The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the ＂rigid body＂ assumption. On the basis of the simplified equations of motion, the longitudin...The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the ＂rigid body＂ assumption. On the basis of the simplified equations of motion, the longitudinal dynamic flight stability of four insects （hoverfly, cranefly, dronefly and hawkmoth） in hovering flight is studied （the mass of the insects ranging from 11 to 1,648 mg and wingbeat frequency from 26 to 157Hz）. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. The validity of the ＂rigid body＂ assumption is tested and how differences in size and wing kinematics influence the applicability of the ＂rigid body＂ assumption is investigated. The primary findings are： （1） For insects considered in the present study and those with relatively high wingbeat frequency （hoverfly, drone fly and bumblebee）, the ＂rigid body＂ assumption is reasonable, and for those with relatively low wingbeat frequency （cranefly and howkmoth）, the applicability of the ＂rigid body＂ assumption is questionable. （2） The same three natural modes of motion as those reported recently for a bumblebee are identified, i.e., one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. （3） Approximate analytical expressions of the eigenvalues, which give physical insight into the genesis of the natural modes of motion, are derived. The expressions identify the speed derivative Mu （pitching moment produced by unit horizontal speed） as the primary source of the unstable oscillatory mode and the stable fast subsidence mode and Zw （vertical force produced by unit vertical speed） as the primary source of the stable slow subsidence mode.展开更多
The proper orthogonal decomposition(POD)and the singular value decomposition(SVD) are used to study the finite difference scheme(FDS)for the nonstationary Navier-Stokes equations. Ensembles of data are compiled from t...The proper orthogonal decomposition(POD)and the singular value decomposition(SVD) are used to study the finite difference scheme(FDS)for the nonstationary Navier-Stokes equations. Ensembles of data are compiled from the transient solutions computed from the discrete equation system derived from the FDS for the nonstationary Navier-Stokes equations.The optimal orthogonal bases are reconstructed by the elements of the ensemble with POD and SVD.Combining the above procedures with a Galerkin projection approach yields a new optimizing FDS model with lower dimensions and a high accuracy for the nonstationary Navier-Stokes equations.The errors between POD approximate solutions and FDS solutions are analyzed.It is shown by considering the results obtained for numerical simulations of cavity flows that the error between POD approximate solution and FDS solution is consistent with theoretical results.Moreover,it is also shown that this validates the feasibility and efficiency of POD method.展开更多
A method is presented to calculate the resistance of a high-speed displacement ship taking the effect of sinkage and trim and viscosity of fluid into account.A free surface flow field is evaluated by solving Reynolds ...A method is presented to calculate the resistance of a high-speed displacement ship taking the effect of sinkage and trim and viscosity of fluid into account.A free surface flow field is evaluated by solving Reynolds averaged Navier-Stokes(RANS) equations with volume of fluid(VoF) method.The sinkage and trim are computed by equating the vertical force and pitching moment to the hydrostatic restoring force and moment.The software Fluent,Maxsurf and MATLAB are used to implement this method.With dynamic mesh being used,the position of a ship is updated by the motion of "ship plus boundary layer" grid zone.The hull factors are introduced for fast calculating the running attitude of a ship.The method has been applied to the ship model INSEAN2340 for different Froude numbers and is found to be efficient for evaluating the flow field,resistance,sinkage and trim.展开更多
We study the vanishing viscosity of the Navier-Stokes equations for interacting shocks. Given an entropy solution to p-system which consists of two different families of shocks interacting at some positive time,we sho...We study the vanishing viscosity of the Navier-Stokes equations for interacting shocks. Given an entropy solution to p-system which consists of two different families of shocks interacting at some positive time,we show that such entropy solution is the vanishing viscosity limit of a family of global smooth solutions to the isentropic Navier-Stokes equations. The key point of the proofs is to derive the estimates separately before and after the interaction time and connect the incoming and outgoing viscous shock profiles.展开更多
