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.     

Zero Mach number limit to compressible quantum magnetohydrodynamic equations with vanishing viscosity coefficients

The connection between the compressible viscous quantum magnetohydrodynamic model with low Mach number and the ideal incompressible magnetohydrodynamic equations is studied in a periodic domain. More precisely, for well‐prepared initial data, we prove the convergence of classical solutions of the compressible viscous quantum magnetohydrodynamic model to the classical solutions of the incompressible ideal magnetohydrodynamic equations with a convergence rate when the Mach number, viscosity coefficient, and magnetic diffusion coefficient simultaneously tend to zero.     

Low Mach number limit of viscous polytropic fluid flows

This paper studies the singular limit of the non-isentropic Navier-Stokes equations with zero thermal coefficient in a two-dimensional bounded domain as the Mach number goes to zero. A uniform existence result is obtained in a time interval independent of the Mach number, provided that the initial data satisfy the “bounded derivative conditions”, that is, the time derivatives up to order two are bounded initially, and Navier?s slip boundary condition is imposed.     

On the nonexistence of a global nontrivial subsonic solution in a 3D unbounded angular domain

In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by the potential equation. By establishing a fundamental a priori estimate on the solution of a second order linear elliptic equation in Ω with Neumann boundary conditions on Ω and Dirichlet boundary value at some point of Ω, we show that there is no global nontrivial subsonic flow with a low Mach number in such a domain Ω.     

Exterior problem for the two-dimensional compressible Euler equation

In this paper we show the existence of a solution, on any time intervals, in suitable Sobolev spaces for the 2D compressible Euler equation in the exterior domain, when the Mach number is sufficiently small. We shall extend results obtained in [8] in the case of an infinity velocity different from zero.

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Sunto In questo lavoro proviamo l'esistenza di una soluzione, su ogni intervallo temporale, in opportuni spazi di Sobolev per le equazioni di Eulero 2D comprimibili in un dominio esterno, quando il numero di Mach è sufficientemente piccolo. Estenderemo i risultati ottenuti in [8] al caso di velocità all'infinito diversa da zero.

     

Low Mach Number Limit for the Navier–Stokes System on Unbounded Domains Under Strong Stratification

We consider the low Mach number singular limit problem for the Navier–Stokes system describing the motion of a compressible fluid under strong stratification in an exterior domain. It is shown that the limit problem is represented by the so-called anelastic approximation. In particular, strong (pointwise) convergence of the acoustic components of the velocity is established by means of an abstract result of Tosio Kato.     

Control of the transition between regular and mach reflection of shock waves

A control problem was considered that makes it possible to switch the flow between stationary Mach and regular reflection of shock waves within the dual solution domain. The sensitivity of the flow was computed by solving adjoint equations. A control disturbance was sought by applying gradient optimization methods. According to the computational results, the transition from regular to Mach reflection can be executed by raising the temperature. The transition from Mach to regular reflection can be achieved by lowering the temperature at moderate Mach numbers and is impossible at large numbers. The reliability of the numerical results was confirmed by verifying them with the help of a posteriori analysis.     

The incompressible limit of the full Navier–Stokes–Fourier system on domains with rough boundaries

We study the incompressible limit of the full Navier–Stokes–Fourier system on condition that the boundary of the spatial domain oscillates with the amplitude and wave length proportional to the Mach number. Assuming the fluid satisfies the complete slip boundary conditions on the oscillating boundary, we identify the asymptotic limit, and, in particular, establish strong (pointwise) convergence of the velocities towards a solenoidal vector field.     

低Mach数翼型绕流数值模拟的低耗散预处理格式

低Mach数流动中,基于可压缩流动的数值模拟算法存在严重的刚性问题,预处理方法可以有效地解决这一问题,但其计算结果不稳定．基于原有的预处理Roe格式,引入可调节参数,得到一种新的低耗散格式．该格式可以减弱边界层以及极低速区域的过度耗散,使得整个流场计算稳定．低Mach数、低Reynolds数定常圆柱绕流和低Mach数、高Reynolds数翼型(NACA0012和S809)绕流3个验证算例表明,带可调节参数的低耗散预处理方法正确可靠,是低速流动数值模拟的有效方法．     

反射型激波风洞中激波与边界层的相互作用

本文研究了反射型激波风洞中由于非完全反射对激波与壁面边界层相互作用的影响,给出了在反射激波坐标系中计算边界层速度分布、温度分布和马赫数分布的计算方法.算例表明,在计及氮气的平衡真实气体效应的情形下,随着入射激波马赫数M_s的增大,边界层的最小马赫数从壁面处移到边界层内;随着喷管喉道面积的增大,边界层的最小马赫数、反射激波的分叉角α和分叉区后的射流速度均随之减小.计算结果与实验值相比是一致的.     

Low Mach number limit of global solutions to 3‐D compressible nematic liquid crystal flows with Dirichlet boundary condition

In this paper, we consider the uniform estimates of strong solutions in the Mach number ? and t ∈ [0,∞) for the compressible nematic liquid crystal flows in a 3‐D bounded domain , provided the initial data are small enough and the density is close to the constant state. Here, we consider the case that the velocity field satisfies the Dirichlet boundary condition. Based on the uniform estimates, we obtain the global convergence of the compressible nematic liquid crystal system to the incompressible nematic liquid crystals system as the Mach number tends to zero.     

