离散化微分模型方程的反应器网络综合

构造基于全混流和交叉流反应器的反应器网络超结构,并建立优化模型,优化模型由复杂的高度非线性的微分／代数方程所构成。本文采用有限元正交配置法离散化微分方程的策略来简化超结构数学模型,将离散化所得的代数方程组与其它约柬条件一起,作为反应器网络超结构的数学模型,然后运用数学软件优化求解。实例研究表明,优化结果与文献相一致或优于文献,表明离散化法求解含有微分模型方程的反应器网络综合问题是有效的。     

过程系统运行安全性的动态柔性分析

针对过程运行系统提出一种简单实用的安全性分析方法,通过对动态过程的微分代数模型采用离散化处理,实现了过程系统的动态柔性分析方法,同时对离散化模型进行单调性分析,然后将区间传播法应用于离散化模型从而简化了系统柔性分析的计算,根据过程运行系统动态柔性分析的结果,得出过程运行状态是否安全的一种判别方法,最后通过案例验证了该方法的正确性。     

Finite element methods for unsteady solidification problems arising in prediction of morphological structure

Galerkin finite element methods are presented for calculation of the dynamic transitions between planar and deep two-dimensional cellular interface morphologies in directional solidification of a binary alloy from models that include solute transport, the phase diagram, and the interfacial free energy between melt and crystals. The unknown melt-solid interface shape is accounted for in the finite element formulation by mapping the equations to a fixed domain. Novel nonorthogonal transformations are introduced combining cylindrical and Cartesian coordinate interface representations for approximating the deep cellular interfaces that evolve from a planar solidification front. The algorithm for time integration combines a fully implicit Adams-Moulton algorithm with the Isotherm-Newton method for solving the nonlinear set of differential-algebraic equations that result from the spatial discretization of the moving-boundary problem. The fully implicit scheme is found to be more accurate and efficient than an explicit predictor-corrector algorithm. Sample calculations show the connectivity between families of shapes with resonant spatial wavelengths.     

Automating the Finite Element Method

The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations. However, the generality of the framework provided by the finite element method is seldom reflected in implementations (realizations), which are often specialized and can handle only a small set of variational problems and finite elements (but are typically parametrized over the choice of mesh). This paper reviews ongoing research in the direction of a complete automation of the finite element method. In particular, this work discusses algorithms for the efficient and automatic computation of a system of discrete equations from a given variational problem, finite element and mesh. It is demonstrated that by automatically generating and compiling efficient low-level code, it is possible to parametrize a finite element code over variational problem and finite element in addition to the mesh.     

A discrete Boltzmann equation model for two-phase shallow granular flows

In this paper a Discrete Boltzmann Equation model (hereinafter DBE) is proposed as solution method of the two-phase shallow granular flow equations, a complex nonlinear partial differential system, resulting from the depth-averaging procedure of mass and momentum equations of granular flows. The latter, as e.g. a debris flow, are flows of mixtures of solid particles dispersed in an ambient fluid.The reason to use a DBE, instead of a more conventional numerical model (e.g. based on Riemann solvers), is that the DBE is a set of linear advection equations, which replaces the original complex nonlinear partial differential system, while preserving the features of its solutions. The interphase drag function, an essential characteristic of any two-phase model, is accounted for easily in the DBE by adding a physically based term. In order to show the validity of the proposed approach, the following relevant benchmark tests have been considered: the 1D simple Riemann problem, the dam break problem with the wet–dry transition of the liquid phase, the dry bed generation and the perturbation of a state at rest in 2D. Results are satisfactory and show how the DBE is able to reproduce the dynamics of the two-phase shallow granular flow.     

A mimetic mass, momentum and energy conserving discretization for the shallow water equations

A spatial semi-discretization is developed for the two-dimensional depth-averaged shallow water equations on a non-equidistant structured and staggered grid. The vector identities required for energy conservation in the continuous case are identified. Discrete analogues are developed, which lead to a finite-volume semi-discretisation which conserves mass, momentum, and energy simultaneously. The key to discrete energy conservation for the shallow water equations is to numerically distinguish storage of momentum from advective transport of momentum. Simulation of a large-amplitude wave in a basin confirms the conservative properties of the new scheme, and demonstrates the enhanced robustness resulting from the compatibility of continuity and momentum equations. The scheme can be used as a building block for constructing fully conservative curvilinear, higher order, variable density, and non-hydrostatic discretizations.     

Parallel multigrid finite volume computation of three-dimensional thermal convection

A parallel implementation of the finite volume method for three-dimensional, time-dependent, thermal convective flows is presented. The algebraic equations resulting from the finite volume discretization, including a pressure equation which consumes most of the computation time, are solved by a parallel multigrid method. A flexible parallel code has been implemented on the Intel Paragon, the Cray T3D, and the IBM SP2 by using domain decomposition techniques and the MPI communication software. The code can use 1D, 2D, or 3D partitions as required by different geometries, and is easily ported to other parallel systems. Numerical solutions for air (Prandtl number Pr = 0.733) with various Rayleigh numbers up to 10⁷ are discussed.     

