层流扩散燃烧在GPU上的并行计算和数值分析

在实际工程应用中,使用传统的CPU串行计算来开展燃烧数值模拟往往难以满足对模拟速度的要求。利用GPU比CPU更强的计算能力,通过在交错网格上将燃烧物理方程离散化,使用预处理稳定双共轭梯度法(PBiCGSTAB)求解离散化方程,并且探索面向GPU编程的矩阵向量乘并行算法和逆矩阵向量乘并行算法,从而给出一种在GPU上数值求解层流扩散燃烧的可行方法。实验结果表明,GPU并行程序获得了相对串行CPU程序约10倍以上的加速效果,且计算结果与实际情况相符,因而所提方法是可行且高效的。     

Comparison of two numerical methods for the stratified flow

The article is devoted to numerical simulation of stratified flows described by the Navier-Stokes equations in Boussinesq approximation. The equations are solved by two high order schemes. The first one using the fifth-order WENO scheme combined with spectral projection to solenoidal field, the second one being based on the second-order AUSM MUSCL scheme with artificial compressibility in dual time.The schemes are used to model a flow around an obstacle moving through the stratified fluid. The setup of the computational case corresponds to the experiment of Chaschechkin and Mitkin [23]. Mutual comparison of results obtained by both schemes as well as of the experimental data is presented.     

Mathematical description of complex chemical kinetics and application to CFD modeling codes

A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.     

The data from the numerical investigation of turbulent combustion in jet flows

The data from the numerical calculations are represented for free subsonic and supersonic turbulent jets subject to chemical reactions (combustion) of the flowing components. The calculations are carried out using averaged Navier–Stokes equations with various turbulent-viscosity models (k–ε, SST, Secundov model) and the large eddy simulation (LES). The Magnussen model and the Zeldovich model are regarded as turbulent combustion models. The calculation data are compared with the experimental data.     

Numerical model of a two-dimensional,non-plane transient magnetohydrodynamic flow

The equations describing two-dimensional three-component magnetohydrodynamic (MHD) transient flows are formulated for a system of spherical coordinates. With the numerical code based on Implicit Continuous Fluid Eulerian (ICE) scheme, MHD flows resulting from a sudden energy release in a stratified medium are examined. Because of the inclusion of out-of-plane components of velocity and magnetic fields, MHD transverse waves are observed in addition to fast, slow and entropy waves. Numerical results for compressible MHD shocks are found in satisfactory agreement with the theoretical predictions.     

A generic structure for scalar and vector boundary element codes using Fortran 90

The boundary element method is an established numerical technique for the solution of the partial differential equations of potential theory and elasticity. Here we present an implementation of the method using the advanced features of Fortran 90. We show how the array, syntax, dynamic memory allocation and modularity allow the development of maintainable, readable and flexible boundary element codes. The ability to reuse large amounts of code independently of any particular integral equation is also demonstrated. Implementations for scalar and vector equations are presented, and the flexibility of the code is demonstrated by presenting multiple element types. The present implementation is illustrated by considering two numerical examples.     

Implementation of the CIP algorithm to magnetohydrodynamic simulations

An implementation of the Constrained Interpolation Profile (CIP) algorithm to magnetohydrodynamic (MHD) simulations is presented. First we transform the original momentum and magnetic induction equations to unfamiliar forms by introducing Elsässer variables [W.M. Elsässer, The hydromagnetic equations, Phys. Rev. (1950)]. In this formulation, while the compressional and pressure gradient terms remain as non-advective terms, the advective and magnetic stress terms are expressed in the form of an advection equation, which enables us to use the CIP algorithm. We have examined some 1D test problems using the code based on this formula. Linear Alfvén wave propagation tests reveal that the developed code is capable of solving any Alfvén wave propagation with only small numerical diffusion and phase errors up to k?h=2.5 (where ?h is the grid spacing). A shock tube test shows good agreement with a previous result with less numerical oscillation at the shock front and the contact discontinuity which are captured within a few grid points. Extension of the 1D code to the multi-dimensional case is straightforward. We have calculated the 3D nonlinear evolution of the Kelvin-Helmholtz instability (KHI) and compared the result with our previous study. We find that our new MHD code is capable of following the 3D turbulence excited by the KHI while retaining the solenoidal property of the magnetic field.     

