一般形式的二维时—空守恒格式

本文将经作者改进后的一维时－空守恒格式推广到了二维情形，得到了一个一般形式的二维Ｅｕｌｅｒ方程时－空守恒格式，该格式对各种不规则几何区域内的流动问题具有很强的适应性，同时它还保留了一维格式的优点。几个典型算例的计算结果表明，本文格式不仅精度高，通用性好，而且对激波等间断具有很高的分辨率。     

7阶WENO-S格式的计算效率研究

WENO-S格式是一类适合于含间断问题数值模拟的加权本质无振荡格式.这类格式的光滑因子满足对单频波为常数,这使得其近似色散关系与线性基底格式一致,并且具有良好的小尺度波动模拟能力．计算效率是数值方法性能指标的一个重要方面.由于WENO-S格式的光滑因子在各子模板上的计算公式除下标不同外形式一致,在计算线性对流方程相邻数值通量时,部分光滑因子完全相同．为此提出一种消除WENO-S格式冗余光滑因子计算的方法.该方法要求一条网格线上用于重构或插值的量可以表示为一个序列.基于此要求分析其对于几种不同物理问题的可行性和使用方法.以7阶WENO-S格式为例介绍了格式性质和去除冗余光滑因子计算的方法.该方法中预先计算和存储一条网格线上的所有光滑因子,在网格点较多的情况下,光滑因子计算次数约为原7阶WENO-S格式的1/4.对一维对流问题、球面波传播问题、二维旋转问题、二维小扰动传播问题及一维和二维无黏流动问题进行了数值模拟.结果表明该格式对多种流动结构具有良好的捕捉能力,并且同时具有良好的计算效率,去除冗余计算后又降低了约20%的计算时间.     

A stabilized extremum-preserving scheme for nonlinear parabolic equation on polygonal meshes

In this paper, a stabilized extremum-preserving scheme is introduced for the nonlinear parabolic equation on polygonal meshes. The so-called harmonic averaging points located at the interface of heterogeneity are employed to define the auxiliary unknowns and can be interpolated by the cell-centered unknowns. This scheme has only cell-centered unknowns and possesses a small stencil. A stabilized term is constructed to improve the stability of this scheme. The stability analysis of this scheme is obtained under standard assumptions. Numerical results illustrate that the scheme satisfies the extremum principle with anisotropic full tensor coefficient problems and has optimal convergence rate in space on distorted meshes.     

A bounded convection scheme for the overlapping control volume approach

This paper introduces a flux-limited scheme FLOCV for the overlapping control volume (OCV) approach to 2D steady and unsteady convection–diffusion problems on structured non-orthogonal grids. FLOCV switches from second- to first-order interpolation in the presence of extrema. Smooth switching between the two is ensured by weighted average second- and first-order upwind differencing, with the weights being dynamically determined. Five convective test problems are solved using this scheme and results are compared with known analytical solutions. It is found that FLOCV approximately retains second-order accuracy of the base discretization scheme on uniform grids and smooth non-uniform orthogonal grids. It is also found effective in removing oscillations for problems with discontinuities on both orthogonal and non-orthogonal grids, with little degradation of accuracy. © 1997 John Wiley & Sons, Ltd.     

二维时-空守恒格式及其在激波传播计算中的应用

将改进后的一维时－空守恒格式推广到了二维情形,得到了一个新的一般形式的二维Ｅｕｌｅｒ方程时－空守恒格式,并用该格式对几个具有复杂波系的流场进行了数值模拟。结果表明,该格式保留了一维格式通用性好、结构简单的优点,其计算结果精度高,对激波等间断具有很强的分辨率。     

A hybrid scheme for the numerical simulation of shock/discontinuity problems

To address accuracy issues for direct numerical simulation, a hybrid scheme based on the weighted compact scheme (WCS) and weighted essentially non-oscillatory (WENO) scheme is developed. The new hybrid method incorporates the advantages of both schemes. Time integration is performed using the fourth-order total variation diminishing Runge–Kutta method with a characteristic filter. The accuracy of the scheme is assessed using several benchmark problems. Results show that the proposed scheme produces a more accurate solution for problems involving shocks and discontinuities in comparison with the traditional shock-capturing methods.     