A <Emphasis Type="Italic">p</Emphasis>-Adaptive Local Discontinuous Galerkin Level Set Method for Willmore Flow

The level set method is often used to capture interface behavior in two or three dimensions. In this paper, we present a combination of a local discontinuous Galerkin (LDG) method and a level set method for simulating Willmore flow. The LDG scheme is energy stable and mass conservative, which are good properties compared with other numerical methods. In addition, to enhance the efficiency of the proposed LDG scheme and level set method, we employ a p-adaptive local discontinuous Galerkin technique, which applies high order polynomial approximations around the zero level set and low order ones away from the zero level set. A major advantage of the level set method is that the topological changes are well defined and easily performed. In particular, given the stiffness and high nonlinearity of Willmore flow, a high order semi-implicit Runge–Kutta method is employed for time discretization, which allows larger time steps. These equations at the implicit time level are linear, we demonstrate an efficient and practical multigrid solver to solve the equations. Numerical examples are given to illustrate that the combination of the LDG scheme and level set method provides an efficient and practical approach to simulate the Willmore flow.     

飞机座舱温度场数值仿真研究

要为飞机座舱空气分配系统以及飞机的环控系统提供更为可靠的设计依据.应寻求更加接近实际的座舱温度场的分布情况.根据飞机座舱内实际存在的传热过程,主要在导热-对流传热的基础上考虑了辐射传热,在利用计算流体动力学(CFD)软件Fluent对飞机座舱温度场的数值仿真过程中,加入了离散坐标辐射模型,主要壁面采用了对流-辐射混合热边界条件,而且考虑了太阳辐射对舱内温度场的影响.针对某战斗机的设计状态点对其座舱温度场进行仿真,得到了该条件下的舱内温度分布和辐射换热量,计算结果跟传统方法进行了比较,表明了实际性和可行性.     

A high order ADI method for separable generalized Helmholtz equations

We present a multilevel high order ADI method for separable generalized Helmholtz equations. The discretization method we use is a one-dimensional fourth order compact finite difference applied to each directional component of the Laplace operator, resulting in a discrete system efficiently solvable by ADI methods. We apply this high order difference scheme to all levels of grids, and then starting from the coarsest grid, solve the discretized equation with an ADI method at each grid level, with the solution from the previous grid level as the initial guess. The multilevel procedure stops as the ADI finishes its iterations on the finest grid. Analytical and experimental results show that the proposed method is highly accurate and efficient while remaining as algorithmically and data-structurally simple as the single grid ADI method.     

On the Use of Low-Pass Filters for Image Processing with Inverse Laplacian Models

A novel signal processing-oriented approach to solving problems involving inverse Laplacians is introduced. The Monogenic Signal is a powerful method of computing the phase of discrete signals in image data, however it is typically used with band-pass filters in the capacity of a feature detector. Substituting low-pass filters allows the Monogenic Signal to produce approximate solutions to the inverse Laplacian, with the added benefit of tunability and the generation of three equivariant properties (namely local energy, local phase and local orientation), which allow the development of powerful numerical solutions for a new set of problems. These principles are applied here in the context of biological cell segmentation from brightfield microscopy image data. The Monogenic Signal approach is used to generate reduced noise solutions to the Transport of Intensity Equation for optical phase recovery, and the resulting local phase and local orientation terms are combined in an iterative level set approach to accurately segment cell boundaries. Potential applications of this approach are discussed with respect to other fields.     

A parallel multiphase flow code for the 3D simulation of explosive volcanic eruptions

A new parallel code for the simulation of the transient, 3D dispersal of volcanic particles in the atmosphere is presented. The model equations, describing the multiphase flow dynamics of gas and solid pyroclasts ejected from the volcanic vent during explosive eruptions, are solved by a finite-volume discretization scheme and a pressure-based iterative non-linear solver suited to compressible multiphase flows. The solution of the multiphase equation set is computationally so demanding that the simulation of the transient 3D dynamics of eruptive columns would not be cost-effective on a single workstation. The new code has been parallelized by adopting an ad hoc domain partitioning scheme that enforces the load balancing in the presence of a large number of topographic blocking-cells. An optimized communication layer has been built over the Message-Passing Interface. It is shown that the present code has a remarkable efficiency on several high-performance platforms and makes it possible, for the first time, to simulate fully 3D eruptive scenarios on realistic volcano topography.     

