Direct Numerical Simulation in a Lid-Driven Cubical Cavity at High Reynolds Number by a Chebyshev Spectral Method

Direct numerical simulation of the flow in a lid-driven cubical cavity has been carried out at high Reynolds numbers (based on the maximum velocity on the lid), between 1.2 10⁴ and 2.2 10⁴. An efficient Chebyshev spectral method has been implemented for the solution of the incompressible Navier–Stokes equations in a cubical domain. The Projection-Diffusion method [Leriche and Labrosse (2000, SIAM J. Sci. Comput. 22(4), 1386–1410), Leriche et al. (2005, J. Sci. Comput., in press)] allows to decouple the velocity and pressure computation in very efficient way and the simple geometry allows to use the fast diagonalisation method for inverting the elliptic operators at a low computational cost. The resolution used up to 5.0 million Chebyshev collocation nodes, which enable the detailed representation of all dynamically significant scales of motion. The mean and root-mean-square velocity statistics are briefly presented     

Fluid-Structure Interaction by the Spectral Element Method

Viscous fluid-structure interaction is treated with an arbitrary Lagrangian- Eulerian formulation. The spatial discretization is performed by the spectral element method for the fluid part where the Navier-Stokes equations are integrated and in the solid part where transient linear elasticity is described by the Navier equations. Time marching algorithms are second-order accurate in time in both the fluid and the solid. The algorithm is applied to the flow in a plane channel partially obstructed by a solid component able to move under the action of the fluid flow.     

Spectral Vanishing Viscosity Method for Large-Eddy Simulation of Turbulent Flows

An efficient spectral vanishing viscosity method for the large-eddy simulation of incompressible flows is proposed, both for standard spectral and spectral element approximations. The approach is integrated in a collocation spectral Chebyshev-Fourier solver and then used to compute the turbulent wake of a cylinder in a crossflow confined geometry (Reynolds number Re=3900)     

Steady Gap Flows by the Spectral and Mortar Element Method

This work aims at observing the effect of the mortar element method applied to a geometry requiring refinement in the vicinity of singularities induced by the presence of sharp corners. We solve the two-dimensional incompressible Navier–Stokes equations with a spectral element method. Mortar elements allow for local polynomial refinement, since they allow for functional nonconformity. The problem solved is the flow in a channel partially obstructed by an obstacle representing a rectangular blade.     

Application of a Spectral Element Method to Two-Dimensional Forward-Facing Step Flow

In the present study, we investigate the two-dimensional laminar flow through a one-sided constriction of a plane channel with a ratio of h:H=1:4 (where h is the step height and H is the channel height). The computational approach employed is based on a mixed implicit/explicit time discretization scheme together with a highly accurate spatial discretization using a P _N –P _N–2 spectral-element method. It is well known that this so-called forward-facing step (FFS) flow exhibits a singularity in the pressure and the velocity derivatives at the corner point. We account for this singularity by a geometric mesh refinement strategy that was proposed in a hp-FEM context. A detailed numerical study of the FFS flow reveals that length and height of the recirculation zone in front of the step are almost constant for creeping flow. In the limit of high Reynolds numbers the length and height of the recirculation zone increase proportional to Re ^0.6 and Re ^0.2, respectively.     

On the Simulation of Unsteady Flow of an Oldroyd-B Fluid by Spectral Methods

We report numerical results on the simulation of unsteady flow of an Oldroyd-B fluid by spectral element methods. Several techniques to cure the instabilities are considered.     

Analysis of a Discontinuous Least Squares Spectral Element Method

This paper addresses the development of a Discontinuous Spectral Least-Squares method. Based on pre-multiplication with a mesh-dependent function a discontinuous functional can be set up. Coercivity of this functional will be established. An example of the approximation to a continuous solution and a solution in which a jump is prescribed will be presented. The discontinuous least-squares method preserves symmetry and positive definiteness of the discrete system.     

切比契夫谱元素局部混合基函数构造

针对切比契夫谱方法,该文首次构造了两类局部混合基函数,据此发展了一种新的谱元素方法:在元素端点采用局部拉格朗日插值基,元素内部采用经调整后的切比契夫多项式。这里的两类混合基函数在计算精度上可与传统的拉格朗日基相媲美,而且元素矩阵具有稀疏特征和数据重用性。该文给出的局部混合基函数对传统的谱元素方法进行了扩充。     

Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method

We study the performance of the multigrid method applied to spectral element (SE) discretizations of the Poisson and Helmholtz equations. Smoothers based on finite element (FE) discretizations, overlapping Schwarz methods, and point-Jacobi are considered in conjunction with conjugate gradient and GMRES acceleration techniques. It is found that Schwarz methods based on restrictions of the originating SE matrices converge faster than FE-based methods and that weighting the Schwarz matrices by the inverse of the diagonal counting matrix is essential to effective Schwarz smoothing. Several of the methods considered achieve convergence rates comparable to those attained by classic multigrid on regular grids.     

A Robust Spectral Element Method for Simulations of Time-Dependent Viscoelastic Flows, Derived from the Brownian Configuration Field Method

This paper is an extension of previous work [4], where a robust numerical method derived from the Brownian configuration field method [8] was introduced in order to simulate the flows of dilute polymeric solutions. In [4], we limited our study to solutions of dumbbells having infinite extensibility (Oldroyd-B model), whereas in this paper, we tackle the more difficult problem of dumbbells having finite extensibility (FENE-P model).     