A RANS flamelet-progress-variable method for computing reacting flows of real-gas mixtures

This paper provides an efficient numerical method for solving reacting flows of industrial interest in the presence of significant real-gas effects. The method combines a state-of-the-art solver of the Reynolds-averaged Navier-Stokes equations - equipped with the low-Reynolds number k-ω turbulence closure - with a combustion flamelet-progress-variable approach. A real-gas model as well as a detailed kinetic scheme are used to generate the flamelet library. The method is tested versus several applications chosen to demonstrate the importance of the real-gas effects and of the kinetic scheme for computing high-pressure combustion. The major contribution of the paper is to provide a single-phase approach which solves turbulent reacting real-gas flows at a computational cost comparable with that of the simulation of a non-reacting flow thanks to the use of the flamelet library.     

A stochastic differential equation code for multidimensional Fokker–Planck type problems

We present a newly developed numerical code that integrates Fokker–Planck type transport equations in four to six spatial dimensions (configuration plus momentum space) and time by means of stochastic differential equations. In contrast to other, similar approaches our code is not restricted to any special configuration or application, but is designed very generally with a modular structure and, moreover, allows for Cartesian, cylindrical or spherical coordinates. Depending on the physical application the code can integrate the equations forward or backward in time. We exemplify the mathematical ideas the method is based upon and describe the numerical realisation and implementation in detail. The code is validated for both cases against an established finite-differences explicit numerical code for a scenario that includes particle sources as well as a linear loss term. Finally we discuss the new possibilities opened up with respect to general applications and newly developed hardware.     

Geometrically non linear 3-D dynamic analysis of shells

This paper presents applications of a new code for shells of arbitrary shape. The geometrically non linear dynamic analysis is based on a total Lagrangian formulation and the direct time integration of the equations of motion. The cost effectiveness of a static condensation is shown and comparison of numerical results for classical examples of the literature (plates, arches and spherical shells) are presented using a full 3-D code.     

An OpenCL implementation for the solution of the time-dependent Schrödinger equation on GPUs and CPUs

Open Computing Language (OpenCL) is a parallel processing language that is ideally suited for running parallel algorithms on Graphical Processing Units (GPUs). In the present work we report on the development of a generic parallel single-GPU code for the numerical solution of a system of first-order ordinary differential equations (ODEs) based on the OpenCL model. We have applied the code in the case of the Time-Dependent Schrödinger Equation of atomic hydrogen in a strong laser field and studied its performance on NVIDIA and AMD GPUs against the serial performance on a CPU. We found excellent scalability and a significant speedup of the GPU over the CPU device. The speedup in the benchmark tended towards a value of about 40 with significant speedups expected against multi-core CPUs. Furthermore, though we do not present the detailed benchmarks here, we also have achieved speedup values of around 75 by performing a slight optimization of the described algorithm.     

Solution of the time-dependent,three-dimensional resistive magnetohydrodynamic equations

Resistive magnetohydrodynamics (MHD) is described by a set of eight coupled, nonlinear, three-dimensional, time-dependent, partial differential equations. A computer code, IMP (Implicit MHD Program), has been developed to solve these equations numerically by the method of finite differences on an Eulerian mesh. In this model, the equations are expressed in orthogonal curvilinear coordinates, making the code applicable to a variety of coordinate systems. The Douglas-Gunn algorithm for Alternating-Direction Implicit (ADI) temporal advancement is used to avoid the limitations in timestep size imposed by explicit methods. The equations are solved simultaneously to avoid synchronization errors. While the continuity and magnetic field equations are expressed as conservation laws, the momentum and energy equations are nonconservative. This is to: (1) provide enhanced numerical stability by eliminating errors introduced by the nonvanishing of τ · B on the finite difference mesh; and, (2) allow the simulation of low β plasmas. The resulting finite difference equations are a coupled system of nonlinear algebraic equations which are solved by the Newton-Raphson iteration technique. We apply our model to a number of problems of importance in magnetic fusion research. Ideal and resistive internal kink instabilities are simulated in a Cartesian geometry. Growth rates and nonlinear saturation amplitudes are found to be in agreement with previous analytic and numerical predictions. We also simulate these instabilities in a torus, which demonstrates the versatility of the orthogonal curvilinear coordinate representation.     

