A coupled pressure-based computational method for incompressible/compressible flows

Pressure-based flow solvers couple continuity and linearized truncated momentum equations to derive a Poisson type pressure correction equation and use the well known SIMPLE algorithm. Momentum equations and the pressure correction equation are typically solved sequentially. In many cases this method results in slow and often difficult convergence. The current paper proposes a novel computational algorithm, solving for pressure and velocity simultaneously within a pressure-correction coupled solution approach using finite volume method on structured and unstructured meshes. The method can be applied to both incompressible and subsonic compressible flows. For subsonic compressible flows, the energy equation is also coupled with flow field and the density of fluid is obtained by equation of state. The procedure eliminates the pressure correction step, the most expensive component of the SIMPLE-like algorithms. The proposed coupled continuity-momentum-energy equation method can be used to simulate steady state or transient flow problems. The method has been tested on several CFD benchmark cases with excellent results showing dramatically improved numerical convergence and significant reduction in computational time.     

A high-order accurate unstructured finite volume Newton–Krylov algorithm for inviscid compressible flows

A fast implicit Newton–Krylov finite volume algorithm has been developed for high-order unstructured steady-state computation of inviscid compressible flows. The matrix-free generalized minimal residual (GMRES) algorithm is used for solving the linear system arising from implicit discretization of the governing equations, avoiding expensive and complex explicit computation of the high-order Jacobian matrix. The solution process has been divided into two phases: start-up and Newton iterations. In the start-up phase an approximate solution with the general characteristics of the steady-state flow is computed by using a defect correction procedure. At the end of the start-up phase, the linearization of the flow field is accurate enough for steady-state solution, and a quasi-Newton method is used, with an infinite time step and very rapid convergence. A proper limiter implementation for efficient convergence of the high-order discretization is discussed and a new formula for limiting the high-order terms of the reconstruction polynomial is introduced. The accuracy, fast convergence and robustness of the proposed high-order unstructured Newton–Krylov solver for different speed regimes is demonstrated for the second, third and fourth-order discretization. The possibility of reducing computational cost required for a given level of accuracy by using high-order discretization is examined.     

基于Cholesky分解的增量式RELM及其在时间序列预测中的应用

针对应用于混沌时间序列预测的正则极端学习机(RELM)网络结构设计问题,提出一种基于Cholesky分解的增量式RELM训练算法.该算法通过逐次增加隐层神经元的方式自动确定最佳的RELM网络结构,并以Cholesky分解方式计算其输出权值,有效减小了隐层神经元递增过程的计算代价.混沌时间序列预测实例表明,该算法可有效实现最佳RELM网络结构的自动确定,且计算效率高.利用该算法训练后的RELM预测模型具有预测精度高的优点,适用于混沌时间序列预测. 关键词： 神经网络 极端学习机 混沌时间序列 时间序列预测     

The MAST FV/FE scheme for the simulation of two-dimensional thermohaline processes in variable-density saturated porous media

A novel methodology for the simulation of 2D thermohaline double diffusive processes, driven by heterogeneous temperature and concentration fields in variable-density saturated porous media, is presented. The stream function is used to describe the flow field and it is defined in terms of mass flux. The partial differential equations governing system is given by the mass conservation equation of the fluid phase written in terms of the mass-based stream function, as well as by the advection–diffusion transport equations of the contaminant concentration and of the heat. The unknown variables are the stream function, the contaminant concentration and the temperature. The governing equations system is solved using a fractional time step procedure, splitting the convective components from the diffusive ones. In the case of existing scalar potential of the flow field, the convective components are solved using a finite volume marching in space and time (MAST) procedure; this solves a sequence of small systems of ordinary differential equations, one for each computational cell, according to the decreasing value of the scalar potential. In the case of variable-density groundwater transport problem, where a scalar potential of the flow field does not exist, a second MAST procedure has to be applied to solve again the ODEs according to the increasing value of a new function, called approximated potential. The diffusive components are solved using a standard Galerkin finite element method. The numerical scheme is validated using literature tests.     

