Numerical models for vehicle exhaust dispersion in complex urban areas

Two numerical models are presented for predicting vehicle exhaust dispersion in complex urban areas with or without the wind field. The models not only reflect the effect of building and street canyon configuration on the pollutant propagation, but also are able to predict the turbulent energy produced by moving vehicles on the road. In particular, in the discrete model, turbulent energy and pollutant concentration produced by each vehicle are dynamically described in the Lagrangian method. The pollutant propagation is calculated with the advection–diffusion equation. The Reynolds averaged Navier–Stokes equations are numerically solved for the wind flows. The movement and heat release rate of the vehicles are treated as sources of the turbulent energy equation for the computation of turbulent energy produced by the moving vehicles. This paper reports the detailed implementation of the models. Four typical numerical tests were carried out to represent the performance of the proposed numerical models. Copyright © 2010 John Wiley & Sons, Ltd.     

基于离散元法的干湿颗粒系统仿真

介绍了基于离散元法的干湿颗粒系统仿真软件DEMSIM。对于干颗粒系统,DEMSIM可以分析二维和三维颗粒系统的弹性和塑性接触碰撞过程;对于湿颗粒系统,DEMSIM采用传统的液桥模型;对于颗粒-流体系统,DEMSIM采用CFD-DEM细观耦合模型模拟。一系列典型算例的模拟分析,验证了干湿颗粒系统仿真软件DEMSIM的精度和有效性。     

A conservative 2D model of inundation flow with solute transport over dry bed

In this paper, a transient 2D coupled vertically averaged flow/transport model is presented. The model deals with all kind of bed geometries and guarantees global conservation and positive values of both water level and solute concentration in the transient solution. The model is based on an upwind finite volume method, using Roe's approximate Riemann solver. A specific modification of the Riemann solver is proposed to overcome the generation of negative values of depth and concentration, that can appear as a consequence of existing wetting/drying and solute advance fronts over variable bed levels, or by the generation of new ones when dry areas appear. The numerical stability constraints of the explicit model are stated incorporating the influence of the flow velocity, the bed variations and the possible appearance of dry cells. Faced to the important restriction that this new stability condition can impose on the time step size, a different strategy to allow stability using a maximum time step, and in consequence a minimum computational cost is presented. Copyright © 2006 John Wiley & Sons, Ltd.     

A semi‐implicit numerical model for urban drainage systems

In this paper, a semi‐implicit numerical model for one‐dimensional urban drainage networks is formulated in such a fashion as to intrinsically account for arbitrary cross sections, for the occurrence of dry areas, for free surface, and for pressurized flows. The governing differential equations are discretized with a consistent mass conservative scheme that naturally applies to all flow regimes. The resulting mildly nonlinear system, at every time step, is efficiently solved with a converging, properly devised, nested Newton‐type algorithm. It will be shown that with the proposed semi‐implicit model, high accuracy can be achieved at a moderate computational cost. Copyright © 2013 John Wiley & Sons, Ltd.     

Error estimate and adaptive refinement for incompressible Navier‐Stokes equations using the discrete least squares meshless method

In this paper, an adaptive refinement strategy based on a node‐moving technique is proposed and used for the efficient solution of the steady‐state incompressible Navier–Stokes equations. The value of a least squares functional of the residual of the governing differential equation and its boundary conditions at nodal points is regarded as a measure of error and used to predict the areas of poor solutions. A node‐moving technique is then used to move the nodal points to the zones of higher numerical errors. The problem is then resolved on the refined distribution of nodes for higher accuracy. A spring analogy is used for the node‐moving methodology in which nodal points are connected to their neighbors by virtual springs. The stiffness of each spring is assumed to be proportional to the errors of its two end points and its initial length. The new positions of the nodal points are found such that the spring system attains its equilibrium state. Some numerical examples are used to illustrate the ability of the proposed scheme for the adaptive solution of the steady‐state incompressible Navier–Stokes equations. The results demonstrate a considerable improvement of the results with a reasonable computational effort by using the proposed adaptive strategy. Copyright © 2011 John Wiley & Sons, Ltd.     

