基于GPU加速的三阶有限体积格式管道瞬变流求解模型

为高效和高精度求解长距离输水系统瞬变流变化过程,应用三阶ENO有限体积格式求解一维管道非恒定流方程组,基于Lax-Friedrichs通量裂分法重构界面通量,上下游界面采用虚拟网格技术并结合交叉管网边界条件建立了一套高效和高精度求解管道瞬变流水锤波的数值模型。引入GPU加速技术,实现对大型输水系统的高效计算。通过特征线法、一阶及二阶Godunov有限体积格式对模型进行验证,结果表明,三阶ENO格式在极低的Courant数时也能保持较好的间断捕捉性能且无非物理振荡。同时,对Courant数的高度不敏感性,使得模型划分网格时具有高度的灵活性并能显著提高计算速度。应用GPU加速技术,发现模型在较多网格数时有明显的加速效果,且加速效果随网格数增多而显著。本文模型可为长距离输水系统非恒定瞬变过程的高效精准快速模拟预测提供理论支撑。     

求解管道耦合水力瞬变模型的Godunov格式

应用特征线差分法求解耦合瞬变问题时存在难以避免的多波插值问题,会引入较大的插值误差。为了解决此问题,本文提出了一种求解管道耦合水力瞬变模型的Godunov计算格式。首先基于有限体积法对模型进行数值离散,然后采用时空均为二阶精度的三步MUSCL-Hancock方法计算单元界面上的数值通量,同时引入斜率限制器函数来抑制虚假的数值振荡。在计算边界单元时,采用Rankine-Hugoniot条件与边界条件相结合的方法建立边界方程,有效降低了计算的复杂程度。实验与仿真对比表明：本文的计算结果与实验结果吻合较好,激波捕捉准确且无虚假的数值振荡,进而证明了该方法的可行性和有效性。     

三维N-S方程计算隐式有限体积法

利用NND有限差分格式，发展了一种新的完全隐式的有限体积数值方法，以求解与时间相关的N－S方程．对通过单元体界面的无粘流和粘性流通量均作隐式处理．对绕流钝锥体和不同攻角的气动辅助实验飞行器的高超声速粘性流和化学反应流获得了定常数值解．对流加热率和流场电子密度的计算值与实验数据进行了比较，符合较好，证实了本方法的精确性．     

黏弹性管道水柱分离弥合水锤有限体积法模型

基于有限体积法二阶Godunov求解格式对黏弹性输水管道中水柱分离弥合现象进行建模和模拟研究. 在传统的弹性管道模型基础上考虑管道黏弹性效应的影响. 在瞬变流控制方程中引入管道黏弹性项和动态摩阻项, 采用有限体积法进行求解, 考虑压力修正系数来模拟自由气体对计算单元的影响, 同时为避免数值模拟结果产生虚假震荡引入斜率限制器MINMOD函数; 通过虚拟单元法进行边界构建, 实现了计算区域的统一计算. 将所建模型计算结果与已有模型结果、试验结果进行对比, 并对影响模型的各参数进行敏感性分析. 结果表明, 本文模型能够准确模拟出纯水锤、水柱分离弥合水锤两种情况下的瞬态压力变化, 均能与试验数据高度吻合; 与传统的特征线方法相比, 当库朗数C_r小于1时, 有限体积法二阶Godunov格式计算结果更准确、稳定; 在压力波动的衰减过程中, 黏弹性效应相比于管道摩阻起主导作用; 与弹性管道模型相比, 考虑管道黏弹性效应后可显著提高模拟结果的准确性, 尤其是压力波峰值的相对误差明显降低.      