含有误差校正的小波神经网络交通流量预测

交通流量的准确预测对于高速路管理者进行决策至关重要。建立了小波神经网络(WNN)交通流量预测模型,并通过预测训练误差和测试误差校正预测结果来提高预测精度。首先构建WNN模型对交通流量进行初步预测,然后利用经验模态分解(EMD)和WNN模型对训练误差和测试误差进行预测。分别用训练误差预测值、测试误差预测值和两种误差预测值的加权对流量初步预测结果进行修正得到最终预测值。采用四川省成灌高速路交通流量数据进行了仿真对比实验,仿真结果表明含有误差校正的小波神经网络模型能有效提高交通流量预测精度,并且利用两种误差加权修正模型的预测精度高于利用测试误差的修正模型和利用训练误差的修正模型。     

High order finite difference methods with subcell resolution for advection equations with stiff source terms

A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with the computed flow variables in the shock region modified by the Harten subcell resolution idea. For numerical experiments, a fifth-order finite-difference WENO scheme and its anti-diffusion WENO variant are considered. A wide range of 1D and 2D scalar and Euler system test cases are investigated. Studies indicate that for the considered test cases, the new method maintains high order accuracy in space for smooth flows, and for stiff source terms with discontinuities, it can capture the correct propagation speed of discontinuities in very coarse meshes with reasonable CFL numbers.     

基于分数阶最大相关熵算法的混沌时间序列预测

为提高最大相关熵算法对混沌时间序列的预测速度和精度,提出了一种新的分数阶最大相关熵算法.在采用最大相关熵准则的基础上,利用分数阶微分设计了一种新的权重更新方法.在alpha噪声环境下,采用新的分数阶最大相关熵算法对Mackey-Glass和Lorenz两类具有代表性的混沌时间序列进行预测,并分析了分数阶的阶数对混沌时间序列预测性能的影响.仿真结果表明:与最小均方算法、最大相关熵算法以及分数阶最小均方算法三类自适应滤波算法相比,所提分数阶最大相关熵算法在混沌时间序列预测中能够有效地抑制非高斯脉冲噪声干扰的影响,具有较快收的敛速度和较低的稳态误差.     

Verified predictions of shape sensitivities in wall-bounded turbulent flows by an adaptive finite-element method

A Continuous Sensitivity Equation (CSE) method is presented for shape parameters in turbulent wall-bounded flows modeled with the standard k–? turbulence model with wall functions. Differentiation of boundary conditions and their complex dependencies on shape parameters, including the two-velocity scale wall functions, is presented in details along with the appropriate methodology required for the CSE method. To ensure accuracy, grid convergence and to reduce computational time, an adaptive finite-element method driven by asymptotically exact error estimations is used. The adaptive process is controlled by error estimates on both flow and sensitivity solutions. Firstly, the proposed approach is applied on a problem with a closed-form solution, derived using the Method of the Manufactured Solution to perform Code Verification. Results from adaptive grid refinement studies show Verification of flow and sensitivity solvers, error estimators and the adaptive strategy. Secondly, we consider turbulent flows around a square cross-section cylinder in proximity of a solid wall. We examine the quality of the numerical solutions by performing Solution Verification and Validation. Then, Sensitivity Analysis of these turbulent flows is performed to investigate the ability of the method to deal with non-trivial geometrical changes. Sensitivity information is used to estimate uncertainties in the flow solution caused by uncertainties in the shape parameter and to perform fast evaluation of flows on nearby configurations.     

基于连续时间广义预测校正的水下非线性追踪博弈控制

针对复杂环境下的追踪控制问题,提出了一种基于连续时间广义预测校正的水下非线性追踪博弈控制算法.利用连续时间广义预测对目标机动偏离趋势进行在线预测补偿校正,将机动目标紧缩于最大捕获概率扇面之内,同时引入零效控制参数和连续时间广义预测校正算法,解决了微分对策动态博弈剩余时间难于估计的问题,提高了系统的响应速度.将算法应用于水下非线性追踪博弈的验证结果表明,该算法兼顾了控制约束与干扰抑制性能,能够实时有效地对抗初始偏差和随机扰动,不仅具有良好的导引效果,而且有效提高了系统对环境干扰的鲁棒性.     

A class of large time step Godunov schemes for hyperbolic conservation laws and applications

A large time step (LTS) Godunov scheme firstly proposed by LeVeque is further developed in the present work and applied to Euler equations. Based on the analysis of the computational performances of LeVeque’s linear approximation on wave interactions, a multi-wave approximation on rarefaction fan is proposed to avoid the occurrences of rarefaction shocks in computations. The developed LTS scheme is validated using 1-D test cases, manifesting high resolution for discontinuities and the capability of maintaining computational stability when large CFL numbers are imposed. The scheme is then extended to multidimensional problems using dimensional splitting technique; the treatment of boundary condition for this multidimensional LTS scheme is also proposed. As for demonstration problems, inviscid flows over NACA0012 airfoil and ONERA M6 wing with given swept angle are simulated using the developed LTS scheme. The numerical results reveal the high resolution nature of the scheme, where the shock can be captured within 1–2 grid points. The resolution of the scheme would improve gradually along with the increasing of CFL number under an upper bound where the solution becomes severely oscillating across the shock. Computational efficiency comparisons show that the developed scheme is capable of reducing the computational time effectively with increasing the time step (CFL number).     

