非正交同位网格下压力与速度耦合算法

发展了一种在非正交同位网格下以笛卡儿速度分量作为动量方程的独立变量、压力与速度耦合的S IM-PLER算法。该算法的特点是显式处理界面速度中的压力交叉导数项,得出压力与压力修正方程,使得压力及压力修正值与界面逆变速度直接耦合。通过对分汊通道内的流动问题进行验证计算,结果表明该算法可以有效而准确地模拟复杂区域内的流动与换热问题。     

基于非结构化同位网格的SIMPLE算法

通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散；扩散项的离散采用二阶中心差分格式；对于压力-速度耦合利用SIMPLE算法进行处理；计算节点的布置采用同位网格技术，界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算，讨论了非结构化同位网格有限体积法在实现SIMPLE算法时，迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知，本文的方法是准确和可信的。     

建筑风压场数值模拟中压力波动的平抑

在以同位网格为基础的简单流场压力计算中,通常采用动量插值方法来平抑流场中的压力波动现象;但是对于建筑风场等复杂的钝体绕流问题,由该平抑方法得到的收敛风压场仍可能存在小幅波动。为彻底解决同位网格格式下的压力波动,除采用动量插值方法外,本文提出了在压力校正方程的界面流速中添加压力梯度差值项的方法。算例分析表明,该方法计算得到的建筑风压场完全避免了压力波动现象,风压解与试验结果吻合良好。     

流固耦合分析的一种改进CBS有限元算法

针对流固耦合问题, 发展了一种基于任意拉格朗日-欧拉(ALE)描述有限元法的弱耦合分区算法. 运用半隐式特征线分裂算法求解Navier-Stokes方程, 在压力Poisson 方程中引入质量源项以满足几何守恒律; 运用子块移动技术更新动态网格, 并配以光滑处理防止网格质量下降; 采用Newmark-β 法求解结构运动方程. 为保持流体-结构界面处速度和动量守恒, 利用修正结合界面边界条件方法求解界面处速度通量和动量通量. 运用本方法分别模拟了不同雷诺数下单圆柱横向和两向流致振动、串列双圆柱两向流致振动. 计算表明, 本文方法计算效率高, 计算结果与已有实验和数值计算数据吻合.     

FV/MC混合算法求解轴对称钝体后湍流流场

介绍一种有限容积／Monte Carlo结合求解湍流流场的相容的混合算法．有限容积法求解Reynolds平均的动量方程和能量方程，Monte Carlo方法求解模化的脉动速度—频率—标量联合的PDF方程．将该算法发展到无结构网格，探讨了在无结构网格中实现两种方法的耦合，包括颗粒定位，颗粒场和平均场之间数据交换等问题．并以二维轴对称钝体后湍流流场作为算例，比较了计算结果与实验结果．     

不同网格扭曲率下压力修正全隐算法——IDEAL求解性能研究

2008年,本文作者和陶文铨等提出了一种用于速度和压力耦合求解的高效稳定压力修正全隐算法IDEAL,该算法通过在每个迭代层次上对压力方程进行两次内迭代计算,完全克服了SIMPLE算法的两个假设,充分满足了速度和压力之间的耦合,从而大大提高了计算的收敛性和健壮性。为了进一步实现IDEAL算法的推广应用,本文基于三维倾斜方腔顶盖驱动流动,研究了IDEAL算法在不同网格扭曲率下的求解特性。研究发现,在不同网格扭曲率下,IDEAL算法的健壮性和收敛性均优于SIMPLE算法,特别在高网格扭曲率情况下,IDEAL算法求解性能更加优于SIMPLE算法。在不同网格扭曲率下,IDEAL算法健壮性保持不变,几乎可以在任意速度亚松弛因子下获得收敛的解,同时IDEAL算法最短计算耗时较SIMPLE算法减少了56%~89%,验证了IDEAL算法的优越性。     

