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 fixe...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.展开更多
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 r...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.展开更多
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 fiel...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.展开更多
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 posed...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.展开更多
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 bet...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.展开更多
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 immiscib...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.展开更多
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 appearan...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.展开更多
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 fi...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.展开更多
A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced ...A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain.展开更多
Self-propulsion of a deformable ellipse immersed in an unbounded inviscid fluid is discussed in order to explore the effect of the deformation and controlled rotation of the body coupled with the shift of its internal...Self-propulsion of a deformable ellipse immersed in an unbounded inviscid fluid is discussed in order to explore the effect of the deformation and controlled rotation of the body coupled with the shift of its internal mass on the self-motion.The ellipse is capable of symmetric deformation along the two orthogonal axes and endowed with some self-regulation ability via the shift and rotation of its internal mass.From the model,the appropriate velocity potential induced by the motion of the ellipse with the deformation in an otherwise undisturbed fluid is derived,and then the equations of motion are obtained by means of integrals of the unsteady fluid pressure.The equations are utilized to explore self-translational behaviors of the ellipse through the cyclic shift of its internal mass and deformation coupled with its own controllable rotation.Analysis and numerical results show that the ellipse can break the kinematic time-reversal symmetry by properly adjusting its own rotation to coordinate with the deformation and the cyclic shift of the inner mass to meet a forward criterion,and push itself to move persistently forward without a regression at zero system momentum,exhibiting some basic serpentine movements according as the ellipse performs complete revolutions or oscillates between two extreme yaw angles during its self-motion.展开更多
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 co...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.展开更多
We prove the local in time existence and a blow up criterion of solution in the Holder spaces for the inviscid Boussinesq system in RN,N ≥ 2, under the assumptions that the initial values θo,uo ∈ Cr, with 1 〈 r ≠ 2.
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 cons...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.展开更多
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 usin...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.展开更多
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 c...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.展开更多
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 ...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.展开更多
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 in...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.展开更多
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...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).展开更多
In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a ...In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a single shock satisfying the entropy condition, then there exist solutions to the viscous conservation laws which converge to the inviscid solution away from the shock discontinuity and the boundary at a rate of ε1 as the viscosity ε tends to zero.展开更多
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 therma...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.展开更多
文摘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.
基金partly supported by NSFC(1080111110971171)+1 种基金the Natural Science Foundation of Fujian Province of China(2010J05011)the Fundamental Research Funds for the Central Universities(2010121006)
文摘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.
文摘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.
基金National Natural Science F oundation of China(No.10 0 2 5 2 10 )
文摘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.
基金the National Science and Technology Major Project,China(Nos.2017-I-0005-0006&2019-II-0020-0041).
文摘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.
基金supported by the Russian Science Foundation(Project 19-19-00598“Hydrodynamics and energetics of drops and droplet jets:formation,motion,break-up,interaction with the contact surface”).
文摘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.
文摘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.
文摘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.
文摘A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain.
基金supported by the National Natural Science Foundation of China(Grant No.11672182).
文摘Self-propulsion of a deformable ellipse immersed in an unbounded inviscid fluid is discussed in order to explore the effect of the deformation and controlled rotation of the body coupled with the shift of its internal mass on the self-motion.The ellipse is capable of symmetric deformation along the two orthogonal axes and endowed with some self-regulation ability via the shift and rotation of its internal mass.From the model,the appropriate velocity potential induced by the motion of the ellipse with the deformation in an otherwise undisturbed fluid is derived,and then the equations of motion are obtained by means of integrals of the unsteady fluid pressure.The equations are utilized to explore self-translational behaviors of the ellipse through the cyclic shift of its internal mass and deformation coupled with its own controllable rotation.Analysis and numerical results show that the ellipse can break the kinematic time-reversal symmetry by properly adjusting its own rotation to coordinate with the deformation and the cyclic shift of the inner mass to meet a forward criterion,and push itself to move persistently forward without a regression at zero system momentum,exhibiting some basic serpentine movements according as the ellipse performs complete revolutions or oscillates between two extreme yaw angles during its self-motion.
基金This research is supported in part by NSFC 10971174,and Zheng Ge Ru Foundation,and Hong Kong RGC Earmarked Research Grants CUHK-4041/11P,CUHK-4042/08P,a Focus Area Grant from the Chinese University of Hong Kong,and a grant from Croucher Foundation.
文摘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.
文摘We prove the local in time existence and a blow up criterion of solution in the Holder spaces for the inviscid Boussinesq system in RN,N ≥ 2, under the assumptions that the initial values θo,uo ∈ Cr, with 1 〈 r ≠ 2.
基金the National Natural Science Foundation of China(11771360,12171401)the Natural Science Foundation of Fujian Province of China(2019J02003).Z.P.Xin was supported by Zheng Ge Ru Foundation,Hong Kong RGC Earmarked Research Grants CUHK14305315,CUHK14302819,CUHK14300917,CUHK14302917,CUHK14300819,and Basic and Applied Basic Research Foundation of Guangdong Province(2020B1515310002).
文摘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.
基金Natural Science Foundation of Jiangsu Province(Grant No.BK20191271)the National Numerical Wind Tunnel Project(Grant No.NNW2019ZT2-B28).
文摘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.
基金supported partly by National Science Foundation of China(10728026)National Basic Research Program of China(2007CB714600).
文摘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.
文摘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.
基金supported by National Science Foundation of USA(Grant No.DMS-1907584)supported by the Fundamental Research Funds for the Central Universities(Grant No.JBK 2202045)+1 种基金supported by National Science Foundation of USA(Grant Nos.DMS-1907519 and DMS-2219384)supported by National Natural Science Foundation of China(Grant No.12271122)。
文摘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.
基金supported by National Natural Science Foundation of China(Grant No.12001236)supported by National Natural Science Foundation of China(Grant No.11731014)supported by National Natural Science Foundation of China(Grant No.11971166)。
文摘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).
基金Acknowledgments The author is supported by Tianyuan Foundation （No. 11026093） and the National Natural Science Foundation of China （Nos. 11101162, 11071086）.
文摘In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a single shock satisfying the entropy condition, then there exist solutions to the viscous conservation laws which converge to the inviscid solution away from the shock discontinuity and the boundary at a rate of ε1 as the viscosity ε tends to zero.
文摘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.