A DNS study of jet control with microjets using an immersed boundary method

In this work, a microjet arrangement to control a turbulent jet is studied by means of direct numerical simulation. A customised numerical strategy was developed to investigate the interactions between the microjets and the turbulent jet. This approach is based on an improved immersed boundary method in order to reproduce realistically the control device while being compatible with the accuracy and the parallel strategy of the in-house code Incompact3d. The 16 converging microjets, so-called fluidevrons, lead to an increase of the turbulent kinetic energy in the near-nozzle region through an excitation at small scale caused by the interaction between the fluidevrons and the main jet. As a consequence, very intense unstable ejections are produced from the centre of the jet toward its surrounding. Further downstream, the turbulent kinetic energy levels are lower with a lengthening of the potential core compared to a natural jet, in agreement with experimental results.     

A finite element model for the simulation of lost foam casting

In this paper, we present a numerical model to simulate the lost foam casting process. We introduce this particular casting first in order to capture the different physical processes in play during a casting. We briefly comment on the possible physical and numerical models used to envisage the numerical simulation. Next we present a model which aims to solve ‘part of’ the complexities of the casting, together with a simple energy budget that enables us to obtain an equation for the velocity of the metal front advance. Once the physical model is established we develop a finite element method to solve the governing equations. The numerical and physical methodologies are then validated through the solution of a two‐ and a three‐dimensional example. Finally, we discuss briefly some possible improvements of the numerical model in order to capture more physical phenomena. Copyright © 2004 John Wiley & Sons, Ltd.     

基于核重构思想的最小二乘配点型无网格方法

介绍重构核点法的基本原理和近似函数的构造方法，并基于核重构思想，应用配点法和最小二乘原理，离散微分方程，建立求解的代数方程，提出了一种基于核重构思想的最小二乘配点型无网格方法．与一般配点法相比，该方法的系数矩阵是有对称正定的，计算精度高，稳定性好．该方法的实施不需要背景网格，不需要进行高斯积分，与Galerkin法相比，具有计算量小、边界条件处理简单的特点，是一种真正的无网格法．对该方法构造过程中的近似函数及其导数的计算、修正函数的计算及方法的实现等问题进行了探讨．文中结合若干典型算例，检验了该方法的有效性．     

Events of High Polymer Activity in Drag Reducing Flows

The mechanism of drag reduction in turbulent flows due to polymers has been investigated with help of a direct numerical simulation. In particular, we consider the interaction between turbulent velocity fluctuations and polymers in terms of elastic energy that can be stored in the polymer. To this end all the terms of the elastic energy budget have been computed. The most interesting term is the production of elastic energy due to turbulent fluctuations, because it describes the interaction between polymers and turbulence. Although this term appears to be small in the average, it turns out that it can reach very large values instantaneously and intermittently, and the energy transfer from polymer to turbulence is located in very well defined areas inside the channel. This implies that locally there is a strong interaction between the polymer and the turbulent flow structure, and this strong interaction is mostly seen in areas of high velocity fluctuations.     

A high-order Runge-Kutta discontinuous Galerkin method with a subcell limiter on adaptive unstructured grids for two-dimensional compressible inviscid flows

A robust, adaptive unstructured mesh refinement strategy for high-order Runge-Kutta discontinuous Galerkin method is proposed. The present work mainly focuses on accurate capturing of sharp gradient flow features like strong shocks in the simulations of two-dimensional inviscid compressible flows. A posteriori finite volume subcell limiter is employed in the shock-affected cells to control numerical spurious oscillations. An efficient cell-by-cell adaptive mesh refinement is implemented to increase the resolution of our simulations. This strategy enables to capture strong shocks without much numerical dissipation. A wide range of challenging test cases is considered to demonstrate the efficiency of the present adaptive numerical strategy for solving inviscid compressible flow problems having strong shocks.     

