用混合网格及各向异性多重网格法求解三维可压紊流流动

采用混合网格求解紊流Navier Stokes方程。在物面附近采用柱状网格 ,其他区域则采用完全非结构网格。方程的求解采用Jamson的有限体积法 ,紊流模型采用两层Baldwin Lomax代数紊流模型。用各向异性多重网格法来加速解的收敛。数值算例表明 ,用混合网格及各向异性多重网格求解紊流流动是非常有效的     

用混合网格求解三维可压雷诺平均Navier—Stokes方程

用混合网格求解了三维紊流 N-S方程。在物面附近采用三棱柱网格 ,其它区域则采用四面体网格。方程的求解采用 Jamson的有限体积法 ,紊流模型采用两层 Baldwin-Lomax代数紊流模型。数值算例表明 ,用混合网格求解三维紊流 Navier-Stokes是非常有效的。     

考虑磁头表面高度不连续性气膜润滑的数值模拟与有效算法

随着磁头滑块的飞行高度不断降低,给气体润滑方程的数值求解带来了诸如计算时间过长、甚至计算发散等方面的问题。为了获得1Tbit/in2的存储密度,磁头滑块尾部的最小飞行高度接近1.5nm。本文基于作者提出的修正气膜润滑方程的线性流率(LFR)模型,考虑磁头滑块表面高度的不连续性,建立了基于有限体积法的气膜润滑方程离散格式,并把网格自适应技术与多重网格法应用到离散方程的迭代算法中,发展了可模拟最小飞行高度为0.5nm时磁头滑块压力分布的数值模拟方法与有效算法。文中以一个具有复杂表面形状的磁头滑块为例,检验了计算方法与算法的有效性。数值结果表明:在磁头滑块最小飞行高度较低时,必须要考虑滑块表面高度的不连续性,否则就得不到收敛的数值计算结果;与FK-Boltzmann模型相比,LFR模型具有较高的计算效率,采用网格自适应技术与多重网格法能有效地提高求解气膜润滑方程的计算效率。     

A finite element/volume method model of the depth‐averaged horizontally 2D shallow water equations

Analysis of surface water flows is of central importance in understanding and predicting a wide range of water engineering issues. Dynamics of surface water is reasonably well described using the shallow water equations (SWEs) with the hydrostatic pressure assumption. The SWEs are nonlinear hyperbolic partial differential equations that are in general required to be solved numerically. Application of a simple and efficient numerical model is desirable for solving the SWEs in practical problems. This study develops a new numerical model of the depth‐averaged horizontally 2D SWEs referred to as 2D finite element/volume method (2D FEVM) model. The continuity equation is solved with the conforming, standard Galerkin FEM scheme and momentum equations with an upwind, cell‐centered finite volume method scheme, utilizing the water surface elevation and the line discharges as unknowns aligned in a staggered manner. The 2D FEVM model relies on neither Riemann solvers nor high‐resolution algorithms in order to serve as a simple numerical model. Water at a rest state is exactly preserved in the model. A fully explicit temporal integration is achieved in the model using an efficient approximate matrix inversion method. A series of test problems, containing three benchmark problems and three experiments of transcritical flows, are carried out to assess accuracy and versatility of the model. Copyright © 2014 John Wiley & Sons, Ltd.     

An Euler solver for three-dimensional turbomachinery flows

A time-marching finite volume numerical procedure is presented for three-dimensional Euler analysis of turbomachinery flows. The proposed scheme is applied to the conservative form of the Euler equations written in general curvilinear co-ordinates. A simple but computationally efficient grid is constructed. Numerical solution results for three 3D turbine cascade flows have been presented and compared with available measurements as well as with another state-of-the-art 3D Euler analysis numerical solution in order to demonstrate the accuracy and computational efficiency of the analysis method. Also, the predicted results are compared with a 3D potential flow solver and comparison is made with the analytical solution. The proposed method is an accurate and reliable technique for solving the compressible flow equations in turbomachinery geometries.     

An implicit mixed finite-volume–finite-element method for solving 3D turbulent compressible flows

The development of new aeronautic projects require accurate and efficient simulations of compressible flows in complex geometries. It is well known that most flows of interest are at least locally turbulent and that the modelling of this turbulence is critical for the reliability of the computations. A turbulence closure model which is both cheap and reasonably accurate is an essential part of a compressible code. An implicit algorithm to solve the 2D and 3D compressible Navier–Stokes equations on unstructured triangular/tetrahedral grids has been extended to turbulent flows. This numerical scheme is based on second-order finite element–finite volume discretization: the diffusive and source terms of the Navier–Stokes equations are computed using a finite element method, while the other terms are computed with a finite volume method. Finite volume cells are built around each node by means of the medians. The convective fluxes are evaluated with the approximate Riemann solver of Roe coupled with the van Albada limiter. The standard k–ϵ model has been introduced to take into account turbulence. Implicit integration schemes with efficient numerical methods (CGS, GMRES and various preconditioning techniques) have also been implemented. Our interest is to present the whole method and to demonstrate its limitations on some well-known test cases in three-dimensional geometries. © 1997 John Wiley & Sons, Ltd.     