内外流一体化飞行器动导数数值预测

研究内外流一体化飞行器通流模型和带整流罩模型，考核强迫振荡法和自激振荡法在内外流一体化飞行器上的适用性，详细分析时间步长、振荡频率等参数对动导数的影响.研究发现，强迫振荡法在内外流一体化飞行器动导数预测中具有较好的适用性，但与常规的纯外流飞行器相比，时间步长的选取、计算时间及振荡频率等参数的选择都有较大不同.对常规的纯外流飞行器，自由振荡法的预测结果与强迫振荡法符合较好，但对内外流一体化飞行器外形，两者相差50%以上，差异的来源及产生的机理尚需开展深入的研究.     

A novel particle tracking velocimetry method for complex granular flow field

Particle tracking velocimetry(PTV) is one of the most commonly applied granular flow velocity measurement methods. However, traditional PTV methods may have issues such as high mismatching rates and a narrow measurement range when measuring granular flows with large bulk density and high-speed contrast. In this study, a novel PTV method is introduced to solve these problems using an optical flow matching algorithm with two further processing steps. The first step involves displacement correction, which is used to solve the mismatching problem in the case of high stacking density.The other step is trajectory splicing, which is used to solve the problem of a measurement range reduction in the case of high-speed contrast The hopper flow experimental results demonstrate superior performance of this proposed method in controlling the number of mismatched particles and better measuring efficiency in comparison with the traditional PTV method.     

适于星上应用的高光谱图像无损压缩算法

针对常见基于预测、变换、矢量量化及其组合的高光谱无损压缩算法压缩比低、压缩算法整体耗时以及硬件实现困难的问题,提出一种适于星上应用的高光谱图像无损压缩算法。首先,沿光谱线的第一谱段图像采用中值预测器进行谱段内预测,其他谱段图像采用谱间预测。谱间预测采用两步双向预测算法,第一步预测采用双向二阶预测器得到参考预测值,第二步预测采用本文提出的改进LUT搜索预测算法得出4个LUT预测值,然后将参考预测值与其比较得出最终的预测值。最后,使用XX-X空间高光谱相机的压缩系统试验设备对该文提出的压缩算法进行了试验验证。结果表明,压缩系统能快速稳定地工作,平均压缩比达到3.05 bpp,与传统方法相比,平均压缩比提高了0.14~2.94 bpp。有效的提高了高光谱图像无损压缩比和解决了压缩算法整体实现困难的问题。     

基于在线误差修正自适应SVR的非线性不确定分数阶混沌系统滑模控制

提出了一种基于在线误差修正自适应SVR的滑模控制方法, 用于解决一类非线性不确定分数阶混沌系统的控制问题. 分别通过对混沌系统非线性函数的离线SVR估计和基于增量学习的状态跟踪误差在线SVR预测, 解决了不确定分数阶混沌系统模型难以预测的问题. 同时根据Lyapunov稳定性理论设计出SVR权值自适应调整律. 本文以分数阶Arneodo 系统为例进行仿真, 仿真结果表明了, 对于带有外界噪声扰动的非线性不确定分数阶混沌系统, 该方法可以在有限时间内将系统稳定至期望状态, 提高对非线性函数的预测精度, 改善控制性能.     

ALE计算中基于声速分布的网格优化技术

基于声速分布,提出一种拉氏流体力学计算中大变形网格优化的数值技术.该方法不但可以优化网格的几何形状且可以提高拉氏流体计算的时间步长.介绍基于声速分布的网格松弛泛函、修正梯度流方程的推导、离散和求解方法,启动/终止网格优化过程的条件,及基于这种网格优化方法的ALE算法.给出Rayleigh-Taylor不稳定性问题等数值算例,用以证明该方法的有效性.     

一维双流体模型的压力修正算法

针对一维双流体模型，通过推导双流体模型的压力修正方程，及相含率修正方程，将原本应用于单相不可压流动的压力修正系列算法推广至双流体模型求解，提出双流体模型的压力修正算法.在离散过程中运用高阶有界格式，在保证二阶以上精度的基础上克服了由相含率分布的阶跃所造成的数值结果非物理震荡.与公开发表算例进行对比，验证求解的可靠性.     