The evolution of laminates in finite crystal plasticity: a variational approach

The analysis and simulation of microstructures in solids has gained crucial importance, virtue of the influence of all microstructural characteristics on a material’s macroscopic, mechanical behavior. In particular, the arrangement of dislocations and other lattice defects to particular structures and patterns on the microscale as well as the resultant inhomogeneous distribution of localized strain results in a highly altered stress–strain response. Energetic models predicting the mechanical properties are commonly based on thermodynamic variational principles. Modeling the material response in finite strain crystal plasticity very often results in a non-convex variational problem so that the minimizing deformation fields are no longer continuous but exhibit small-scale fluctuations related to probability distributions of deformation gradients to be calculated via energy relaxation. This results in fine structures that can be interpreted as the observed microstructures. In this paper, we first review the underlying variational principles for inelastic materials. We then propose an analytical partial relaxation of a Neo-Hookean energy formulation, based on the assumption of a first-order laminate microstructure, thus approximating the relaxed energy by an upper bound of the rank-one-convex hull. The semi-relaxed energy can be employed to investigate elasto-plastic models with a single as well as multiple active slip systems. Based on the minimization of a Lagrange functional (consisting of the sum of energy rate and dissipation potential), we outline an incremental strategy to model the time-continuous evolution of the laminate microstructure, then present a numerical scheme by means of which the microstructure development can be computed, and show numerical results for particular examples in single- and double-slip plasticity. We discuss the influence of hardening and of slip system orientations in the present model. In contrast to many approaches before, we do not minimize a condensed energy functional. Instead, we incrementally solve the evolution equations at each time step and account for the actual microstructural changes during each time step. Results indicate a reduction in energy when compared to those theories based on a condensed energy functional.     

Comparison of linear spring and nonlinear FEM methods in dynamic coupled analysis of floating structure and mooring system

This paper compares the dynamic coupled behavior of floating structure and mooring system in time domain using two numerical methods for the mooring lines such as the linear spring method and the nonlinear FEM (Finite Element Method). In the linear spring method, hydrodynamic coefficients and forces on the floating body are calculated using BEM (Boundary Element Method) and the time domain equation is derived using convolution. The coupled solution is obtained by simply adding the pre-determined spring constants of the mooring lines into the floating body equation. In FEM, the minimum energy principle is applied to formulate the nonlinear dynamic equation of the mooring system with a discrete numerical model. The ground contact model and Morison formula for drag forces are also included in the formulation. The coupled solution is obtained by iteratively solving the floating body equation and the FEM equation of the mooring system. Two example structures such as weathervane ship and semi-submersible structure are analyzed using linear spring and nonlinear FEM methods and the difference of those two methods are presented. By analyzing the cases with or without surge-pitch or sway-roll coupling stiffness of mooring lines in the linear spring method, the effect of coupling stiffness of the mooring system is also discussed.     

多重应力奇异性及其强度系数的数值分析方法

以具有两个应力奇异性次数的平面问题为例,提出了一种利用普通的数值分析结果确定奇异点附近多重应力奇异性的各阶次数以及相应的应力强度系数的数值分析方法,计算实例表明,本方法可以精确地求得各阶应力奇异性的次数,并且可以很方便地应用外插法确定出对应的应力强度系数。     

A hybrid Lagrangian–Eulerian particle‐level set method for numerical simulations of two‐fluid turbulent flows

A coupled Lagrangian interface‐tracking and Eulerian level set (LS) method is developed and implemented for numerical simulations of two‐fluid flows. In this method, the interface is identified based on the locations of notional particles and the geometrical information concerning the interface and fluid properties, such as density and viscosity, are obtained from the LS function. The LS function maintains a signed distance function without an auxiliary equation via the particle‐based Lagrangian re‐initialization technique. To assess the new hybrid method, numerical simulations of several ‘standard interface‐moving’ problems and two‐fluid laminar and turbulent flows are conducted. The numerical results are evaluated by monitoring the mass conservation, the turbulence energy spectral density function and the consistency between Eulerian and Lagrangian components. The results of our analysis indicate that the hybrid particle‐level set method can handle interfaces with complex shape change, and can accurately predict the interface values without any significant (unphysical) mass loss or gain, even in a turbulent flow. The results obtained for isotropic turbulence by the new particle‐level set method are validated by comparison with those obtained by the ‘zero Mach number’, variable‐density method. For the cases with small thermal/mass diffusivity, both methods are found to generate similar results. Analysis of the vorticity and energy equations indicates that the destabilization effect of turbulence and the stability effect of surface tension on the interface motion are strongly dependent on the density and viscosity ratios of the fluids. Copyright © 2007 John Wiley & Sons, Ltd.     

