THE LOW MACH NUMBER LIMIT FOR ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A REVISED MAXWELL'S LAW

We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error system, it is proven that the solutions of the isentropic Navier-Stokes equations with a revised Maxwell's law converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.

A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction.In this work,a novel scheme based on a specific level set ghost fluid method and an implicit-explicit(IMEX)flux splitting is proposed to overcome this timestep restriction.A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface.In this part of the domain,the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases.It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method.Applica-tions to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.

A NOVEL SLIGHTLY COMPRESSIBLE MODEL FOR LOW MACH NUMBER PERFECT GAS FLOW CALCULATION

By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved very efficient, for it is kept within thep-v frame but does not have to satisfy the time consuming divergence-free condition in order to get the incompressible Navier-Stokes equation solution. Writing the equations in the form of conservation laws, we have derived the characteristic systems which are necessary for numerical calculations. A cell-centered finite-volume method with flux difference upwind-biased schemes is used for the equation solutions and a new Exact Newton Relaxation (ENR) implicit method is developed. Various computed results are presented to validate the present model. Laminar flow solutions over a circular cylinder with wake developing and vortex shedding are presented. Results for inviscid flow over a sphere are compared in excellent agreement with the exact analytic incompressible solution. Three-dimensional viscous flow solutions over sphere and prolate spheroid are also calculated and compared well with experiments and other incompressible solutions. Finally, good convergent performances are shown for sphere viscous flows.

LOW MACH NUMBER LIMIT ON EXTERIOR DOMAINS

This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.

LOW MACH NUMBER LIMIT OF A COMPRESSIBLE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS MODEL

In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals.

A Conservative Pressure-Correction Method on Collocated Grid for Low Mach Number Flows

A novel extension to SMAC scheme is proposed for variable density flows under low Mach number approximation. The algorithm is based on a predictor—corrector time integration scheme that employs a projection method for the momentum equation. A constant-coefficient Poisson equation is solved for the pressure following both the predictor and corrector steps to satisfy the continuity equation at each time step. The proposed algorithm has second order centrally differenced convective fluxes with upwinding based on Cell Peclet number while diffusive flux are viscous fourth order accurate. Spatial discretization is performed on a collocated grid system that offers computational simplicity and straight forward extension to curvilinear coordinate systems. The algorithm is kinetic energy preserving. Further in this paper robustness and accuracy are demonstrated by performing test on channel flow with non-Boussinesq condition on different temperature ratios.

The low Mach number limit of non-isentropic magnetohydrodynamic equations with large temperature variations in bounded domains

This paper verifies the low Mach number limit of the non-isentropic compressible magnetohydrodynamic(MHD)equations with or without the magnetic diffusion in a three-dimensional bounded domain when the temperature variation is large but finite.The uniform estimates of strong solutions are established in a short time interval independent of the Mach number,provided that the slip boundary condition for the velocity and the Neumann boundary condition for the temperature are imposed and the initial data is well-prepared.

Airfoil Aeroelastic Flutter Analysis Based on Modified Leishman-Beddoes Model at Low Mach Number

Based on modified Leishman-Beddoes （L-B） state space model at low Mach number （lower than 0.3）, the airfoil aeroelastic system is presented in this paper. The main modifications for L-B model include a new dynamic stall criterion and revisions of normal force and pitching moment coefficient. The bifurcation diagrams, the limit cycle oscillation （LCO） phase plane plots and the time domain response figures are applied to investigating the stall flutter bifurcation behavior of airfoil aeroelastic systems with symmetry or asymmetry. It is shown that the symmetric periodical oscillation happens after subcritical bifurcation caused by dynamic stall, and the asymmetric periodical oscillation, which is caused by the interaction of dynamic stall and static divergence, only happens in the airfoil aeroelastic system with asymmetry. Validations of the modified L-B model and the airfoil aeroelastic system are presented with the experimental airload data of NACA0012 and OA207 and experimental stall flutter data of NACA0012 respectively. Results demonstrate that the airfoil aeroelastic system presented in this paper is effective and accurate, which can be applied to the investigation of airfoil stall flutter at low Mach number.

