多介质流体计算的Lax-Friedrichs格式

针对当前多介质流体计算中出现的速度和压强在介质界面处产生伪振荡的问题，我们设计了一种基于非平衡态的Lax-Friedrichs格式．我们构造的算法保证了多个守恒性质：总质量和分质量守恒，总动量和总能量守恒，它还可以保证分质量非负．更重要的是它消除了速度和压强在介质界面处的伪振荡．数值例子表明这一算法是有效的．     

用于高速可压缩流体分析的带多维耗散格式的自适应Delaunay三角剖分

利用自适应Delaunay三角剖分并结合胞格中心迎风算法,分析非粘滞高速可压缩流体问题.推导了多维耗散格式,并采用非结构化三角网格的迎风算法,改善了激波的计算结果.解精度评价中引入误差估计,在网格重划分算法中,解梯度变化大的区域生成小单元格,解梯度变化小的区域使用大单元格.该格式能进一步推广到高阶时空的解精度分析中.通过稳态和不稳态的高速可压缩流体超音速激波和激波传播特性的分析,可以评估该算法的效率.     

一维多介质可压缩流动的守恒型界面追踪方法

本文针对一维问题的ProntTracking方法,提出了一种较易实现的守恒型界面追踪方法.利用双波近似求解Riemann问题来确定界面处的数值通量,在固定的网格上采用统一的有限体积格式进行内点和交界面点的计算,通过守恒插值以及守恒量的重新分配,保证数值解在全场实现一致守恒,将该方法应用于一维多介质可压缩流动的模拟,给出了满意的数值模拟结果.     

结构振动诱导流场及附加质量的数值分析

将大型柔性结构低速振动诱导流体流场的问题, 归结为无粘性不可压缩无旋流动平面问题．在偶极子配置法基础上,发展了一种在结构和流体接触面上混合配置源汇和偶极子的奇点配置法,能够计算翼型、柱型等结构在流体中低速振动时诱导的流体流场并推导出流场的动能表达式,最终得到流体附加质量．给出了几个具有解析解的算例验证了此方法的可靠性．     

多介质流体界面的守恒型跟踪法

本文中,我们对茅德康在【D.K.Mao,Towards front-tracking based on conservation in two space dimensionsⅡ,tracking discontinuities in capturing fashion,J.Comput.Phys.,226,(2007),pp 1550-1588】一文中所建立的守恒型跟踪法进行了改进,成功将算法运用到多介质流体界面的计算中.最后,我们使用改进后的算法计算了两个数值算例,验证了算法的有效性.     

电场驱动直射流的动量方程

给出了电场驱动直射流的一维动量守恒方程．该方程是用应力分量表示的,适用于任何流体本构关系,只要流体是不可压缩的．结果显示,为了使方程封闭,需要沿轴向和径向两个方向的本构关系．然而,当附加应力张量的迹为0时,只需要沿轴向的一个本构关系就足够了．还发现,射流的第二主应力差的零阶近似总为0．与其他类型的动量方程做了比较．     

可压缩格子Boltzmann模型的启示性稳定理论

１引言格子Ｂｏｌｔｚｍａｎｎ方法（ＬＢＭ）是近几年发展起来的一种模拟复杂系统的新方法［１］［２］［３］这种方法已经在流体力学各领域得到应用．最近,许多研究工作集中于用ＬＢＭ模型计算可压缩流体流动．Ａｌｅｘａｎｄｅｒ和Ｃｈｅｎ等［４］提出了可以计算激波的等温模型,模型中的音速是可以选择的．Ｑｉａｎ和Ｏｒｓｚａｇ［５］分析了ＬＢＧＫ模型在可压缩区域内的非线性偏差,给出了激波结构的ＬＢＭ结果．Ｑｉａｎ和Ｏｒｓｚａｇ［６］也计算了弱可压缩的高Ｒｅ数问题,并用于计算Ｋｏｌ－ｍｏｇｏｒｏｖ流．Ａｎｃｏｎａ［…     

有缺失数据的META-MARKOV模型的局部计算

根据meta Markov模型的特征,本文提出了有缺失数据的meta Markov模型的局部计算方法．由于最小可压缩集与局部计算关系密切,本文给出了一种搜索包含预先给定的子集的最小可压缩集的算法．     

一类流固耦合系统强解的存在性问题

本文主要讨论一类多刚体与粘性系数依赖于密度的不可压缩流体耦合系统的强解存在性问题.首先,利用变量替换建立本文研究对象对应的非线性微分方程,然后,利用Garlerkin逼近方法获得线性化问题的光滑解,从而可以构造出原问题的逼近解.通过估计逼近解的一致有界性,最后证明了一类描述多刚体在不可压缩流体中运动的耦合系统强解的存在...     