High‐accuracy upwind method using improved characteristics speeds for incompressible flows

In this study, the Nervier–Stokes equations for incompressible flows, modified by the artificial compressibility method, are investigated numerically. To calculate the convective fluxes, a new high‐accuracy characteristics‐based (HACB) scheme is presented in this paper. Comparing the HACB scheme with the original characteristic‐based method, it is found that the new proposed scheme is more accurate and has faster convergence rate than the older one. The second order averaging scheme is used for estimating the viscose fluxes, and spatially discretized equations are integrated in time by an explicit fourth‐order Runge–Kutta scheme. The lid driven cavity flow and flow in channel with a backward facing step have been used as benchmark problems. It is shown that the obtained results using HACB scheme are in good agreement with the standard solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

A numerical method to simulate turbulent cavitating flows

The objective of this paper is to develop a numerical method for simulating multiphase cavitating flows on unstructured grids. The multiphase medium is represented using a homogeneous mixture model that assumes thermal equilibrium between the liquid and vapor phases. We develop a predictor–corrector approach to solve the governing Navier–Stokes equations for the liquid/vapor mixture, together with the transport equation for the vapor mass fraction. While a non-dissipative and symmetric scheme is used in the predictor step, a novel characteristic-based filtering scheme with a second order TVD filter is developed for the corrector step to handle shocks and material discontinuities in non-ideal gases and mixtures. Additionally, a sensor based on vapor volume fraction is proposed to localize dissipation to the vicinity of discontinuities. The scheme is first validated for simple one dimensional canonical problems to verify its accuracy in predicting jump conditions across material discontinuities and shocks. It is then applied to two turbulent cavitating flow problems – over a hydrofoil using RANS and over a wedge using LES. Our results show that the simulations are in good agreement with experimental data for the above tested cases, and that the scheme can be successfully applied to both RANS and LES methodologies.     

Modeling intermittent contact for flexible multibody systems

This paper consists of two parts. The first part presents a complementarity based recursive scheme to model intermittent contact for flexible multibody systems. A recursive divide-and-conquer framework is used to explicitly impose the bilateral constraints in the entire system. The presented approach is an extension of the hybrid scheme for rigid multibody systems to allow for small deformations in form of local mode shapes. The normal contact and frictional complementarity conditions are formulated at position and velocity level, respectively, for each body in the system. The recursive scheme preserves the essential characteristics of the contact model and formulates a minimal size linear complementarity problem at logarithmic cost for parallel implementation. For a certain class of contact problems in flexible multibody systems, the complementarity based time-stepping scheme requires prohibitively small time-steps to retain accuracy. Modeling intermittent contact for this class of contact problems motivated the development of an iterative scheme. The second part of the paper describes this iterative scheme to model unilateral constraints for a multibody system with relatively fewer contacts. The iterative scheme does not require a traditional complementarity formulation and allows the use of any higher order integration methods. A comparison is then made between the traditional complementarity formulation and the presented iterative scheme via numerical examples.     

Improved laminar predictions using a stabilised time-dependent simple scheme

A new scheme which can solve unsteady incompressible flows is described in this paper. The scheme is a variant of the SIMPLE methodology. Typically, a scheme of this type tends to suffer from stability problems, which this new scheme overcomes by taking small intermediate steps within a time step. The calculations made in the intermediate steps are damped to enhance the stability of the scheme. The new stabilised scheme is evaluated for laminar flow around a square cylinder, impulsively started laminar flow over a backward-facing step and fluctuating laminar flow over a backward-facing step. Comparisons are made with other numerical predictions and experimental data. In general, good agreement is found, except for the fluctuating laminar flow over a backward-facing step problem. The new scheme is found to have the same level of accuracy, stability and efficiency in comparison with the PISO scheme, but it is easier to code. © 1998 John Wiley & Sons, Ltd.     

Contribution to the improvement of the QUICK scheme for the resolution of the convection–diffusion problems

The present paper deals with the improvement of a QUICK scheme for the resolution of convection–diffusion problems. In order to avoid any unstability problems and to increase the convergence speed a new deferred correction is suggested. Checking the required stability criteria, benefits are taken from the accuracy of the central difference scheme when it is possible. Otherwise, a upwind scheme is introduced in the deferred correction term warranting the stability of the whole scheme. Tests have been carried out on a wall driven square cavity and on a buoyancy driven cavity. Comparisons have been achieved with reference data in order to assess the accuracy of the present scheme. Further comparison with other differentiation scheme demonstrate that the present formulation is fast and accurate.     

A remedy for numerical oscillations in weakly compressible smoothed particle hydrodynamics

Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) can lead to non‐physical oscillations in the pressure and density fields when simulating incompressible flow problems. This in turn may result in tensile instability and sometimes divergence. In this paper, it is shown that this difficulty originates from the specific form of spatial discretization used for the pressure term when solving the mass conservation equation. After describing the pressure–velocity decoupling problem associated with the so‐called colocated grid methods, a modified approach is presented that overcomes this problem using a different discretization scheme for the second derivative of pressure. The modified scheme is employed for solving a number of benchmark problems including both single‐phase and two‐phase test cases. Copyright © 2010 John Wiley & Sons, Ltd.     