Symbolic–Numeric Indirect Method for Solving Optimal Control Problems for Large Multibody Systems

This work presents a methodological framework, based on an indirect approach, for the automatic generation and numerical solution of Optimal Control Problems (OCP) for mechatronic systems, described by a system of Differential Algebraic Equations (DAEs). The equations of the necessary condition for optimality were derived exploiting the DAEs structure, according to the Calculus of Variation Theory. A collection of symbolic procedures was developed within general-purpose Computer Algebra Software. Those procedures are general and make it possible to generate both OCP equations and their jacobians, once any DAE mathematical model, objective function, boundary conditions and constraints are given. Particular attention has been given to the correct definition of the boundary conditions especially for models described with set of dependent coordinates. The non-linear symbolic equations, their jacobians with the sparsity patterns, generated by the procedures above mentioned, are translated into a C++ source code. A numerical code, based on a Newton Affine Invariant scheme, was also developed to solve the Boundary Value Problems (BVPs) generated by such procedures. The software and methodological framework here presented were successfully applied to the solution of the minimum-lap time problem of a racing motorcycle.     

New numerical method for the solutions of the MCDF equations based on the CIP method

A new numerical method based on the constrained interpolation profile (CIP) method to solve the Multiconfiguration Dirac-Fock (MCDF) equations is presented. The radial wave functions are represented by the values and the spatial derivatives on an arbitrary grid system, and approximated by cubic polynomials. Owing to this representation, the values and the spatial derivatives of the effective charge distribution and inhomogeneous term are calculated using the previous cycle's wave functions. Then the homogeneous MCDF equations are integrated to obtain two linearly independent solutions, which are used to construct the Green function, by the adaptive stepsize controlled Runge-Kutta method controlling the truncation errors within a prescribed accuracy. The radial wave function is improved by taking the convolution of the Green function and the inhomogeneous term. The effectiveness of this numerical procedure is investigated after implementing it into the relativistic atomic structure code GRASP92.     

Direct numerical simulation of turbulent flows in fuel rod bundles

Numerical methods for solving conservation equations using the DINUS code are presented. The DINUS code has been developed for direct numerical simulation of thermal-hydraulic phenomena in fuel rod bundles. To examine the methods, two test problems have been studied: turbulent flows between parallel plates and in a Triangular-Arrayed rod bundle.     

面向彩印标签的手机数码识别及应用

针对Android手机拍摄标签数字码实时识别的需要,以及拍摄图像具有分辨率低、亮度不均匀、背景复杂等特点,由手机拍摄直接获得灰度图像后,通过数字区域投影定位,获取只包含数字的图像;采用二值化进行灰度图像到黑白图像的变换;通过投影及归一化处理进行数字码图像分割,并对每个数字码图像进行细化获取细化数字码;基于统计学抽取数字码的特征;建立数字码模式特征后,采用最近邻域判别函数进行数字码识别,取得了良好的识别效果。     

Thermal Investigation for Solid Rocket Motor Nozzle Inserts Material

A time-resolved numerical computational approach, involving the combustion of double-base propellant is performed on thermal protection material for SRM nozzle. An implicit Navier-Stokes Solver is selected to simulate two-dimensional axial-symmetric unsteady turbulent flow of compressible fluid. The governing equations are discredited by using the finite Volume method. S-A turbulence model is employed. CFD scheme is implemented to investigate the temperature distribution causes at nozzle throat inserts comp...     

Study of stress waves in geomedia and effect of a soil cover layer on wave attenuation using a 1-D finite-difference method

The propagation and attenuation of blast-induced stress waves differs between geomedia such as rock or soil mass. This paper numerically studies the propagation and attenuation of blast-induced elastoplastic waves in deep geomedia by using a one-dimensional (1-D) finite-difference code. Firstly, the elastoplastic Cap models for rock and soil masses are introduced into the governing equations of spherical wave motion and a FORTRAN code based on the finite difference method is developed. Secondly, an underground spherical blast is simulated with this code and verified by software, RENEWTO. The propagation of stress-waves in rock and soil masses is numerically investigated, respectively. Finally, the effect of a soil cover layer on the attenuation of stress waves in the rear rock mass is studied. It is determined that large plastic deformation of geomedia can effectively dissipate the energy of stress-waves inward and the developed 1-D finite difference code coupled with elastoplastic Cap models is convenient and effective in the numerical simulations for underground spherical explosion.     

A testbench of arbitrary accuracy for electromagnetic simulations

Several electromagnetic problems for verification purposes in computational electromagnetics are introduced. Details about the formulation of a generalized eigenvalue problem for non‐lossy and lossy materials are provided to obtain a fast and ready‐to‐use way of verification. Codes written using the symbolic toolbox from MATLAB are detailed to obtain an arbitrary accuracy for the proposed problems. Finally, numerical results in a finite element method code are presented together with the analytical values to show the accuracy of the code proposed.