All Speed Scheme for the Low Mach Number Limit of the Isentropic Euler Equations

An all speed scheme for the Isentropic Euler equations is presented in thispaper. When the Mach number tends to zero, the compressible Euler equations converge to their incompressible counterpart, in which the density becomes a constant. Increasing approximation errors and severe stability constraints are the main difficultyin the low Mach regime. The key idea of our all speed scheme is the special semiimplicit time discretization, in which the low Mach number stiff term is divided intotwo parts, one being treated explicitly and the other one implicitly. Moreover, the fluxof the density equation is also treated implicitly and an elliptic type equation is derivedto obtain the density. In this way, the correct limit can be captured without requesting the mesh size and time step to be smaller than the Mach number. Compared withprevious semi-implicit methods [11,13,29], firstly, nonphysical oscillations can be suppressed by choosing proper parameter, besides, only a linear elliptic equation needs tobe solved implicitly which reduces much computational cost. We develop this semiimplicit time discretization in the framework of a first order Local Lax-Friedrichs (orRusanov) scheme and numerical tests are displayed to demonstrate its performances.

SPECTRAL METHOD FOR FLUID FLOW WITH LOW MACH NUMBER

The fluid flow with low Mach numberm is governed by the following differential eqnations:

A simple lattice Boltzmann scheme for low Mach number reactive flows

For simulating low Mach number reactive flows, a simple and coupled lattice Boltzmann (CLB) scheme is proposed, by which the fluid density can bear significant changes. Different from the existing hybrid lattice Boltzmann (HLB) scheme and non-coupled lattice Boltzmann (NCLB) scheme, this scheme is strictly lattice Boltzmann style and the fluid density couples directly with the temperature. Because it has got rid of the constraint of traditional thought in lattice Boltzmann scheme,on the basis of the equality among the particle speed c, the time step △t and the lattice grid spacing △x held, both c and △t can be adjusted in this scheme according to a "characteristic temperature" instead of the local temperature. The whole algorithm becomes more stable and efficient besides inheriting the intrinsically outstanding strong points of conventional lattice Boltz-mann scheme. In this scheme, we also take into account different molecular weights of species, so it is more suitable for simulating actual low Mach number reactive flows than previous work. In this paper, we simulated a so-called "counter-flow" premixed propane-air flame, and the results got by our scheme are much better than that obtained by NCLB. And the more important thing is that the exploration in this work has offered a kind of brand-new train of thought for building other novel lattice Boltzmann scheme in the future.

圆柱及切割圆柱低Mach数绕流气动声辐射

以柱体绕流声辐射为研究对象,探讨低Mach数流动气动声定量预测方法。首先,理论分析Lighthill声类比理论与基于流体动力学压力对时间求导的扰动分离模型之间内在联系。其次,利用计算流体动力学对圆柱及其尾部切割后的亚临界流态绕流进行二维数值求解,分析两种湍流模型的流场计算效果。最后,分别使用声类比理论FW-H方程及扰动分离模型进行柱体绕流气动声辐射定量预测,分析声指向性及频谱特性。数值结果表明声类比理论与扰动分离模型预测的声辐射频谱相似,但前者的幅值略高;圆柱尾部切割使尾流脉动增强,导致声辐射变大。

三维可压缩Boltzmann模型及其在低Mach数湍流中的应用（英文）

改进了有限差分格子Boltzmann方法(FDLBM),以直接数值模拟气动噪声.基于LB求解器特性,采用动力学方程中的恒定对流速度以实施高阶迎风差分,提高了声波和湍流的分辨率.通过建立一个新的三维粒子模型,计算得到了任意比热容的三维可压缩Navier-Stokes系统.此外,利用Bhatnagar-Gross-Krook(BGK)碰撞算子,通过引入热流量修正,实现了Prandtl数的可变性.在激波管内弱声波以及伴随有温度梯度的Taylor-Couette层流的验证计算中,提出的新方法结果良好.此外也对NACA0012翼型绕流进行了三维模拟.其中,Reynolds数、Mach数和攻角分别取2×105,8.75×10-2以及9°.计算发现,在机翼前缘附近的分离气流位置,以及表面压力波动强度的Mach数依赖性方面,数值计算结果与实验结果相吻合.