成品油管道顺序输送二维模型优化求解

将一种简化的自适应网格应用于顺序输送二维混油模型的计算中,网格的疏密程度由速度和浓度梯度控制且用动网格取代传统的固定网格。混油模型中采用混掺长度理论计算速度场和扩散系数,并考虑了油品黏度变化对混油的影响。提高传统数值解法的精度,减少计算量,使之适应于长输管线顺序输送的混油数值计算。通过在计算机上的数值模拟实验,证明了该方法的有效性,分析了雷诺数、输送顺序对混油的影响并得到混油随输送距离的变化规律。     

双曲型守恒律的高阶、高分辨有限体积法

有限体积法是一种离散积分形式守恒律的数值方法。它可以吸收有限元法和有限差分法的一些重要思想与技巧。由于它可方便地利用多种类型的网格(结构网格和非结构网格),从而非常适用于处理复杂计算区域,目前已成为一种在计算流体力学中十分重要的方法。本文将针对二维双曲守衡律,对高精度、高分辨的有限体积法及其近年来的进展做一简要介绍。      

基于水力瞬变与扩展卡尔曼滤波的管道流体监测与泄漏定位

引入一种长输管道流体监测与泄漏定位的新方法,将管道流动的瞬变流模型转化为状态空间模型的描述,以管线沿程流量、压强水头为状态变量,管道进口流量和出口压力视做非线性动态系统的控制输入,出口流量和进口压力观测序列构成系统的测量向量。基于小信号原理首先线性化处理非线性模型,然后用扩展的卡尔曼滤波器结合传统的双曲方程特征线解法估计泄漏尺寸与位置,并实时模拟出管道流体的压力流量过程及其沿管道的分布。试验和仿真算例表明此法模拟的管道流动状态能较快收敛到稳定状态,并且泄漏尺寸估计与定位的结果与给定值比较吻合。因此引入扩展的卡尔曼滤波能够提高瞬变流模拟管道非定常流动的准确性和跟踪能力。     

求解对流扩散方程的一种高效的有限体积法

考虑无结构三角网格上求解对流扩散方程的有限体积法.引入一种梯度函数的计算方法,将现有方法中计算解变量在网格单元中心和网格单元边界的梯度的两个独立过程改造成一个过程来完成,发展了一种求解对流扩散方程的高效的有限体积法.数值实验结果表明,该方法完全达到了已有方法同样的精度,而在计算速度上有明显的提高.     

轴对称高速碰撞问题的拉格朗日无结构网格有限体积法的并行计算

给出计算轴对称高速碰撞问题的拉格朗日无结构三角形网格有限体积法的并行格式,并给出以小巨型机ＡｌｉａｎｔＦＸ／４０为目标计算机的算例数值模拟结果和效率分析。     

缝洞型多孔介质中多相流的有限体积法数值模拟

本文研究的碳酸盐岩油藏储集体属于缝洞型多孔介质.这类缝洞型多孔介质由裂缝、溶蚀孔洞和低孔隙度低渗透率的基岩组成.裂缝是空隙流体流动的主要通道;溶蚀孔洞大小从几厘米到数米不等,渗透率和孔隙度都很高,是流体主要的储集空间.由于缝洞型多孔介质空隙空间的复杂性和强非均质性,数值计算中基本控制方程的空间离散应采用非结构化网格的计算模型.本文采用有限体积法模拟缝洞型多孔介质中多相流体的流动,并给出了相应的单元中心格式有限体积法的计算公式.裂缝介质和溶洞介质中单元间多相流体的流动考虑为高速非达西流,其质量通量采用Forchheimer定律计算.非线性方程的离散选取全隐式格式,并采用Newton-Raphson迭代进行求解.通过两个二维模型注水驱油的数值模拟,验证了本文方法的有效性.     

管系内一维可压缩流动数值建模与特性分析

针对复杂管系内可压缩流体,基于有限体积法,采用HLLC(Harten-Lax-van Leer Contact)格式和黎曼求解器构建了有限控制体数值离散方法,引入虚拟节点用于连接有限控制体,借助虚拟节点给出控制体之间数值通量的计算格式,发展了一种管道内一维流动数值建模方法.针对含有分支管路的管系,在管道连接部位构建了分...     

Theoretical analysis on hydraulic transient resulted by sudden increase of inlet pressure for laminar pipeline flow

Hydraulic transient, which is resulted from sudden increase of inlet pressure for laminar pipeline flow, is studied. The partial differential equation, initial and boundary conditions for transient pressure were constructed, and the theoretical solution was obtained by variable-separation method. The partial differential equation, initial and boundary conditions for flow rate were obtained in accordance with the constraint correlation between flow rate and pressure while the transient flow rate distribution was also solved by variable-separation method. The theoretical solution conforms to numerical solution obtained by method of characteristics (MOC) very well.     