Development of a hybrid particle‐mesh method for two‐phase flow simulations

A hybrid particle‐mesh method was developed for efficient and accurate simulations of two‐phase flows. In this method, the main component of the flow is solved using the constrained interpolated profile/multi‐moment finite volumemethod; the two‐phase interface is rendered using the finite volume particle (FVP) method. The effect of surface tension is evaluated using the continuum surface force model. Numerical particles in the FVP method are distributed only on the surface of the liquid in simulating the interface between liquid and gas; these particles are used to determine the density of each mesh grid. An artificial term was also introduced to mitigate particle clustering in the direction of maximum compression and sparse discretization errors in the stretched direction. This enables accurate interface tracking without diminishing numerical efficiency. Two benchmark simulations are used to demonstrate the validity of the method developed and its numerical stability. Copyright © 2016 John Wiley & Sons, Ltd.     

有限体积法在二维固体力学问题中的应用

推导了矩形单元的二维固体力学有限体积法公式，与解析解及有限元解进行了比较，讨论了有限体积法在非线性问题中的应用     

Finite‐volume‐type VOF method on dynamically adaptive quadtree grids

This paper describes a finite‐volume volume‐of‐fluid (VOF) method for simulating viscous free surface flows on dynamically adaptive quadtree grids. The scheme is computationally efficient in that it provides relatively fine grid resolution at the gas–liquid interface and coarse grid density in regions where flow variable gradients are small. Special interpolations are used to ensure volume flux conservation where differently sized neighbour cells occur. The numerical model is validated for advection of dyed fluid in unidirectional and rotating flows, and for two‐dimensional viscous sloshing in a rectangular tank. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical viscosity reduction in the resolution of the shallow water equations with turbulent term

A first‐order finite volume model for the resolution of the 2D shallow water equations with turbulent term is presented. An upwind discretization of the equations that include the turbulent term is carried out. A method to reduce the excess of numerical viscosity (or diffusion) produced by the upwinding of the flux term is proposed. Two different discretizations of the turbulent term are compared, and results for uniform distributions of the viscosity are presented. Finally, two discretizations of the time derivative which are more efficient than Euler's are proposed and compared. Copyright © 2008 John Wiley & Sons, Ltd.     

A ghost-cell immersed boundary method for large eddy simulation of flows in complex geometries

An efficient ghost-cell immersed boundary (IB) method is proposed for large eddy simulations of three-dimensional incompressible flow in complex geometries. In the framework of finite volume method, the Navier–Stokes equations are integrated using an explicit time advancement scheme on a collocated mesh. Since the IB method is known to generate an unphysical velocity field inside the IB that violates the mass conservation of the cells near the IB, a new IB treatment is devised to eliminate the unphysical velocity generated near the IB and to improve the pressure distribution on the body surface. To validate the proposed method, both laminar and turbulent flow cases are presented. In particular, large eddy simulations were performed to simulate the turbulent flows over a circular cylinder and a sphere at subcritical Reynolds numbers. The computed results show good agreements with the published numerical and experimental data.     

An efficient and accurate algebraic interface capturing method for unstructured grids in 2 and 3 dimensions: The THINC method with quadratic surface representation

We present in this paper an efficient and accurate volume of fluid (VOF) type scheme to compute moving interfaces on unstructured grids with arbitrary quadrilateral mesh elements in 2D and hexahedral elements in 3D. Being an extension of the multi‐dimensional tangent of hyperbola interface capturing (THINC) reconstruction proposed by the authors in Cartesian grid, an algebraic VOF scheme is devised for arbitrary quadrilateral and hexahedral elements. The interface is cell‐wisely approximated by a quadratic surface, which substantially improves the numerical accuracy. The same as the other THINC type schemes, the present method does not require the explicit geometric representation of the interface when computing numerical fluxes and thus is very computationally efficient and straightforward in implementation. The proposed scheme has been verified by benchmark tests, which reveal that this scheme is able to produce high‐quality numerical solutions of moving interfaces in unstructured grids and thus a practical method for interfacial multi‐phase flow simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Simulation of shallow flows over variable topographies using unstructured grids

Simulation of shallow flows over variable topographies is a challenging case for most available shock‐capturing schemes. This problem arises because the source terms and flux gradients are not balanced in the numerical computations. Treatments for this problem generally work well on structured grids, but they are usually too expensive, and most of them are not directly applicable to unstructured grids. In this paper we propose two efficient methods to treat the source terms without upwinding and to satisfy the compatibility condition on unstructured grids. In the first method, the calculation of the bed slope source term is performed by employing a compatible approximation of water depth at the cell interfaces. In the second one, different components of the bed slope term are considered separately and a compatible discretization of the components is proposed. The present treatments are applicable for most schemes including the Roe's method without changing the performance of the original scheme for smooth topographies. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical simulation of droplet ejection of thermal inkjet printheads

