THE INVISCID AND NON-RESISTIVE LIMIT IN THE CAUCHY PROBLEM FOR 3-D NONHOMOGENEOUS INCOMPRESSIBLE MAGNETO-HYDRODYNAMICS

In this paper,the inviscid and non-resistive limit is justified for the local-in-time solutions to the equations of nonhomogeneous incompressible magneto-hydrodynamics （MHD）in R3.We prove that as the viscosity and resistivity go to zero,the solution of the Cauchy problem for the nonhomogeneous incompressible MHD system converges to the solution of the ideal MHD system.The convergence rate is also obtained simultaneously.

AN INVISCID MODEL FOR THE BASE PRESSURE OF TRANSONIC TURBINE CASCADE

An inviscid base pressure model for transonic turbine blade has been presented. It has been shown that for a given back pressure the base pressure at the trailing edge, and the profile loss of a turbine blade are fixed according to the model and the base pressure can be calculated with the help of an inviscid numerical scheme. A parameteric study on the model shows that a blade profile with positive curvature downstream of the throat is advantageous for generating less loss, whilst the worst situation is when the exit flow reaches the sonic condition.

THE COMBINED INVISCID AND NON-RESISTIVE LIMIT FOR THE NONHOMOGENEOUS INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH NAVIER BOUNDARY CONDITIONS

In this paper, we establish the existence of the global weak solutions for the non-homogeneous incompressible magnetohydrodynamic equations with Navier boundary condi-tions for the velocity field and the magnetic field in a bounded domain Ω R^3. Furthermore,we prove that as the viscosity and resistivity coefficients go to zero simultaneously, these weaksolutions converge to the strong one of the ideal nonhomogeneous incompressible magneto-hydrodynamic equations in energy space.

INVISCID INCOMPRESSIBLE AND COMPRESSIBLE FLOW EQUATIONS UNDER SPACE-TIME TRANSFORMATION

The equations governing incompressible and compressible inviscid flows and written in the physical frame ( t,x,y,z ) are known to be linearly well posed and exhibit elliptic or hyperbolic nature. The linear well posedness is considered here for these equations under a space time transformation ( t,x,y,z)→(τ,ξ,η,ζ ), where the pseudo time τ and the new space coordinate ( ξ,η,ζ ) all depend on ( t,x,y,z ). Such a transformation could be useful for uniformly treating problems in which the flow is fast unsteady somewhere and slow unsteady or steady elsewhere. It is found that the transformation may alter the ellipticity, the hyperbolicty, and even the well posedness of the original equations. In one dimension, the transformed incompressible flow equations become weakly hyperbolic and the compressible ones could degenerate to elliptical equations. In high dimensions there are conditions such that the transformed equations become ill posed.

Oscillations of an Inviscid Encapsulated Drop

The problem relating to the small-amplitude free capillary oscillations of an encapsulated spherical drop is solved theoretically in the framework of asymptotic methods.Liquids are supposed to be inviscid and immiscible.The formulas derived are presented for different parameters of the inner and outer liquids,including densities,thickness of the outer liquid layer,and the surface and interfacial tension coefficients.The frequencies of oscillation of the encapsulated drop are studied in relation to several“modes”which can effectively be determined in experiments by photo and video analysis.The results are presented in terms of oscillation frequencies reported as a function of the mode number,the spherical layer thickness and the relation between the(surface and interfacial)tension coefficients.It is revealed that the influence of the liquids’parameters(and related variations)on the drop oscillation changes dramatically depending on whether oscillations are“in-phase”or“out-of-phase”.Frequencies for“in-phase”type oscillations can be correlated with linear functions of the shell thickness and the relative values of interfacial tension coefficient whereas the analogous dependencies for the“out-of-phase”type oscillation are essentially non-linear.

Inviscid Limits of the Complex Generalized Ginzburg-Landau Equations

1 Introduction Derivative Ginzburg-Landau equation appeared in many physical problem. It was derived for instability waves in hydrodynamic such as the nonlinear growth of Rayleigh-Benard convective rolls, the appearance of Taylor Vortices in the couette flow between counter-rotating cylinders.