一维具有阻尼和摩擦项的可压缩流体欧拉方程组当压力消失时黎曼解的极限

该文研究带有复合源项的一维可压缩流体欧拉方程组的黎曼问题,其中源项可以是摩擦项,也可以是阻尼项,也可以是阻尼和摩擦两者都具有.与齐次型不同,非齐次守恒律方程组的黎曼解是非自相似的.当绝热指数γ→1即压力消失时,讨论带有复合源项的一维可压缩流体欧拉方程组的黎曼解中集中现象和真空状态的形成,证明包含两条激波的黎曼解收敛于零压下的delta激波解,包含两条稀疏波的黎曼解收敛于零压下的两条接触间断解,其中连接两条接触间断解的中间状态是真空状态.     

Remarks on the solvability of transonic flow problems

The paper is devoted to the study of the viscosity method and upwinding in the transonic flow problems. We weaken the conditions from [6,7] under which we can obtain a nonviscous compressible transonic flow as a limit of viscous solutions, if the viscosity and heat conductivity tend to zero. Further, we give the justification of the density upwinding applied often in the calculation of transonic potential flows.     

Investigation of secondary flow on an infinite yawed cylinder in a compressible stream

In this paper a study of the secondary flow on an infinite yawed cylinder in a compressible stream is made at stagnation for unit Prandtl number and for a given Mach number. The secondary flow profiles are calculated for different edge inclination angles. The chordwise and spanwise velocity profiles given by Crabtree¹ are used here in the calculation. It is found that the secondary flow profiles are the same for complementary edge inclination angles and they are maximum for the edge inclination angle of 45°. A comparison with the incompressible flow profiles² is made. It is found that the magnitude of the secondary flow profiles in a compressible stream is less than that in an incompressible stream for the same edge inclination angle.     

Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.     

A curvilinear finite-volume method to solve compressible gas dynamics in semi-Lagrangian coordinates

We present a new finite-volume method to solve compressible gas dynamics in semi-Lagrangian coordinates on curvilinear grids. The approach relies on a weak formulation to compute the mesh velocity using an acoustic Riemann solver approximation. We prove this method to be both conservative and entropic.     

Coupling of compressible and incompressible flow regions using the multiple pressure variables approach

In many cases, multiphase flows are simulated on the basis of the incompressible Navier–Stokes equations. This assumption is valid as long as the density changes in the gas phase can be neglected. Yet, for certain technical applications such as fuel injection, this is no longer the case, and at least the gaseous phase has to be treated as a compressible fluid. In this paper, we consider the coupling of a compressible flow region to an incompressible one based on a splitting of the pressure into a thermodynamic and a hydrodynamic part. The compressible Euler equations are then connected to the Mach number zero limit equations in the other region. These limit equations can be solved analytically in one space dimension that allows to couple them to the solution of a half‐Riemann problem on the compressible side with the help of velocity and pressure jump conditions across the interface. At the interface location, the flux terms for the compressible flow solver are provided by the coupling algorithms. The coupling is demonstrated in a one‐dimensional framework by use of a discontinuous Galerkin scheme for compressible two‐phase flow with a sharp interface tracking via a ghost‐fluid type method. The coupling schemes are applied to two generic test cases. The computational results are compared with those obtained with the fully compressible two‐phase flow solver, where the Mach number zero limit is approached by a weakly compressible fluid. For all cases, we obtain a very good agreement between the coupling approaches and the fully compressible solver. Copyright © 2014 John Wiley & Sons, Ltd.     

Mathematical modelling of compressible viscous fluid flow in a male rotor‐housing gap of screw machines

This contribution is devoted to the mathematical modelling of a compressible viscous fluid flow through a 2‐D model of the male rotor‐housing gap in screw machines. Numerical solution of the nonlinear conservative system of the compressible Navier‐Stokes equations is obtained by means of the cell‐centred finite volume formulation of the explicit two‐step TVD MacCormack scheme proposed by Causon on a structured quadrilateral grid using the own developed numerical code. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global existence for slightly compressible hydrodynamic flow of liquid crystals in two dimensions

In two dimensions, we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions. As shown by Ding et al. (2013), when the parameter λ → ∞, the solutions to the compressible liquid crystal system approximate that of the incompressible one. Furthermore, Ding et al. (2013) proved that the regular incompressible limit solution is global in time with small enough initial data. In this paper, we show that the solution to the compressible liquid crystal flow also exists for all time, provided that λ is sufficiently large and the initial data are almost incompressible.     

CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix–vector multiplies with the sampling matrix. For compressible signals, the running time is just O(Nlog²N), where N is the length of the signal.     

A duality method for the compressible Reynolds equation. Application to simulation of read/write processes in magnetic storage devices

In this work the authors present a new numerical algorithm to approximate the solution of compressible Reynolds equation with additional first-order slip flow terms. This equation appears when modelling read/write processes in magnetic storage devices such as hard disks. The proposed numerical method is based on characteristics approximation for convection (dominating) terms and a duality method applied to a maximal monotone operator which represents the nonlinear diffusive term. Several test examples illustrate the good performance of the method.