Diffusive wave in the low Mach limit for non-viscous and heat-conductive gas

The low Mach number limit for one-dimensional non-isentropic compressible Navier–Stokes system without viscosity is investigated, where the density and temperature have different asymptotic states at far fields. It is proved that the solution of the system converges to a nonlinear diffusion wave globally in time as Mach number goes to zero. It is remarked that the velocity of diffusion wave is proportional with the variation of temperature. Furthermore, it is shown that the solution of compressible Navier–Stokes system also has the same phenomenon when Mach number is suitably small.     

基于Roe格式的可压与不可压流的统一计算方法

摘要：以Navier-Stokes方程为基础，基于有限体积的时间推进的预处理技术．提出了一个可以用来求解可压与不可压流场的统一的计算方法，原始变量选用压力、速度与温度，通过矩阵变换与重构，使得对流项系数矩阵在可压与小可压条件下都不会奇异．将可压与不可压流场的计算方法统一起来。采用Roe格式计算对流通量，采用中心差分格式计算扩散通量．算例表明，该方法可以进行高Mach数、中等Mach数、低Mach数及不可压流场的计算。由于采用了Roe格式，该方法还可以捕获不连续流场的间断面。     

An implicit finite volume method for the solution of 3D low Mach number viscous flows using a local preconditioning technique

This paper presents a cell-centered high order finite volume scheme for the solution of the three-dimensional (3D) Navier–Stokes equations with low Mach number. The system of non-linear equations is solved by means of a fully implicit pseudo-transient scheme. Each pseudo-time step is solved by a Newton-GMRes procedure. A local preconditioning technique is used to scale the speed of sound and to improve the system condition number for low Mach number and low cell Reynolds number. This preconditioning is applied to the AUSM+up flux vector splitting function. The method is tested on 2D and 3D low Mach number laminar flows.     

Shock Wave Structure in a Rarefied Polyatomic Gas Based on Extended Thermodynamics

A theory of the shock wave structure in a rarefied polyatomic gas is developed on the basis of the recent new approach to extended thermodynamics. We summarize the following points (i) and (ii) based on the previous study on this subject and also show the new point (iii): (i) The theory can explain the change of types of the shock wave structure observed experimentally with the increase of the Mach number from unity; the nearly symmetric shock wave structure (Type A, small Mach number), the asymmetric structure (Type B, moderate Mach number), and the structure composed of thin and thick layers (Type C, large Mach number). (ii) The theoretical prediction of the mass density profile agrees well with experimental data. (iii) The points (i) and (ii) are not strongly affected by the details of the temperature dependence of the bulk viscosity.     

Incompressible limits of the Navier-Stokes equations for all time

We study the asymptotic behaviors of the regular solutions to the compressible Navier-Stokes equations for “well-prepared” initial data for all time as the Mach number tends to zero, by deriving a differential inequality with certain decay property. The estimates obtained in this paper are uniform both in time and Mach number.     

The compressible Gortler problem in two-dimensional boundary layers

In this paper the authors investigate the growth rates of Görtlervortices in a compressible flow in the inviscid limit of largeGörtler number. Numerical solutions are obtained for O(1)wavenumbers. The further limits of (i) large Mach number and(ii) large wavenumber with O(1) Mach number are considered.It is shown that two different types of disturbance mode canappear in this problem. The first is a wall layer mode, so namedas it has its eigenfunctions trapped in a thin layer near thewall. The other mode investigated is confined to a thin layeraway from the wall and termed a trapped-layer mode for largewavenumbers and an adjustment-layer mode for large Mach numbers,since then this mode has its eigenfunctions concentrated inthe temperature adjustment layer. It is possible to investigatethe near crossing of the modes which occurs in each of the limitsmentioned. The inviscid limit does not predict a fastest growingmode, but does enable a most dangerous mode to be identifiedfor O(1) Mach number. For hypersonic flow the most dangerousmode depends on the size of the Görtler number.     

Rotating compressible fluids under strong stratification

We consider the Navier–Stokes system written in the rotational frame describing the motion of a compressible viscous fluid under strong stratification. The asymptotic limit for low Mach and Rossby numbers and large Reynolds number is studied on condition that the Froude number characterizing the degree of stratification is proportional to the Mach number. We show that, at least for the well prepared data, the limit system is the same as for the problem without stratification—a variant of the incompressible planar Euler system.     

Zero Mach number limit of the compressible Hall-magnetohydrodynamic equations

In this paper, we study the low Mach number limit of the compressible Hall-magnetohydrodynamic equations. It is justified rigorously that, for the well-prepared initial data, the classical solutions of the compressible Hall-magnetohydrodynamic equations converge to that of the incompressible Hall-magnetohydrodynamic equations as the Mach number tends to zero.     

Viscous fluid flow at all speeds: analysis and numerical simulation

In [43] a finite volume method for reliable simulations of inviscid fluid flows at high as well as low Mach numbers based on a preconditioning technique proposed by Guillard and Viozat [14] is presented. In this paper we describe an extension of the numerical scheme for computing solutions of the Euler and Navier-Stokes equations. At first we show the high resolution properties, accuracy and robustness of the finite volume scheme in the context of a wide range of complicated transonic and supersonic test cases whereby both inviscid and viscous flow fields are considered. Thereafter, the validity of the method in the low Mach number regime is proven by means of an asymptotic analysis as well as numerical simulations. Whereas in [43] the asymptotic analysis of the scheme is focused on the behaviour of the continuous and discrete pressure distribution for inviscid low speed simulations we prove both the physical sensible discrete pressure field for viscous low Mach number flows and the divergence free condition of the discrete velocity field in the limit of a vanishing Mach number with respect to the simulation of inviscid fluid flow.