A predictor–corrector algorithm for the coupling of stiff ODEs to a particle population balance

In this paper a novel predictor–corrector algorithm is presented for the solution of coupled gas-phase – particulate systems. The emphasis of this work is the study of soot formation, but the concepts can be applied to other systems. This algorithm couples a stiff ODE solver to a Monte Carlo population balance solver. Such coupling has been achieved previously for similar systems using a Strang operator splitting algorithm, however, that algorithm demonstrated several numerical issues which resulted in a high computational cost to acquire adequate precision. In particular a source-sink instability was identified whereby a large-magnitude source term present in the ODE system was competing with a similarly sized sink term in the population balance. This instability required that the splitting step size was very small in order to keep numerical error sufficiently low. A predictor–corrector algorithm has been formulated to negate this instability. An additional efficiency is gained with this algorithm as a principal computational cost of the Strang splitting algorithm is removed: the requirement to re-initialise the ODE solver every splitting step. The numerical convergence of the new algorithm is demonstrated, and its efficiency is compared to that of the Strang splitting algorithm. Substantial computation time savings are demonstrated, which allow a fixed error in three studied system functionals to be achieved with an order-of-magnitude reduction in computation time.     

Motion predicted online dynamic MRI reconstruction from partially sampled k-space data

In this work we address the problem of reconstructing dynamic MRI sequences in an online fashion, i.e. reconstructing the current frame given that the previous frames have been already reconstructed. The reconstruction consists of a prediction and a correction step. The prediction step is based on an Auto-Regressive AR(1) model. Assuming that the prediction is good, the difference between the predicted frame and the actual frame (to be reconstructed) will be sparse. In the correction step, the difference between the predicted frame and the actual frame is estimated from partially sampled K-space data via a sparsity promoting least squares minimization problem. We have compared the proposed method with state-of-the-art methods in online dynamic MRI reconstruction. The experiments have been carried out on 2D and 3D Dynamic Contrast Enhanced (DCE) MRI datasets. Results show that our method yields the least reconstruction error.     

A lagged implicit segregated data reconstruction procedure to treat open boundaries

The problem of treating open boundaries is still a challenging one. Applying fully developed condition is constrained to long enough domains. Without having enough physical evidence about what happens on boundaries, the domain extent could not be shortened and computational costs could not be reduced. From the advent of free (open) boundary conditions, they were confined to mixed finite element procedures. Recent works have extended their application to coupled finite volume solvers based on the shape function data reconstruction. A wider class of flow solvers available, however, rely on the segregated procedure where the velocity components and pressure are solved in succession. Moreover, many finite volume algorithms do not use the shape function reconstruction. In this work, by proposing a lagged implicit procedure, we have extended the application of the open boundary condition to these wider classes of flow solvers. The proposed extension is a combination of lagged implicit data reconstruction and overall mass conservation enforcement, which is easily applicable to any segregated and coupled flow solver. To validate the compatibility of this extension, benchmark problem of backward facing step is solved on successively truncated domains, where open boundary may pass through recirculation zones. Results show that the proposed extension works fine. For that problem, it reduced the computational domain length (and hence memory) by a factor of 4.6 and the required computational time by a factor of 21. Flow passing a cylinder is also solved which proves that the method could be applied to external flow problems as well.     

The Riemann Problem for the one-dimensional,free-surface Shallow Water Equations with a bed step: Theoretical analysis and numerical simulations

In this paper, the solution of the Riemann Problem for the one-dimensional, free-surface Shallow Water Equations over a bed step is analyzed both from a theoretical and a numerical point of view. Particular attention has been paid to the wave that is generated at the location of the bed discontinuity. Starting from the classical Shallow Water Equations, considering the bed level as an additional variable, and adding to the system an equation imposing its time invariance, we show that this wave is a contact wave, across which one of the Riemann invariants, namely the energy, is not constant. This is due to the fact that the relevant problem is nonconservative. We demonstrate that, in this type of system, Riemann Invariants do not generally hold in contact waves. Furthermore, we show that in this case the equations that link the flow variables across the contact wave are the Generalized Rankine–Hugoniot relations and we obtain these for the specific problem. From the numerical point of view, we present an accurate and efficient solver for the step Riemann Problem to be used in a finite-volume Godunov-type framework. Through a two-step predictor–corrector procedure, the solver is able to provide solutions with any desired accuracy. The predictor step uses a well-balanced Generalized Roe solver while the corrector step solves the exact nonlinear system of equations that consitutes the problem by means of an iterative procedure that starts from the predictor solution. In order to show the effectiveness and the accuracy of the proposed approach, we consider several step Riemann Problems and compare the exact solutions with the numerical results obtained by using a standard Roe approach far from the step and the novel two-step algorithm for the fluxes over the step, achieving good results.