Numerical Method for Non-Linear Conservation Laws: Inviscid Burgers Equation

This paper deals with the Burgers equation which is the most common model used in the nonlinear conservation laws. Here the theoretical aspect of conservation law is discussed by using inviscid Burgers equation. At first, we introduce the general non-linear conservation law as a partial differential equation and its solution procedure by the method of characteristic. Next, we present the weak solution of the problem with entropy condition. Taking into account shock wave and rarefaction wave, the Riemann problem has also been discussed. Finally, the finite volume method is considered to approximate the numerical solution of the inviscid Burgers equation with continuous and discontinuous initial data. An illustration of the problem is provided by some examples. Moreover, the Godunov method provides a good approximation for the problem.

On the inviscid limit of the compressible Navier-Stokes equations near Onsager's regularity in bounded domains

The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded domain.We establish a Kato-type criterion for the validity of the inviscid limit for the weak solutions of the Navier-Stokes equations in a function space with the regularity index close to Onsager’s critical threshold.In particular,we prove that under such a regularity assumption,if the viscous energy dissipation rate vanishes in a boundary layer of thickness in the order of the viscosity,then the weak solutions of the Navier-Stokes equations converge to a weak admissible solution of the Euler equations.Our approach is based on the commutator estimates and a subtle foliation technique near the boundary of the domain.

Numerical and experimental investigation of quantitative relationship between secondary flow intensity and inviscid blade force in axial compressors

The secondary flow attracts wide concerns in the aeroengine compressors since it has become one of the major loss sources in modern high-performance compressors.But the research about the quantitative relationship between secondary flow and inviscid blade force needs to be more detailed.In this paper,a database of 889 three-dimensional linear cascades was built.An indicator,called Secondary Flow Intensity(SFI),was used to express the loss caused by secondary flow.The quantitative relationship between the SFI and inviscid blade force deterioration was researched.Blade oil flow and Computation Fluid Dynamics(CFD)results of some cascades were also used to cross-validate.Results suggested that all numerical cascade cases can be divided into 3 clusters by the SFI,which are called Clusters A,B and C in the order of the increasing SFI indicator.The corner stall,known as the strong corner separation,only happens when the SFI is high.Both calculations and oil flow experiments show that the SFI would stay at a low level if the vortex core at the endwall surface does not appear.The strong interaction of Kutta condition and endwall cross-flow is considered the dominant mechanism of higher secondary flow losses,rather than the secondary flow penetration depth on the suction surface.In conclusion,the inviscid blade force spanwise deterioration is strongly related to the SFI.The correlation of the SFI and spanwise inviscid blade force deterioration is given in this paper.The correlation could provide a quantitative reference for estimating secondary flow losses in the design.

含新型间断探测器的混合WCNS格式在间断无粘可压流的应用

为了让高精度数值格式在含间断和小尺度涡等复杂结构的超声速无粘可压缩流动情况下,仍能鲁棒地捕捉激波并快速得到流场高保真的模拟结果,研究了以子模板导数组合为基础的光滑度量算法,构造了精度与鲁棒性兼顾的新型间断探测器,使间断识别对小尺度涡也具有高分辨率;研究了混合加权紧致非线性格式(weighted compact nonlinear scheme, WCNS)方法,对流场中的光滑与间断区域分别使用线性与非线性加权格式求解,从而克服单一非线性格式在光滑区分辨率难以达到设计精度的问题。数值实验表明,使用新型间断探测器的混合WCNS格式对一维、二维Euler方程模拟结果良好,并且相比于在全流场使用局部特征分解的原始WCNS方法有计算效率的提高。

On the Inviscid Limit of the 3D Navier–Stokes Equations with Generalized Navier-Slip Boundary Conditions

In this paper,we investigate the vanishing viscosity limit problem for the 3-dimensional(3D)incompressible Navier-Stokes equations in a general bounded smooth domain of R^3 with the generalized Navier-slip boundary conditions u^ε·n=0,n×(ω^ε)=[Bu^ε]τon∂Ω.Some uniform estimates on rates of convergence in C([0,T],L2(Ω))and C([0,T],H^1(Ω))of the solutions to the corresponding solutions of the ideal Euler equations with the standard slip boundary condition are obtained.