不同网格扭曲率下压力修正全隐算法——IDEAL求解性能研究

2008年,本文作者和陶文铨等提出了一种用于速度和压力耦合求解的高效稳定压力修正全隐算法IDEAL,该算法通过在每个迭代层次上对压力方程进行两次内迭代计算,完全克服了SIMPLE算法的两个假设,充分满足了速度和压力之间的耦合,从而大大提高了计算的收敛性和健壮性.为了进一步实现IDEAL算法的推广应用,本文基于三维倾斜方腔顶盖驱动流动,研究了IDEAL算法在不同网格扭曲率下的求解特性.研究发现,在不同网格扭曲率下,IDEAL算法的健壮性和收敛性均优于SIMPLE算法,特别在高网格扭曲率情况下,IDEAL算法求解性能更加优于SIMPLE算法.在不同网格扭曲率下,IDEAL算法健壮性保持不变,几乎可以在任意速度亚松弛因子下获得收敛的解,同时IDEAL算法最短计算耗时较SIMPLE算法减少了56%~89%,验证了IDEAL算法的优越性.     

同位网格上SIMPLE算法收敛特性的Fourier分析

应用Fourier方法研究了同位网格上SIMPLE算法求解浅水方程的收敛特性,并就松弛因子组合及阻力项的影响进行了分析.结果表明,采用合适的松弛因子组合可以很快地消除高频区域的误差,同时也可逐步消减迭代中低频区域的误差以获得收敛解.在保证收敛的前提下,低频误差分量决定了迭代速度,而且浅水方程中阻力项越大越利于SIMPLE算法收敛.     

拼接网格技术在复杂流场数值模拟中的应用研究

采用分区拼接网格技术,对 DLR-F6 机翼/机身胜架/短舱复杂组合体进行拼接网格分布.并采用 Menter SST 湍流模型,通过求解 Navier-Stokes 方程,对该组合体外流场以及发动机短舱内流场进行了一体化数值模拟,与相应风洞实验数据及分区搭接网格计算结果进行了比较与分析,验证了拼接网格技术的高效性与可靠性.同时通过分析对比不同插值方法的计算结果,研究了插值方法对拼接精度的影响;通过分析对比几组不同的拼接网格算例,总结出了 3 个拼接网格的基本实施准则.证明了拼接网格能够大幅度减小计算网格数目,可以更加灵活地分布网格节点,这样既可以缩短计算时间,又可以降低对内存的需求,提高了计算效率;同时无论整体的力系数,还是局部的压力分布流场细节都能够满足工程精度.     

利用非结构化网格方法对翼型绕流的数值研究

利用同位非结构化网格上的压力加权修正算法 ,对翼型湍流绕流进行了数值分析。详细地给出了一孤立翼型在不同攻角下的分离流结构及翼型表面压力分布 ,为了显示非结构化网格方法在求解多连通流动区域的优越性 ,对双翼型绕流进行了数值计算。在数值分析中 ,对阵面推进法进行改进来生成三角形网格 ,采用有限控制体方法直接在物理空间中的非结构化网格单元上离散 Navier- Stokes方程及 k- ε方程 ,形成的代数方程组通过预条件矩阵共轭梯度平方法求解。计算结果表明 :当流动为附着流时 ,计算结果与实验值吻合程度令人相当满意 ;而在分离区内 ,计算结果与实验值存在一定的误差 ,需对分离区内的湍流模型做进一步的改进。     

A volume-tracking method for incompressible multifluid flows with large density variations

A numerical technique (FGVT) for solving the time-dependent incompressible Navier–Stokes equations in fluid flows with large density variations is presented for staggered grids. Mass conservation is based on a volume tracking method and incorporates a piecewise-linear interface reconstruction on a grid twice as fine as the velocity–pressure grid. It also uses a special flux-corrected transport algorithm for momentum advection, a multigrid algorithm for solving a pressure-correction equation and a surface tension algorithm that is robust and stable. In principle, the method conserves both mass and momentum exactly, and maintains extremely sharp fluid interfaces. Applications of the numerical method to prediction of two-dimensional bubble rise in an inclined channel and a bubble bursting through an interface are presented. © 1998 John Wiley & Sons, Ltd.     

