Two‐dimensional flow past circular cylinders using finite volume lattice Boltzmann formulation

In this article, an extension to the total variation diminishing finite volume formulation of the lattice Boltzmann equation method on unstructured meshes was presented. The quadratic least squares procedure is used for the estimation of first‐order and second‐order spatial gradients of the particle distribution functions. The distribution functions were extrapolated quadratically to the virtual upwind node. The time integration was performed using the fourth‐order Runge–Kutta procedure. A grid convergence study was performed in order to demonstrate the order of accuracy of the present scheme. The formulation was validated for the benchmark two‐dimensional, laminar, and unsteady flow past a single circular cylinder. These computations were then investigated for the low Mach number simulations. Further validation was performed for flow past two circular cylinders arranged in tandem and side‐by‐side. Results of these simulations were extensively compared with the previous numerical data. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical method for computing two-dimensional unsteady rarefied gas flows in arbitrarily shaped domains

A high-order accurate method for analyzing two-dimensional rarefied gas flows is proposed on the basis of a nonstationary kinetic equation in arbitrarily shaped regions. The basic idea behind the method is the use of hybrid unstructured meshes in physical space. Special attention is given to the performance of the method in a wide range of Knudsen numbers and to accurate approximations of boundary conditions. Examples calculations are provided.     

浅水方程组的数值方法

构造了浅水方程组的二阶精度的TVD格式。格式由简单的TVD Runge-Kutta型时间离散和有坡度限制的空间对称离散格式组成。数值耗散项用局部棱柱化河道流的特征变量构造。格式的主要优点是能够计算天然河道中浅水方程组的弱解并且构造简单。格式能够求出天然河道或非平底部渠道中的精确静水解。给出了渠道溃坝问题数值解与解析解的比较,验证格式精度高。实际天然河道型梯级水库溃坝的数值实验表明格式稳定,适应性强。     

叶片的周向弯曲与弦向弯曲及其数值分析

六十年代提出的静叶片的倾斜或弯曲方法是以透平轴的平行线为转动轴将叶片转动（构成倾斜叶片）或沿叶高弯曲（构成弯曲叶片）。本文提出将转动轴在Ｓ１平面旋转到弦向，然后倾斜或弯曲叶片，称这种叶片为弦向倾斜或弯曲叶片。应用欧拉方程和高精度ＴＶＤ格式对不同弯曲方法的叶片的数值分析表明弦向弯曲叶片控制径向二次流的能力大于周向弯曲叶片。     

On convergence of numerical schemes for hyperbolic conservation laws with stiff source terms

We deal in this study with the convergence of a class of numerical schemes for scalar conservation laws including stiff source terms. We suppose that the source term is dissipative but it is not necessarily a Lipschitzian function. The convergence of the approximate solution towards the entropy solution is established for first and second order accurate MUSCL and for splitting semi-implicit methods.

     

非线性随机结构动力可靠度的密度演化方法

建议了一类新的非线性随机结构动力可靠度分析方法。基于非线性随机结构反应分析的概率密度演化方法,根据首次超越破坏准则对概率密度演化方程施加相应的边界条件,求解带有初、边值条件的概率密度演化方程,可以给出非线性随机结构的动力可靠度。研究了数值计算技术,建议了具有自适应功能的TVD差分格式。以具有双线型恢复力性质的8层框架结构为例进行了地震作用下的动力可靠度分析,与随机模拟结果的比较表明,所建议的方法具有较高的精度和效率。     

Centred TVD schemes for hyperbolic conservation laws

New first- and high-order centred methods for conservation lawsare presented. Convenient TVD conditions for constructing centredTVD schemes are then formulated and some useful results areproved. Two families of centred TVD schemes are constructedand extended to nonlinear systems. Some numerical results arealso presented.     

A class of the fourth order finite volume Hermite weighted essentially non-oscillatory schemes

In this paper, we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory (HWENO) schemes based on the work (Computers & Fluids, 34: 642–663 (2005)) by Qiu and Shu, with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws. The key idea of HWENO is to evolve both with the solution and its derivative, which allows for using Hermite interpolation in the reconstruction phase, resulting in a more compact stencil at the expense of the additional work. The main difference between this work and the formal one is the procedure to reconstruct the derivative terms. Comparing with the original HWENO schemes of Qiu and Shu, one major advantage of new HWENO schemes is its robust in computation of problem with strong shocks. Extensive numerical experiments are performed to illustrate the capability of the method. Corresponding author This work was partially supported by the National Natural Science Foundation of China (Grant No. 10671097), the European project ADIGMA on the development of innovative solution algorithms for aerodynamic simulations, Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry and the Natural Science Foundation of Jiangsu Province (Grant No. BK2006511)     

A finite volume scheme for two-phase compressible flows

In gas-particle two-phase flows, when the concentration of the disperesed phase is low, certain assumptions may be made which simplify considerably the equations one has to solve. The gas and particle flows are then linked only via the interaction terms. One may therefore uncouple the full system of equations into two subsystems: one for the gas phase, whose homogeneous part reduces to the Euler equations; and a second system for the particle motion, whose homogeneous part is a degenerate hyperbolic system. The equations governing the gas phase flow may be solved using a high-resolution scheme, while the equations describing the motion of the dispersed phase are treated by a donor-cell method using the solution of a particular Riemann problem. Coupling is then achieved via the right-hand-side terms. To illustrate the capabilities of the proposed method, results are presented for a case specially chosen from among the most difficult to handle, since it involves certain geometrical difficulties, the treatment of regions in which particles are absent and the capturing of particle fronts.     

Numerical study on flow separation control over NACA0015 aerofoil using electromagnetic fields

In this study, a flow solver was developed based on the governing RANS equations of compressible flows and was further extended to include the effects of electromagnetic forces namely Lorentz forces. Lorentz forces may be added as a source term in the governing fluid flow equations. Numerical studies were carried out for NACA0015 aerofoil at high angles of incidences from 15° to 30° and compared with some available cases of experimental and incompressible numerical solutions. The hydrodynamics performance was improved using a magnetic momentum coefficient of up to 0.048. The size of flow separation zone was decreased or completely eliminated by increasing this coefficient. The overall drag was not changed considerably, however the overall lift was increased up to 80 percent at stall angles.