Double method of characteristics to analyze hydraulic-thermal transients of pipeline flow

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A mesh patching method for finite volume modelling of shallow water flow

A new mesh‐patching model is presented for shallow water flow described by the 2D non‐linear shallow water (NLSW) equations. The mesh‐patching model is based on AMAZON, a high‐resolution NLSW engine with an improved HLLC approximate Riemann solver. A new patching algorithm has been developed, which not only provides improved spatial resolution of flow features in particular parts of the mesh, but also simplifies and speeds up the (structured) grid generation process for an area with complicated geometry. The new patching technique is also compatible with increasingly popular parallel computing and adaptive grid techniques. The patching algorithm has been tested with moving bores, and results of test problems are presented and compared to previous work. Copyright © 2005 John Wiley & Sons, Ltd.     

Explicit characteristic‐based finite volume element method for level set equation

Accurate modeling of interfacial flows requires a realistic representation of interface topology. To reduce the computational effort from the complexity of the interface topological changes, the level set method is widely used for solving two‐phase flow problems. This paper presents an explicit characteristic‐based finite volume element method for solving the two‐dimensional level set equation. The method is applicable for the case of non‐divergence‐free velocity field. Accuracy and performance of the proposed method are evaluated via test cases with prescribed velocity fields on structured grids. By given a velocity field, the motion of interface in the normal direction and the mean curvature, examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time. Copyright © 2010 John Wiley & Sons, Ltd.     

A bore-capturing finite volume method for open-channel flows

A high-resolution finite volume hydrodynamic solver is presented for open-channel flows based on the 2D shallow water equations. This Godunov-type upwind scheme uses an efficient Harten–Lax–van Leer (HLL) approximate Riemann solver capable of capturing bore waves and simulating supercritical flows. Second-order accuracy is achieved by means of MUSCL reconstruction in conjunction with a Hancock two-stage scheme for the time integration. By using a finite volume approach, the computational grid can be irregular which allows for easy boundary fitting. The method can be applied directly to model 1D flows in an open channel with a rectangular cross-section without the need to modify the scheme. Such a modification is normally required for solving the 1D St Venant equations to take account of the variation of channel width. The numerical scheme and results of three test problems are presented in this paper. © 1998 John Wiley & Sons, Ltd.     

Finite volume method for three-dimensional transonic potential flow through turbomachinery blade rows

A finite-volume method has been developed for the calculation of transonic, potential flows through 3-D turbomachinery blades with complex geometries. The exact transonic potential flow equation is solved on a mesh constructed from small volume elements. A transformation is introduced through which cuboids of the physical plane are mapped into computational cubes. Two sets of overlapping volumes are used. While the thermodynamic properties are calculated at the primary volume centres, the flux balance is established on the secondary volumes. For transonic flows an artificial compressibility term (upwind density gradient) is added to density to produce the necessary directional bias in the hyperbolic region. The successive point over-relaxation Gauss-Seidel method has been used to solve the non-linear partial differential equations. Comparisons with experiments and/or other numerical solutions for various turbomachinery configurations show that the 3-D finite-volume approach is a relatively accurate, reliable and fast method for inviscid, transonic flow predictions through turbomachinery blade rows     

A finite volume method for viscous incompressible flows using a consistent flux reconstruction scheme

An incompressible Navier–Stokes solver using curvilinear body‐fitted collocated grid has been developed to solve unconfined flow past arbitrary two‐dimensional body geometries. In this solver, the full Navier–Stokes equations have been solved numerically in the physical plane itself without using any transformation to the computational plane. For the proper coupling of pressure and velocity field on collocated grid, a new scheme, designated ‘consistent flux reconstruction’ (CFR) scheme, has been developed. In this scheme, the cell face centre velocities are obtained explicitly by solving the momentum equations at the centre of the cell faces. The velocities at the cell centres are also updated explicitly by solving the momentum equations at the cell centres. By resorting to such a fully explicit treatment considerable simplification has been achieved compared to earlier approaches. In the present investigation the solver has been applied to unconfined flow past a square cylinder at zero and non‐zero incidence at low and moderate Reynolds numbers and reasonably good agreement has been obtained with results available from literature. Copyright © 2006 John Wiley & Sons, Ltd.