We investigate the zero dissipation limit problem of the one-dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that...We investigate the zero dissipation limit problem of the one-dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that the unique solution to the Navier-Stokes equations exists for all time, and converges to the Riemann solution to the corresponding Euler equations with the same Riemann initial data uniformly on the set away from the shocks, as the viscosity vanishes. In contrast to previous related works, where either the composite wave is absent or the effects of initial layers are ignored, this gives the first mathematical justification of this limit for the compressible isentropic Navier-Stokes equations in the presence of both composite wave and initial layers. Our method of proof consists of a scaling argument, the construction of the approximate solution and delicate energy estimates.展开更多
The zero dissipation limit for the one-dimensional Navier-Stokes equations of compressible,isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions is investigated in this pa...The zero dissipation limit for the one-dimensional Navier-Stokes equations of compressible,isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions is investigated in this paper.In a paper(Comm.Pure Appl.Math.,46,1993,621-665) by Z.P.Xin,the author constructed a sequence of solutions to one-dimensional Navier-Stokes isentropic equations converging to the rarefaction wave as the viscosity tends to zero.Furthermore,he obtained that the convergence rate is ε 1/4 | ln ε|.In this paper,Xin's convergence rate is improved to ε1/3|lnε|2 by different scaling arguments.The new scaling has various applications in related problems.展开更多
This paper introduces a numerical model for studying the evolution of a periodic wave train, shoaling, and breaking in surf zone. The model can solve the Reynolds averaged Navier-Stokes （RANS） equations for a mean f...This paper introduces a numerical model for studying the evolution of a periodic wave train, shoaling, and breaking in surf zone. The model can solve the Reynolds averaged Navier-Stokes （RANS） equations for a mean flow, and the k-ε equations for turbulence kinetic energy k and turbulence dissipation rate ε. To track a free surface, the volume of fluid （VOF） function, satisfying the advection equation was introduced. In the numerical treatment, third-order upwind difference scheme was applied to the convection terms of the RANS equations in order to reduce the effect of numerical viscosity. The shoaling and breaking processes of a periodic wave train on gently sloping beaches were modeled. The computed wave heights of a sloping beach and the distribution of breaking wave pressure on a vertical wall were compared with laboratory data.展开更多
In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function ...In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.展开更多
We prove a blow-up criterion in terms of the upper bound of the density for the strong solution to 2D compressible Navier-Stokes equations in a bounded domain. The initial vacuum is allowed. The proof is based on the ...We prove a blow-up criterion in terms of the upper bound of the density for the strong solution to 2D compressible Navier-Stokes equations in a bounded domain. The initial vacuum is allowed. The proof is based on the new a priori estimate for 2D compressible Navier-Stokes equations and a logarithmic estimate for Lamé system.展开更多
In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeli...In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.展开更多
Supercritical fluid has been widely applied in many industrial applications.The traditional Reynolds-averaged Navier-Stokes(RANS)equations are directly applied for turbulent flow and heat transfer of the supercritical...Supercritical fluid has been widely applied in many industrial applications.The traditional Reynolds-averaged Navier-Stokes(RANS)equations are directly applied for turbulent flow and heat transfer of the supercritical fluid,ignoring turbulent effect of the thermal physical properties due to the intense nonlinearity.This paper deduces a set of Reynolds-averaged Navier-Stokes equations for supercritical fluid(SCF-RANS equations)to depict turbulent flow and heat transfer of the supercritical fluid taking all the physical parameters as variables.The SCF-RANS equations include many new correlation terms due to fluctuation of the thermal physical properties.Model methods for the new correlation term have been discussed for closing the SCF-RANS equations.Some of them have relatively mature models,while others are completely new and need profound physical theoretical analysis for proposing reasonable models.This paper provides referable information for these new correlations as far as authors know.The SCF-RANS equations not only provide the formulation special for flow and heat transfer of the supercritical fluid,but also represent the most sophisticate form of the RANS equations,for every involved physical property has been considered as variable without any simplification.展开更多
