formulation for flows of a Newtonian fluid in multiply-connected domains. Three particular issues, namely (i) the derivation of the stream-function values on separate boundaries, (ii) the implementation of cross derivatives in irregular regions, and (iii) the treatment of double boundary conditions, are studied in the context of Cartesian grids and approximants based on integrated multiquadric functions in one dimension. Several test problems, i.e. steady flows between a rotating circular cylinder and a fixed square cylinder and also between eccentric cylinders maintained at different temperatures, are investigated. Results obtained are compared well with numerical data available in the literature.     

Modeling of delta-wing type vortex generators

A numerical model of delta-wing type vortex generator was developed in two steps.The first step was to obtain a parameterized model of the shedding vortex based on delta-wing theory,which relates the geometry parameters and flow field parameters to the strength of shedding vortex which directly decides the source term.In the second step,a method was proposed to add source terms into the flow control equations so that the shedding vortex could be simulated numerically.As soon as the numerical model was compl...     

Improving spatial resolution characteristics of finite difference and finite volume schemes by approximate deconvolution pre-processing

A pre-processing step is proposed as a general method to enhance resolution properties of low order numerical differentiation and interpolation. Pre-processing operators are designed by taking two or more terms in the approximate deconvolution formula and using a local filter whose response characteristics are close to those of the numerical operation considered; operators for second order central differencing for first and second derivatives and also for a finite volume method are determined. In addition to the higher resolution the effective order of the truncation error can also be increased. The repeated filtering operations couple the operation over a wider stencil without using direct formulas. The effect of improving the resolution properties is illustrated first by computing the propagation of a square wave by a 1D, linear convection equation. Next, pre-processing is implemented in a standard finite volume code for solving Navier-Stokes equations for incompressible flow. In the Taylor-Green vortex flow, the improvements in order behaviour are demonstrated. The instability of plane Poiseuille flow, which is a sensitive test of resolution ability, shows that the predicted growth rates with the pre-processing scheme are more accurate than those obtained with a second order scheme. Direct numerical simulations of turbulent channel flow show that the improvement allows accurate solutions to be found on smaller grids.     

A numerical investigation of turbulent flows in a spanwise rotating channel

A numerical investigation of fully developed turbulent flow in a spanwise rotating channel is performed to study turbulence characteristics subject to system rotation. The work provides insight into several salient features of the spanwise rotating turbulent channel flows, including the near-wall vortical structures, turbulence energy cascade and redistribution, and vortex stretching. The influence of system rotation on the near-wall vortical structures is investigated based on the vorticity fluctuations and their probability density functions (PDF). The properties of the Lamb vector fluctuation and the corresponding PDF are examined to reveal the effect of rotation on the turbulence energy cascade and production in the rotating channel. The budgets of Reynolds stresses and fluctuating enstrophy are analyzed to elucidate the role of the Coriolis force on turbulence energy redistribution between the streamwise and wall-normal directions and the mechanisms of vortex stretching for the generation of the vorticity fluctuations near the pressure and suction walls.     

Formulation and multigrid solution of Cauchy-Riemann optimal control problems

The formulation of optimal control problems governed by Cauchy-Riemann equations is presented. A distributed control mechanism through divergence and curl sources is considered with the boundary conditions of mixed type. A Lagrange multiplier framework is introduced to characterize the solution to Cauchy-Riemann optimal control problems as the solution of an optimality system of four first-order partial differential equations and two optimality conditions. To solve the optimality system, staggered grids and multigrid methods are investigated. It results that staggered grids provide a natural collocation of the optimization variables and second-order accurate solutions are obtained. The proposed multigrid scheme is based on a coarsening by a factor of three that results in a nested hierarchy of staggered grids. On these grids a distributed-Gauss-Seidel and gradient-based smoothing scheme is employed. Results of numerical experiments validate the proposed optimal control formulation and demonstrate the effectiveness of the staggered-grids multigrid solution procedure.     

A high precision triangular laminated anisotropic shallow thin shell finite element

A high precision triangular laminated shallow thin shell finite element has been developed based on the classical lamination theory. The stiffness matrix is obtained explicitly by pre and post multiplying a few basic matrices. The formulation is almost an order of magnitude faster than those available for similar order elements. The numerical results of the example problems presented demonstrate that both displacements and stresses are predicted accurately with moderately coarse grids. A complete listing of FORTRAN subroutines is presented for users, to ease implementation of the algorithm.     

Numerical simulation of vortical flows in the near field of jets from notched circular nozzles

The vortex dominated flows in the near field of jets from notched circular nozzles are investigated using direct numerical simulation. The nozzles studied include a normal circular nozzle, a V-shaped notched nozzle, and an A-shaped notched nozzle, all with the same circular cross-section. The vortical structures resulting from these different circular nozzles are visualized by using a numerical dye visualization technique. Results for the V-shaped notched nozzle are compared with available experimental measurements using laser-induced fluorescence techniques. In addition to azimuthal vortex rings created because of the shear-layer between the jet and the ambient fluid, the computations also reveal streamwise vortex pairs both inside and outside the vortex rings that spread outward as the vortex rings move downstream. Comparisons of the three different nozzles show that, unlike in the case of the circular nozzle where the streamwise vortex pairs emerge evenly along the nozzle lip, streamwise vortex pairs for the notched circular nozzles are produced only at peak and trough locations. Analysis of the mixing characteristics of the three types of nozzles shows that the notches in the nozzle exit significantly enhance jet mixing.     

Uniformly convergent numerical method for singularly perturbed parabolic initial-boundary-value problems with equidistributed grids

In this article, we study the numerical solution of singularly perturbed parabolic convection–diffusion problems exhibiting regular boundary layers. To solve these problems, we use the classical upwind finite difference scheme on layer-adapted nonuniform grids. The nonuniform grids are obtained by equidistribution of a positive monitor function, which is a linear combination of a constant and the second-order spatial derivative of the singular component of the solution on every temporal level. Truncation error and the stability analysis are obtained. Parameter-uniform error estimates are derived for the numerical solution. To support the theoretical results, numerical experiments are carried out.     

Application of optimal control theory to flexible robotic manipulations

The dynamic equatios of a single link flexible robotic manipulator and the measurements are formulated. The observer and the control law are derived based on optimal control theory. The numerical results of several cases obtained through computer simulation are presented here. The issues of nonlinearity and sampling rate, and the effects of gravity, white noises, and damping are investigated. The feasibility of real-time control of flexible robotic manipulators is discussed.