Direct Minimization of the Discontinuous Least-Squares Spectral Element Method for Viscoelastic Fluids

In this paper direct minimization of the discontinuous least-squares spectral element formulation is described. The method will beapplied to the Upper Convected Maxwell (UCM) model which describes a viscoelastic fluid. The new ideas presented in this paper consist of the weak coupling of the fluxes in the least-squares formulations instead of imposing weak continuity of the dependent variables. Furthermore, direct minimization is employed instead of the conventional variational least-squares formulation. The resulting system is solved iteratively using LSQR.     

Identification and Reconstruction of a Small Leak Zone in a Pipe by a Spectral Element Method

This paper deals with the identification of a zone permitting fluid to leak out of a drain. Using the analogy with crack identification by boundary measurements, we give uniqueness and stability results and we propose an algorithm for the numerical solution of the problem. Since the forward problem consists of a mixed boundary value problem with a strong anisotropy, we discretize it by a mortar spectral element method.     

Adaptive Spectral Element Simulations of Thin Premixed Flame Sheet Deformations

The high order Spectral Element Method is used to solve the reaction-diffusion-advection problem as described by the premixed flame case. An h–p adaptive refinement-coarsening algorithm is developed based on a posteriori error estimators. Simulations of the wrinkling of a premixed flame front are used to illustrate how the mesh is adaptively refined. A similar, idealized heat transfer problem is used to show the adaptive refinement and coarsening of the mesh. Adaptivity efficiently provides high resolution in areas of the domain where large or rapidly varying physical changes exist, while saving unnecessary computation where the solution is smooth or physical phenomena have passed by.     

A Discontinuous Spectral Element Method for the Level Set Equation

Level set methodology is crucially pertinent to tracking moving singular surfaces or thin fronts with steep gradients in the numerical solutions of partial differential equations governing complex flow fields. This methodology must be consistent with the basic solution technique for the partial differential equations. To this end, a discontinuous spectral element approach is developed for level set advection and reinitialization as these methods are becoming increasingly popular for the solution of the fluid dynamic problems. Example computations are provided, which demonstrate the high order accuracy of the method.     

Stabilization Methods for Spectral Element Computations of Incompressible Flows

A stabilization method for the spectral element computation of incompressible flow problems is investigated. It is based on a filtering procedure which consists in filtering the velocity field by a spectral vanishing Helmholtz-type operator at each time step. Relationship between this filtering procedure and SVV-stabilization method, introduced recently in [JCP, 2004, 196(2), p680], is established. A number of numerical examples are presented to show the accuracy and stabilization capability of the method.     

Simulations of Time-Dependent Flows of Viscoelastic Fluids with Spectral Element Methods

This paper presents the application of spectral element methods to simulate the time-dependent flow of viscoelastic fluids in non-trivial geometries using a closed-form differential constitutive equation. As an example, results relative to the flow of a FENE-CR fluid in a two-dimensional four-to-one contraction are given.     

运动系统稳定性的计算机仿真研究

运动稳定性对机构工作性能有重大影响。对于复杂的多参数系统，难以通过理论分析来预测系统的运动趋势，尤其对于存在弹簧，阻尼器等非线性零部件的机械系统。该文采用有限元分析对运动过程进行实时仿真（real time simulation,RTS)研究，模拟运动系统的实际运动过程，从而分析研究运动稳定性与结构参数的关系。该文介绍了这种方法的基本原理和建模方法，并分析了一组弹簧连接物体的运动稳定性。分析结果表明，该方法能够有效地在设计阶段对结构的动力学性能进行预测与评价。     

A Legendre-Spectral Element Method for Flow and Heat Transfer About an Accelerating Droplet

The problem of flow and heat transfer associated with a spherical droplet accelerated from rest under gravitational force is studied; using a Legendre-spectral element method in conjunction with a mixed time integration procedure to advance the solution in time. An influence matrix technique which exploits the superposition principle is adapted to resolve the lack of vorticity boundary conditions and to decouple the equations from the interfacial couplings. The computed flow and temperature fields, the drag coefficient, the Nusselt number, and the interfacial velocity and vorticity are presented for a drop moving vertically in a quiescent gas of infinite extent to illustrate the evolution of the flow and temperature fields. Comparison of the predicted drag coefficient and the Nusselt number against previous numerical and experimental results indicate good agreement.     

微型法-珀腔阵列光谱探测器读出电路的模拟与设计

针对微型法-珀腔阵列光谱探测器读出电路的单芯片集成化设计,在研究分析微型法-珀腔阵列光谱探测器的结构和工作原理的基础上,提出了基于2μm标准CMOS工艺的8位线阵微型法-珀腔阵列光谱探测器读出电路方案,研究了电路中各元器件的结构与结构参数,在ORCAD软件平台下完成了读出电路各单元电路与系统电路的设计、仿真与优化,利用TANNER软件完成了微型法-珀腔阵列光谱探测器读出电路的版图设计及版图验证。该电路工作电压为 5 V,总功耗为4.82μW,版图面积0.37 mm×0.22 mm。