Towards an Accurate and Robust Roe-Type Scheme for All Mach Number Flows

We propose an accurate and robust Roe-type scheme applied to the compressible Euler system at all Mach numbers.To study the occurrence of unstable modes during the shock wave computation,a shock instability analysis of several Roe-type schemes is carried out.This analysis approach allows to propose a simple and effective modification to eliminate shock instability of the Roe method for hypersonic flows.A desirable feature of this modification is that it does not resort to any additional numerical dissipation on linear degenerate waves to suppress the shock instability.With an all Mach correction strategy,the modified Roe-type scheme is further extended to solve flow problems at all Mach numbers.Numerical results that are obtained for various test cases indicate that the new scheme has a good performance in terms of accuracy and robustness.

水平分层低马赫数运动介质中的声传播

针对海流对水声传播的影响,基于高斯波束追踪方法,利用高频近似的低马赫数亥姆霍兹方程,建立了三维低马赫数运动介质下的声传播模型,并将该模型应用于浅海与深海水平分层介质下的声传播问题。仿真结果表明,海流能定性定量地改变声传播模式。浅海环境下,声速梯度大于流速梯度,导致顺逆流声线反转点的差别随着距离增加而增大;此外声线到达结构也会发生较大改变。深海环境下,流速梯度大于声速梯度,顺流方向表面声道消失,使得表层顺逆流传播损失相差10 dB以上,同时水平分层环境中也会产生三维声传播效应。因此在流速梯度与声速梯度相当甚至更大时,海流对声传播的影响不能被忽略。

高速列车受电弓的低马赫数过渡式空腔射流降噪研究

受电弓及其空腔部位是高速列车主要的气动噪声源,降低这种噪声尤为重要。在以往的高速列车气动噪声研究中,对受电弓空腔部位的关注较少。针对高速列车受电弓及其空腔气动降噪问题,文中采用数值计算方法,研究简化的高速列车模型在350 km·h^(-1)下,受电弓空腔前缘射流降噪处理方式的流场特性和噪声传播规律。结果表明,在纯空腔前缘施加射流可以显著降低空腔内和受电弓附近的非定常流动,当射流速度为27 m·s^(-1)时,空腔后壁声源在空腔顶部和侧部辐射噪声的声压级降低最大值为5 dB,受电弓侧面监测点的噪声显著降低。文中研究为低马赫数下的过渡式空腔射流降噪研究提供了参考。

Extension of the pressure correction method to zero-Mach number compressible flows

In the present paper,the classical pressure correction method was extended into low Mach number compressible flow regime by integrating equation of state into SIMPLE algorithm.The self-developed code based on this algorithm was applied to predicting the lid-driven cavity flow and shock tube prob-lems,and the results showed good agreement with benchmark solutions and the Mach number can reach the magnitude of as low as 10-5.The attenuation of sound waves in viscous medium was then simulated.The results agree well with the analytical solutions given by theoretical acoustics.This demonstrated that the present method could also be implemented in acoustics field simulation,which is crucial for thermoacoustic simulation.

低马赫数射流噪声的数值计算研究

针对抗性消声器中扩张结构和尾管引起的射流噪声问题,建立了低马赫数射流噪声有限元分析模型。基于双方程k-ε紊流模型理论对射流速度场进行了计算,发现喷射流的势核周围形成一段湍化程度极高的气流。采用Lighthill-Curle声学理论预测了射流噪声,并通过试验对比验证了模型和数值计算方法的正确性。研究表明,喷射噪声主要集中在势核周围,说明势核是引起射流噪声的主要原因。通过对指向性的研究表明,低马赫数射流最大噪声主要分布范围为15°~60°。

声波衰减的数值模拟

为了采用计算流体力学方法对热声制冷机进行数值模拟,以突破热声热机现有计算方法的限制,基于压力修正算法的基本思想开发了用于模拟非稳态小马赫数可压缩流动的数值程序,并将其应用于声波衰减的数值模拟.对一维及二维声波衰减过程的模拟显示,数值计算的结果与声学理论的预测符合良好,说明了方法的正确性.

低马赫数流动数值模拟方法的研究

在文献[1,2]提出的一种低马赫数流动数值模拟新方法的基础上,本文作者进一步优化了算法,确定了该方法适用的马赫数范围,讨论了参数σ对计算的影响。大量的定常/非定常、低雷诺数/高雷诺数流动的计算结果表明这种方法具有计算精度高。