Global Well-Posedness of the Inviscid Heat-Conductive Resistive Compressible MHD in a Strip Domain

This paper concerns the inviscid,heat conductive and resistive compressible MHD system in a horizontally periodic flat strip domain.The global well-posedness of the problem around an equilibrium with the positive constant density and temperature and a uniform non-horizontal magnetic field is established,and the solution decays to the equilibrium almost exponentially.Our result reveals the strong stabilizing effect of the transversal magnetic field and resistivity as the global well-posedness of compressible inviscid heat-conductive flows in multi-D is unknown.

The Ghost Cell Method and its Applications for Inviscid Compressible Flow on Adaptive Tree Cartesian Grids

In this paper,an immersed boundary algorithm is developed by combining the ghost cell method with adaptive tree Cartesian grid method.Furthermore,the proposed method is successfully used to evaluate various inviscid compressible flow with immersed boundary.The extension to three dimensional cases is also achieved.Numerical examples demonstrate the proposed method is effective.

STUDY OF INTERACTION BETWEEN VORTICES AND A FREE SURFACE* PART I:INVISCID FLOW

Vortex method is developed to study the interaction between free surface and vortex systems. The. vortex systems, considered here, include vortex pairs, an infinite vortex sheet, and a trailing-edge vortex sheet. The computational results reproduces qualitatively the deformation of free surface under the action of vortices, which is observed in experiments.

Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

In this paper,we study the Cauchy problem for the Benjamin-Ono-Burgers equation ∂_(t)u−ϵ∂^(2)/_(x)u+H∂^(2)_(x)u+uu_(x)=0,where H denotes the Hilbert transform operator.We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space H~σ(R)(σ■0),which is a subspace of L2(ℝ).It is worth noting that the low-frequency part of H~σ(R)is scaling critical,and thus the small data is necessary.The high-frequency part of H~σ(R)is equal to the Sobolev space Hσ(ℝ)(σ■0)and reduces to L2(ℝ).Furthermore,we also obtain its inviscid limit behavior in H~σ(R)(σ■0).

A sharp-interface immersed boundary method for simulating high-speed compressible inviscid flows

This paper presents a robust sharp-interface immersed boundary method for simulating inviscid compressible flows over stationary and moving bodies.The flow field is governed by Euler equations,which are solved by using the open source library OpenFOAM.Discontinuities such as those introduced by shock waves are captured by using Kurganov and Tadmor divergence scheme.Wall-slip boundary conditions are enforced at the boundary of body through reconstructing flow variables at some ghost points.Their values are obtained indirectly by interpolating from their mirror points.A bilinear interpolation is employed to determine the variables at the mirror points from boundary conditions and flow conditions around the boundary.To validate the efficiency and accuracy of this method for simulation of high-speed inviscid compressible flows,four cases have been simulated as follows:supersonic flow over a 15°angle wedge,transonic flow past a stationary airfoil,a piston moving with supersonic velocity in a shock tube and a rigid circular cylinder lift-off from a flat surface triggered by a shock wave.Compared to the exact analytical solutions or the results in literature,good agreement can be achieved.

The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space

We prove that in dimensions three and higher the Landau-Lifshitz-Gilbert equation with small initial data in the critical Besov space is globally well-posed in a uniform way with respect to the Gilbert damping parameter. Then we show that the global solution converges to that of the Schr¨odinger maps in the natural space as the Gilbert damping term vanishes. The proof is based on some studies on the derivative Ginzburg-Landau equations.

Flow Patterns and Thermal Drag in a One-Dimen-sional Inviscid Channel with Heating or Cooling

In this paper investigations on the flow patterns and the thermal drag phenomenon in one -dimensional inviscid channel flow with heating or cooling are described and discussed:expressions of flow rate ratio and thermal drag coefficient for different flow patterns and its physical mechanism are presented.