A robust algorithm for computing fluid flows on highly non‐smooth staggered grids

A new method for computing the fluid flow in complex geometries using highly non‐smooth and non‐orthogonal staggered grid is presented. In a context of the SIMPLE algorithm, pressure and physical tangential velocity components are used as dependent variables in momentum equations. To reduce the sensitivity of the curvature terms in response to coordinate line orientation change, these terms are exclusively computed using Cartesian velocity components in momentum equations. The method is then used to solve some fairly complicated 2‐D and 3‐D flow field using highly non‐smooth grids. The accuracy of results on rough grids (with sharp grid line orientation change and non‐uniformity) was found to be high and the agreement with previous experimental and numerical results was quite good. Copyright © 2008 John Wiley & Sons, Ltd.     

A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered finite volume/finite element method for solution of the two dimensional (2D) incompressible Navier-Stokes equations on unstructured grids.An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling.The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by joining the centroid of cells sharing the common vertex.For the temporal integration of the momentum equations,an implicit second-order scheme is utilized to enhance the computational stability and eliminate the time step limit due to the diffusion term.The momentum equations are discretized by the vertex-centered finite volume method (FVM) and the pressure Poisson equation is solved by the Galerkin finite element method (FEM).The momentum interpolation is used to damp out the spurious pressure wiggles.The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both velocity and pressure.The classic test cases,the lid-driven cavity flow,the skew cavity flow and the backward-facing step flow,show that numerical results are in good agreement with the published benchmark solutions.     

An efficient finite difference scheme for free‐surface flows in narrow rivers and estuaries

This paper presents a free‐surface correction (FSC) method for solving laterally averaged, 2‐D momentum and continuity equations. The FSC method is a predictor–corrector scheme, in which an intermediate free surface elevation is first calculated from the vertically integrated continuity equation after an intermediate, longitudinal velocity distribution is determined from the momentum equation. In the finite difference equation for the intermediate velocity, the vertical eddy viscosity term and the bottom‐ and sidewall friction terms are discretized implicitly, while the pressure gradient term, convection terms, and the horizontal eddy viscosity term are discretized explicitly. The intermediate free surface elevation is then adjusted by solving a FSC equation before the intermediate velocity field is corrected. The finite difference scheme is simple and can be easily implemented in existing laterally averaged 2‐D models. It is unconditionally stable with respect to gravitational waves, shear stresses on the bottom and side walls, and the vertical eddy viscosity term. It has been tested and validated with analytical solutions and field data measured in a narrow, riverine estuary in southwest Florida. Model simulations show that this numerical scheme is very efficient and normally can be run with a Courant number larger than 10. It can be used for rivers where the upstream bed elevation is higher than the downstream water surface elevation without any problem. Copyright © 2003 John Wiley & Sons, Ltd.     

Direct simulation of flows with suspended paramagnetic particles using one-stage smoothed profile method

The so-called smoothed profile method, originally suggested by Nakayama and Yamamoto and further improved by Luo et al. in 2005 and 2009, respectively, is an efficient numerical solver for fluid-structure interaction problems, which represents the particles by a certain smoothed profile on a fixed grid and constructs some form of body force added into the momentum (Navier-Stokes) equation by ensuring the rigidity of particles. For numerical simulations, the method first advances the flow and pressure fields by integrating the momentum equation except the body-force (momentum impulse) term in time and next updates them by separately taking temporal integration of the body-force term, thus requiring one more Poisson-equation solver for the extra pressure field due to the rigidity of particles to ensure the divergence-free constraint of the total velocity field. In the present study, we propose a simplified version of the smoothed profile method or the one-stage method, which combines the two stages of velocity update (temporal integration) into one to eliminate the necessity for the additional solver and, thus, significantly save the computational cost. To validate the proposed one-stage method, we perform the so-called direct numerical simulations on the two-dimensional motion of multiple inertialess paramagnetic particles in a nonmagnetic fluid subjected to an external uniform magnetic field and compare their results with the existing benchmark solutions. For the validation, we develop the finite-volume version of the direct simulation method by employing the proposed one-stage method. Comparison shows that the proposed one-stage method is very accurate and efficient in direct simulations of such magnetic particulate flows.     