In this study, we present a method to predict the droplet ejection in thermal inkjet printheads including the growth and collapse of a vapor bubble and refill of the firing chamber. The three‐dimensional Navier–Stokes equations are solved using a finite‐volume approach with a fixed Cartesian mesh. The piecewise‐linear interface calculation‐based volume‐of‐fluid method is employed to track and reconstruct the ink–air interface. A geometrical computation based on Lagrangian advection is used to compute the mass flux and advance the interface. A simple and efficient model for the bubble dynamics is employed to model the effect of ink vapor on the adjacent ink liquid. To solve the surface tension‐dominated flow accurately, a hierarchical curvature‐estimation method is proposed to adapt to the local grid resolution. The numerical methods mentioned earlier have been implemented in an internal simulation code, CFD3. The numerical examples presented in the study show good performance of CFD3 in prediction of surface tension‐dominated free‐surface flows, for example, droplet ejection in thermal inkjet printing. Currently, CFD3 is used extensively for printhead development within Hewlett‐Packard. Copyright © 2015 John Wiley & Sons, Ltd.     

A fractional two‐step implicit algorithm using curvilinear collected grids

An efficient fractional two‐step implicit algorithm is reported to simulate incompressible fluid flows in a boundary‐fitted curvilinear collocated grid system. Using the finite volume method, the convection terms are discretized by the high‐accuracy Roe's scheme to minimize numerical diffusion. An implicitness coefficient Π is introduced to accelerate the rate of convergence. It is demonstrated that the proposed algorithm links the fractional step method to the pressure correction procedure, and the SIMPLEC method could be considered as a special case of the fractional two‐step implicit algorithm (when Π=1). The proposed algorithm is applicable to unsteady flows and steady flows. Three benchmark two‐dimensional laminar flows are tested to evaluate the performance of the proposed algorithm. Performance is measured by sensitivity analyses of the efficiency, accuracy, grid density, grid skewness and Reynolds number on the solutions. Results show that the model is efficient and robust. Copyright © 2006 John Wiley & Sons, Ltd.     

Calculation of three‐dimensional turbulent flow with a finite volume multigrid method

A numerical method for the efficient calculation of three‐dimensional incompressible turbulent flow in curvilinear co‐ordinates is presented. The mathematical model consists of the Reynolds averaged Navier–Stokes equations and the k–ε turbulence model. The numerical method is based on the SIMPLE pressure‐correction algorithm with finite volume discretization in curvilinear co‐ordinates. To accelerate the convergence of the solution method a full approximation scheme‐full multigrid (FAS‐FMG) method is utilized. The solution of the k–ε transport equations is embedded in the multigrid iteration. The improved convergence characteristic of the multigrid method is demonstrated by means of several calculations of three‐dimensional flow cases. Copyright © 1999 John Wiley & Sons, Ltd.     

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-vanLeerContact)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支管路拟一维流动数值计算模型。基于所发展的一维流动数值方法,建立了变径管道和含60°分支管道内流动计算模型,验证了该方法的收敛性和有效性;基于虚拟节点的数值格式处理变径管激波问题具有一定精度优势。研究了变径管和分支管模型中可压缩流体激波、稀疏波等的传播机理,分析了管径对相邻支管压力的影响,为工程管路设计提供了参考。     

A finite volume method for fluid flow in polar cylindrical grids

In the numerical simulation of fluid flows using a polar cylindrical grid, grid lines meet at a single point on the axis of the polar cylindrical grid system; this makes the grids around the axis degenerate from being general quadrilaterals into triangles. Therefore, a special treatment must be performed when the axis has to be included in the computational domain in order to solve a non-axisymmetrical fluid flow problem. In this paper a new numerical method has been developed to deal with the difficulty of the axis when the control volume technique is used with a non-staggered grid arrangement. Two illustrative examples of the proposed method are presented for simulating the fluid flows on the axis and all the numerical results obtained for the two examples are shown to be in good agreement with the available analytical solutions. © 1998 John Wiley & Sons, Ltd.     

非结构混合网格高超声速绕流与磁场干扰数值模拟

对均匀磁场干扰下的二维钝头体无粘高超声速流场进行了基于非结构混合网格的数值模拟.受磁流体力学方程组高度非线性的影响及考虑到数值模拟格式的精度,目前在此类流场的数值模拟中大多使用结构网格及有限差分方法,因而在三维复杂外形及复杂流场方面的研究受到限制.本文主要探索使用非结构网格(含混合网格)技术时的数值模拟方法.控制方程为耦合了Maxwell方程及无粘流体力学方程的磁流体力学方程组,数值离散格式采用Jameson有限体积格心格式,5步Runge-Kutta显式时间推进.计算模型为二维钝头体,初始磁场均匀分布.对不同磁感应强度影响下的高超声速流场进行了数值模拟,并与有限的资料进行了对比,得到了较符合的结果.