应变能中耦合项对旋转悬臂梁振动频率的影响

大范围运动悬臂梁的动力学建模问题对动力学特性分析及控制系统设计具有极其重要的作用. 当前研究多采用一次近似模型,其忽略了由轴向和横向变形所产生的应变能中的耦合项,然而这些项对动力学特性会产生影响. 通过讨论应变能的选取方式,计入了应变能中的耦合项;利用哈密尔顿原理建立结构的耦合振动模型;再借助瑞利—里兹法,以无大范围运动时的振型函数作为基本解组,得到了结构振动广义特征方程并求解. 通过数值算例对比分析,指出考虑应变能耦合项得到的频率与不考虑应变能耦合项得到的频率存在明显差别.      

Hybrid methods for airframe noise numerical prediction

This paper describes some significant steps made towards the numerical simulation of the noise radiated by the high-lift devices of a plane. Since the full numerical simulation of such configuration is still out of reach for present supercomputers, some hybrid strategies have been developed to reduce the overall cost of such simulations. The proposed strategy relies on the coupling of an unsteady nearfield CFD with an acoustic propagation solver based on the resolution of the Euler equations for midfield propagation in an inhomogeneous field, and the use of an integral solver for farfield acoustic predictions.In the first part of this paper, this CFD/CAA coupling strategy is presented. In particular, the numerical method used in the propagation solver is detailed, and two applications of this coupling method to the numerical prediction of the aerodynamic noise of an airfoil are presented.Then, a hybrid RANS/LES method is proposed in order to perform some unsteady simulations of complex noise sources. This method allows for significant reduction of the cost of such a simulation by considerably reducing the extent of the LES zone. This method is described and some results of the numerical simulation of the three-dimensional unsteady flow in the slat cove of a high-lift profile are presented. While these results remain very difficult to validate with experiments on similar configurations, they represent up to now the first 3D computations of this kind of flow.     

A novel implicit method for coastal hydrodynamics modeling: application to the Arcachon lagoon

The present Note reports on numerical modeling of shallow flows in coastal areas. Successful numerical simulations of such flows should be able to cope with strong irregularities of the bathymetry and to reproduce the covering/uncovering (wetting/drying) of tidal flats due to the tidal oscillations of the free surface. Also, adoption of large time steps is necessary to simulate phenomena which last actually several days or months. In the present study, a new numerical model based on an implicit resolution of the shallow water equations is proposed. A penalty method has been employed for numerical treatment of dry zones emerging during the wetting and drying processes. The capability of the present model has been verified by comparison with standard test cases. Further applications and comparisons have been also carried out to simulate the tidal propagation in the Arcachon lagoon. To cite this article: A. Le Dissez et al., C. R. Mecanique 333 (2005).     

A Newton multigrid method for steady-state shallow water equations with topography and dry areas

A Newton multigrid method is developed for one-dimensional (1D) and two-dimensional (2D) steady-state shallow water equations (SWEs) with topography and dry areas. The nonlinear system arising from the well-balanced finite volume discretization of the steady-state SWEs is solved by the Newton method as the outer iteration and a geometric multigrid method with the block symmetric Gauss-Seidel smoother as the inner iteration. The proposed Newton multigrid method makes use of the local residual to regularize the Jacobian matrix of the Newton iteration, and can handle the steady-state problem with wet/dry transition. Several numerical experiments are conducted to demonstrate the efficiency, robustness, and well-balanced property of the proposed method. The relation between the convergence behavior of the Newton multigrid method and the distribution of the eigenvalues of the iteration matrix is detailedly discussed.     

Flow past a sphere in density-stratified fluid

Stratified flow past a three-dimensional obstacle such as a sphere has been a long-lasting subject of geophysical, environmental and engineering fluid dynamics. In order to investigate the effect of the stratification on the near wake, in particular, the unsteady vortex formation behind a sphere, numerical simulations of stratified flows past a sphere are conducted. The time-dependent Navier–Stokes equations are solved using a three-dimensional finite element method and a modified explicit time integration scheme. Laminar flow regime is considered, and linear stratification of density is assumed under Boussinesq approximation. The effects of stratification is implemented by density transport without diffusion. The computed results include the characteristics of the near wake as well as the effects of stratification on the separation angle. Under increased stratification, the separation on the sphere is suppressed and the wake structure behind the sphere becomes planar, resembling that behind a vertical cylinder. With further increase in stratification, the wake becomes unsteady, and consists of planar vortex shedding similar to von Karman vortex streets.     

Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order

Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.