南水北调新线路-三峡水库引水济黄济华北段工程地质条件

由于汉江丹江口水库不是稳定可靠的水源基地, 加上频繁出现的黄河断流、渭河干涸以及黄河全流域缺水等问题, 现有的东线、中线方案不能解决, 只有三峡引水工程能够解决, 且效益巨大。本文介绍三峡水库引水工程的地质概况和工程地质条件。该工程不存在解决不了的重大技术问题和地质问题。     

A modular,operator‐splitting scheme for fluid–structure interaction problems with thick structures

We present an operator‐splitting scheme for fluid–structure interaction (FSI) problems in hemodynamics, where the thickness of the structural wall is comparable to the radius of the cylindrical fluid domain. The equations of linear elasticity are used to model the structure, while the Navier–Stokes equations for an incompressible viscous fluid are used to model the fluid. The operator‐splitting scheme, based on the Lie splitting, separates the elastodynamics structure problem from a fluid problem in which structure inertia is included to achieve unconditional stability. We prove energy estimates associated with unconditional stability of this modular scheme for the full nonlinear FSI problem defined on a moving domain, without requiring any sub‐iterations within time steps. Two numerical examples are presented, showing excellent agreement with the results of monolithic schemes. First‐order convergence in time is shown numerically. Modularity, unconditional stability without temporal sub‐iterations, and simple implementation are the features that make this operator‐splitting scheme particularly appealing for multi‐physics problems involving FSI. Copyright © 2013 John Wiley & Sons, Ltd.     

Application of a 3-D FEM/FDM Overlapping Scheme to Heat and Mass Transfer and Moving-Boundary Problems

A 3-D FEM/FDM overlapping scheme for viscous, incompressible flow problems is presented that combines the finite element method, which is best suited to analyze flow in any arbitrarily shaped flow geometry, with the finite difference method, which is advantageous in both computing time and computer storage. The combination of both methods enables large-scale viscous flow to be analyzed, which is crucial both for detailed analysis of 3-D flows and for solving flow problems around moving bodies, A modified ABM AC method is used as the basic algorithm, to which a sophisticated time integration scheme, proposed by the present authors, has been applied. In this paper, some numerical results including 3-D heat and mass transfer problem and moving-boundary problems are presented.     

A duality recipe for non-convex variational problems

The aim of this paper is to present a general convexification recipe that can be useful for studying non-convex variational problems. In particular, this allows us to treat such problems by using a powerful primal–dual scheme. Possible further developments and open issues are given.     

Flux vector splitting solutions for coupling hydraulic transient of gas-liquid-solid three-phase flow in pipelines

The gas-liquid-solid three-phase mixed flow is the most general in multiphase mixed transportation. It is significant to exactly solve the coupling hydraulic transient problems of this type of multiphase mixed flow in pipelines. Presently, the method of characteristics is widely used to solve classical hydraulic transient problems. However, when it is used to solve coupling hydraulic transient problems, excessive interpolation errors may be introduced into the results due to unavoidable multiwave interpolated calculations. To deal with the problem, a finite difference scheme based on the Steger-Warming flux vector splitting is proposed. A flux vector splitting scheme is established for the coupling hydraulic transient model of gas-liquid-solid three-phase mixed flow in the pipelines. The flux subvectors are then discretized by the Lax-Wendroff central difference scheme and the Warming-Beam upwind difference scheme with second-order precision in both time and space. Under the Rankine-Hugoniot conditions and the corresponding boundary conditions, an effective solution to those points located at the boundaries is developed, which can avoid the problem beyond the calculation region directly induced by the second-order discrete technique. Numerical and experimental verifications indicate that the proposed scheme has several desirable advantages including high calculation precision, excellent shock wave capture capability without false numerical oscillation, low sensitivity to the Courant number, and good stability.     

A class of finite difference schemes for interface problems with an HOC approach

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparisons of some difference forms for compressible flow in cylindrical geometry on arbitrary Lagrangian and Eulerian framework

The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical symmetry properties of the numerical schemes are discussed, and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian (ALE) method. Numerical results are presented to compare three discrete configurations, i.e., the control volume scheme, the area weighted scheme, and the plane scheme with the addition of a geometrical source. The fact that the singularity arises from the geometrical source term in the plane scheme is illustrated. A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.     

Algebraic-Complex Scheme for Dirichlet–Neumann Data for Parabolic System

In this paper, we use the Laplace–Laplace transformation and complex analysis to give a systematical scheme to determine the proper boundary conditions for initial-boundary value problems in the half space and to construct exponentially sharp pointwise structures of the boundary data. Here, we have used the boundary value problems with the Robin boundary conditions for the convection heat equations and the linearized compressible Navier–Stokes equation with a constant convection velocity to demonstrate this scheme.