In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Sto...In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the Gateaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.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
This paper aims to give a detailed presentation of long-wave instabilities of shear layers for NavierStokes equations,and in particular to give a simple and easy-to-read presentation of the study of the OrrSommerfeld ...This paper aims to give a detailed presentation of long-wave instabilities of shear layers for NavierStokes equations,and in particular to give a simple and easy-to-read presentation of the study of the OrrSommerfeld equation and to detail the analysis of its adjoint.Using these analyses,we prove the existence of long-wave instabilities in the cases of slowly rotating fuids,slightly compressible fuids,or fuids with Navier boundary conditions,under smallness conditions.展开更多
The combined quasi-neutral and non-relativistic limit of compressible Navier-Stokes-Maxwell equations for plasmas is studied.For well-prepared initial data,it is shown that the smooth solution of compressible Navier-S...The combined quasi-neutral and non-relativistic limit of compressible Navier-Stokes-Maxwell equations for plasmas is studied.For well-prepared initial data,it is shown that the smooth solution of compressible Navier-Stokes-Maxwell equations converges to the smooth solution of incompressible Navier-Stokes equations by introducing new modulated energy functional.展开更多
Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered.They consist of the 3D incompressible Navier-Stokes equations,subject to time-depende...Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered.They consist of the 3D incompressible Navier-Stokes equations,subject to time-dependent external forces and coupled with either a convective Allen-Cahn or Cahn-Hilliard equation.Such systems can be viewed as generalizations of the Navier-Stokes equations to two-phase fluids.Using the trajectory approach,the authors prove the existence of the trajectory attractor for both systems.展开更多
This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain.Under appropriate assumption on the delay term,we...This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain.Under appropriate assumption on the delay term,we establish the existence of pullback attractors for the fluid flow model,which is dependent on the past state.Inspired by the idea in Zelati and Gal’s paper(JMFM,2015),the robustness of pullback attractors has been proved via upper semi-continuity in last section.展开更多
A mathematical model for unsteady electro-and aerodynamic processes in the presence of a plasma actuator has been elaborated through physical modeling of the dielectric barrier discharge.A specialized computational fl...A mathematical model for unsteady electro-and aerodynamic processes in the presence of a plasma actuator has been elaborated through physical modeling of the dielectric barrier discharge.A specialized computational fluid dynamics package has been developed accordingly in order to calculate steady and unsteady laminar and turbulent flows.For the numerical simulation of the dielectric barrier discharge,in particular,two equations have been added to the Navier-Stokes equations and solved.They describe the distribution of the applied voltage and the charged particles density.The impact of the plasma actuator on air has been accounted for through the Lorentz force,included as a source term in the momentum balance equation.The system of governing equations for the considered hydrodynamics and electrodynamics has been written in an arbitrary curvilinear coordinate system in dimensionless form and integrated in the framework of a finite volume method.A TVD scheme with a third-order ISNAS flow limiter has been chosen for the convective terms approximation.The obtained block-matrix system of linear algebraic equations has been solved by the generalized minimal residual(GMRES)method with ILU(k)preconditioning.Using this approach,the occurrence of a propulsion force,emerging as a result of the action of plasma actuators on a cylinder in quiescent air,has been investigated.The possibility to mitigate the cylinder drag coefficient with the help of the plasma actuators,due to the ensuing suppression of the Karman vortex street,has been demonstrated.展开更多
In this paper we investigate the nonconforming P_(1) finite element ap-proximation to the sequential regularization method for unsteady Navier-Stokes equations.We provide error estimates for a full discretization sche...In this paper we investigate the nonconforming P_(1) finite element ap-proximation to the sequential regularization method for unsteady Navier-Stokes equations.We provide error estimates for a full discretization scheme.Typi-cally,conforming P_(1) finite element methods lead to error bounds that depend inversely on the penalty parameter ∈.We obtain an ∈-uniform error bound by utilizing the nonconforming P_(1) finite element method in this paper.Numerical examples are given to verify theoretical results.展开更多