Error estimation in the integration of ordinary differential equations

Linear initial value problems, particularly involving first order differential equations, can be transformed into systems of higher order and treated as boundary value problems. Finite difference analogues considered for obtaining approximate solutions of these boundary value problems are proved to be fourth order convergent processes, by deriving considerable sharper bounds for the discretization error. Numerical examples are given to demonstrate the usefulness of our error bounds.     

GPU-acceleration for Moving Particle Semi-Implicit method

The MPS (Moving Particle Semi-implicit) method has been proven useful in computation free-surface hydrodynamic flows. Despite its applicability, one of its drawbacks in practical application is the high computational load. On the other hand, Graphics Processing Unit (GPU), which was originally developed for acceleration of computer graphics, now provides unprecedented capability for scientific computations.The main objective of this study is to develop a GPU-accelerated MPS code using CUDA (Compute Unified Device Architecture) language. Several techniques have been shown to optimize calculations in CUDA. In order to promote the acceleration by GPU, particular attentions are given to both the search of neighboring particles and the iterative solution of simultaneous linear equations in the Poisson Pressure Equation.In this paper, 2-dimensional calculations of elliptical drop evolution and dam break flow have been carried out by the GPU-accelerated MPS method, and the accuracy and performance of GPU-based code are investigated by comparing the results with those by CPU. It is shown that results of GPU-based calculations can be obtained much faster with the same reliability as the CPU-based ones.     

A pseudo-linear time algorithm for the optimal discrete speed minimizing energy consumption

Discrete Event Dynamic Systems - We consider the classical problem of minimizing off-line the total energy consumption required to execute a set of n real-time jobs on a single processor with a...     

A finite difference model for air pollution simulation

A 3-D model for atmospheric pollutant transport is proposed considering a set of coupled convection–diffusion–reaction equations. The convective phenomenon is mainly produced by a wind field obtained from a 3-D mass consistent model. In particular, the modelling of oxidation and hydrolysis of sulphur and nitrogen oxides released to the surface layer is carried out by using a linear module of chemical reactions. The dry deposition process, represented by the so-called deposition velocity, is introduced as a boundary condition. Moreover, the wet deposition is included in the source term of the governing equations using the washout coefficient. Before obtaining a numerical solution, the problem is transformed using a terrain conformal coordinate system. This allows to work with a simpler domain in order to build a mesh that provides finite difference schemes with high spatial accuracy. The convection–diffusion–reaction equations are solved with a high order accurate time-stepping discretization scheme which is constructed following the technique of Lax and Wendroff. Finally, the model is tested with a numerical experiment in La Palma Island (Canary Islands).     

A numerical model for the investigation of the flow and isotope concentration field in an ultracentrifuge

A numerical code is built up with 36000 cards and 343 subroutines to investigate the interconnected fields of velocity, temperature, pressure and isotope concentration in a gas centrigue. The full set of Navier-Stokes equations (i.e. continuity, momentum and energy equations), the gas state law and the diffusion equation, associated with proper boundary conditions, form the basic mathematical model. This system is solved numerically by the use of a finite element method and direct resolution. An important informatic environment gives flexibility to the code. One typical example illustrates the possibilities of computations.     

All Mach Number Second Order Semi-implicit Scheme for the Euler Equations of Gas Dynamics

This paper presents an asymptotic preserving (AP) all Mach number finite volume shock capturing method for the numerical solution of compressible Euler equations of gas dynamics. Both isentropic and full Euler equations are considered. The equations are discretized on a staggered grid. This simplifies flux computation and guarantees a natural central discretization in the low Mach limit, thus dramatically reducing the excessive numerical diffusion of upwind discretizations. Furthermore, second order accuracy in space is automatically guaranteed. For the time discretization we adopt an Semi-IMplicit/EXplicit (S-IMEX) discretization getting an elliptic equation for the pressure in the isentropic case and for the energy in the full Euler case. Such equations can be solved linearly so that we do not need any iterative solver thus reducing computational cost. Second order in time is obtained by a suitable S-IMEX strategy taken from Boscarino et al. (J Sci Comput 68:975–1001, 2016). Moreover, the CFL stability condition is independent of the Mach number and depends essentially on the fluid velocity. Numerical tests are displayed in one and two dimensions to demonstrate performance of our scheme in both compressible and incompressible regimes.     

含曲率的水平集方程在非结构四边形网格上的数值离散方法

在非结构四边形网格上,含曲率的水平集方程采用伽辽金等参有限元方法空间离散,时间离散采用半隐格式．离散形成的线性方程组的系数矩阵是对称的稀疏矩阵,采用共轭梯度法求解．数值算例表明,在笛卡儿网格和随机网格上,含曲率的水平集方程离散格式可达到近似二阶精度．重新初始化方程的离散格式精度可达到近似一阶精度．给出了非结构四边形网格上不光滑界面以曲率收缩的运动过程．在不采用重新初始化的情况下,收缩过程未出现不稳定现象．