Parallel computation of viscous incompressible flows using Godunov‐projection method on overlapping grids

The Godunov‐projection method is implemented on a system of overlapping structured grids for solving the time‐dependent incompressible Navier–Stokes equations. This projection method uses a second‐order fractional step scheme in which the momentum equation is solved to obtain the intermediate velocity field which is then projected on to the space of divergence‐free vector fields. The Godunov procedure is applied to estimate the non‐linear convective term in order to provide a robust discretization of this terms at high Reynolds number. In order to obtain the pressure field, a separate procedure is applied in this modified Godunov‐projection method, where the pressure Poisson equation is solved. Overlapping grids are used to discretize the flow domain, as they offer the flexibility of simplifying the grid generation around complex geometrical domains. This combination of projection method and overlapping grid is also parallelized and reasonable parallel efficiency is achieved. Numerical results are presented to demonstrate the performance of this combination of the Godunov‐projection method and the overlapping grid. Copyright © 2002 John Wiley & Sons, Ltd.     

Mie-Grneisen状态方程可压缩多流体流动的PPM方法

采用流体体积分数的混合型多流体数值模型，将piecewise parabolic method (PPM)方法应用于可压缩多流体流动的数值模拟，拓展了以前提出的模型和数值方法，使它能够处理一般的Mie-Grneisen状态方程。采用双波近似和两层迭代算法求解一般状态方程的Riemann问题；并根据多流体接触界面无振荡原则设计高精度计算格式，对典型的纯界面平移问题可以从理论上证明本算法在接触间断附近压力和速度没有振荡，而且数值模拟结果表明界面数值耗散也被控制在2~3个网格之内。模拟了多种复杂的可压缩多流体流动，算例结果表明本文方法可以有效地处理接触间断、激波等物理问题，且具有耗散小精度高的特点。     

Accurate numerical estimation of interphase momentum transfer in Lagrangian–Eulerian simulations of dispersed two-phase flows

The Lagrangian–Eulerian (LE) approach is used in many computational methods to simulate two-way coupled dispersed two-phase flows. These include averaged equation solvers, as well as direct numerical simulations (DNS) and large-eddy simulations (LES) that approximate the dispersed-phase particles (or droplets or bubbles) as point sources. Accurate calculation of the interphase momentum transfer term in LE simulations is crucial for predicting qualitatively correct physical behavior, as well as for quantitative comparison with experiments. Numerical error in the interphase momentum transfer calculation arises from both forward interpolation/approximation of fluid velocity at grid nodes to particle locations, and from backward estimation of the interphase momentum transfer term at particle locations to grid nodes. A novel test that admits an analytical form for the interphase momentum transfer term is devised to test the accuracy of the following numerical schemes: (1) fourth-order Lagrange Polynomial Interpolation (LPI-4), (3) Piecewise Cubic Approximation (PCA), (3) second-order Lagrange Polynomial Interpolation (LPI-2) which is basically linear interpolation, and (4) a Two-Stage Estimation algorithm (TSE). A number of tests are performed to systematically characterize the effects of varying the particle velocity variance, the distribution of particle positions, and fluid velocity field spectrum on estimation of the mean interphase momentum transfer term. Numerical error resulting from backward estimation is decomposed into statistical and deterministic (bias and discretization) components, and their convergence with number of particles and grid resolution is characterized. It is found that when the interphase momentum transfer is computed using values for these numerical parameters typically encountered in the literature, it can incur errors as high as 80% for the LPI-4 scheme, whereas TSE incurs a maximum error of 20%. The tests reveal that using multiple independent simulations and higher number of particles per cell are required for accurate estimation using current algorithms. The study motivates further testing of LE numerical methods, and the development of better algorithms for computing interphase transfer terms.     

Numerical computation of an impinging jet with uniform wall suction

The paper presents numerical predictions of a turbulent axisymmetric jet impinging onto a porous plate, based on a finite volume method of solving the Navier-Stokes equations for an incompressible air jet with the K–ε turbulence model. The velocity and pressure terms of the momentum equations are solved by the SIMPLE (semi-implicit method for pressure-linked equation) method. In this study, non-uniform staggered grids are used. The parameters of interest include the nozzle-to-wall distance and the suction velocity. The results of the present calculations are compared with available data reported in the literature. It is found that suction effects reduce the boundary layer thickness and increase the velocity gradient near the wall.