基金The project supported by the National Natural Science Foundation of China(10232010 and 10472008)
文摘The equations of motion of an insect with flapping wings are derived and then simplified to that of a flying body using the ＂rigid body＂ assumption. On the basis of the simplified equations of motion, the longitudinal dynamic flight stability of four insects （hoverfly, cranefly, dronefly and hawkmoth） in hovering flight is studied （the mass of the insects ranging from 11 to 1,648 mg and wingbeat frequency from 26 to 157Hz）. The method of computational fluid dynamics is used to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. The validity of the ＂rigid body＂ assumption is tested and how differences in size and wing kinematics influence the applicability of the ＂rigid body＂ assumption is investigated. The primary findings are： （1） For insects considered in the present study and those with relatively high wingbeat frequency （hoverfly, drone fly and bumblebee）, the ＂rigid body＂ assumption is reasonable, and for those with relatively low wingbeat frequency （cranefly and howkmoth）, the applicability of the ＂rigid body＂ assumption is questionable. （2） The same three natural modes of motion as those reported recently for a bumblebee are identified, i.e., one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. （3） Approximate analytical expressions of the eigenvalues, which give physical insight into the genesis of the natural modes of motion, are derived. The expressions identify the speed derivative Mu （pitching moment produced by unit horizontal speed） as the primary source of the unstable oscillatory mode and the stable fast subsidence mode and Zw （vertical force produced by unit vertical speed） as the primary source of the stable slow subsidence mode.
基金the National Natural Science Foundation of China(Grant Nos.10471100,40437017,and 60573158)Beijing Jiaotong University Science and Technology Foundation
文摘The proper orthogonal decomposition(POD)and the singular value decomposition(SVD) are used to study the finite difference scheme(FDS)for the nonstationary Navier-Stokes equations. Ensembles of data are compiled from the transient solutions computed from the discrete equation system derived from the FDS for the nonstationary Navier-Stokes equations.The optimal orthogonal bases are reconstructed by the elements of the ensemble with POD and SVD.Combining the above procedures with a Galerkin projection approach yields a new optimizing FDS model with lower dimensions and a high accuracy for the nonstationary Navier-Stokes equations.The errors between POD approximate solutions and FDS solutions are analyzed.It is shown by considering the results obtained for numerical simulations of cavity flows that the error between POD approximate solution and FDS solution is consistent with theoretical results.Moreover,it is also shown that this validates the feasibility and efficiency of POD method.
基金the National Natural Science Foundation of China (No.50879090)the Advanced Research Program of GAD of the P.L.A (No.7131005)
文摘A method is presented to calculate the resistance of a high-speed displacement ship taking the effect of sinkage and trim and viscosity of fluid into account.A free surface flow field is evaluated by solving Reynolds averaged Navier-Stokes(RANS) equations with volume of fluid(VoF) method.The sinkage and trim are computed by equating the vertical force and pitching moment to the hydrostatic restoring force and moment.The software Fluent,Maxsurf and MATLAB are used to implement this method.With dynamic mesh being used,the position of a ship is updated by the motion of "ship plus boundary layer" grid zone.The hull factors are introduced for fast calculating the running attitude of a ship.The method has been applied to the ship model INSEAN2340 for different Froude numbers and is found to be efficient for evaluating the flow field,resistance,sinkage and trim.
基金supported by National Basic Research Program of China(973 Program)(Grant No.2011CB808002)the National Center for Mathematics and Interdisciplinary Sciences,Academy of Mathematics and Systems Science,Chinese Academy of Sciences and the Chinese Academy of Sciences Program for Cross&Cooperative Team of the Science&Technology Innovation,National Natural Sciences Foundation of China(Grant Nos.11171326,11371064 and 11401565)the General Research Fund of Hong Kong(Grant No.City U 103412)
文摘We study the vanishing viscosity of the Navier-Stokes equations for interacting shocks. Given an entropy solution to p-system which consists of two different families of shocks interacting at some positive time,we show that such entropy solution is the vanishing viscosity limit of a family of global smooth solutions to the isentropic Navier-Stokes equations. The key point of the proofs is to derive the estimates separately before and after the interaction time and connect the incoming and outgoing viscous shock profiles.
基金supported by National Natural Science Foundation of China(Grant Nos.11226170,10976026 and 11271305)China Postdoctoral Science Foundation Funded Project(Grant No.2012M511640)+1 种基金Hunan Provincial Natural Science Foundation of China(Grant No.13JJ4095)National Science Foundation of USA(Grant Nos.DMS-0807406 and DMS-1108994)
文摘We investigate the zero dissipation limit problem of the one-dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that the unique solution to the Navier-Stokes equations exists for all time, and converges to the Riemann solution to the corresponding Euler equations with the same Riemann initial data uniformly on the set away from the shocks, as the viscosity vanishes. In contrast to previous related works, where either the composite wave is absent or the effects of initial layers are ignored, this gives the first mathematical justification of this limit for the compressible isentropic Navier-Stokes equations in the presence of both composite wave and initial layers. Our method of proof consists of a scaling argument, the construction of the approximate solution and delicate energy estimates.
基金supported by the National Natural Science Foundation of China for Outstanding Young Scholars(No. 10825102)the National Basic Research Program of China (973 Program) (No. 2011CB808002)
文摘The zero dissipation limit for the one-dimensional Navier-Stokes equations of compressible,isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions is investigated in this paper.In a paper(Comm.Pure Appl.Math.,46,1993,621-665) by Z.P.Xin,the author constructed a sequence of solutions to one-dimensional Navier-Stokes isentropic equations converging to the rarefaction wave as the viscosity tends to zero.Furthermore,he obtained that the convergence rate is ε 1/4 | ln ε|.In this paper,Xin's convergence rate is improved to ε1/3|lnε|2 by different scaling arguments.The new scaling has various applications in related problems.
基金Supported by the High-Tech Research and Development Program of China (863 Program, No. 2001AA633070 2003AA604040)the National Natural Science Foundation of China (No. 40476015).
文摘This paper introduces a numerical model for studying the evolution of a periodic wave train, shoaling, and breaking in surf zone. The model can solve the Reynolds averaged Navier-Stokes （RANS） equations for a mean flow, and the k-ε equations for turbulence kinetic energy k and turbulence dissipation rate ε. To track a free surface, the volume of fluid （VOF） function, satisfying the advection equation was introduced. In the numerical treatment, third-order upwind difference scheme was applied to the convection terms of the RANS equations in order to reduce the effect of numerical viscosity. The shoaling and breaking processes of a periodic wave train on gently sloping beaches were modeled. The computed wave heights of a sloping beach and the distribution of breaking wave pressure on a vertical wall were compared with laboratory data.
基金supported by the NSFC(11931013)the GXNSF(2022GXNSFDA035078)。
文摘In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 0<α<1;this includes the timeweighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.
基金supported by National Natural Science Foundation of China (Grant Nos. 10771097, 10931007)supported by National Natural Science Foundation of China (Grant Nos. 10990013, 11071007)and SRF for ROCS,SEM
文摘We prove a blow-up criterion in terms of the upper bound of the density for the strong solution to 2D compressible Navier-Stokes equations in a bounded domain. The initial vacuum is allowed. The proof is based on the new a priori estimate for 2D compressible Navier-Stokes equations and a logarithmic estimate for Lamé system.
基金supported by the National Natural Science Foundation of China(Grant Nos.11372068 and 11572350)the National Basic Research Program of China(Grant No.2014CB744104)
文摘In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.
基金the support of National Key R&D Plan of China(2017YFB0903601)National Natural Science Foundation of China(51606186)+1 种基金Newton Advanced Fellowship of the Royal Society(NA170093)Strategic Priority Research Program of the Chinese Academy of Sciences(XDA21070200)。
文摘Supercritical fluid has been widely applied in many industrial applications.The traditional Reynolds-averaged Navier-Stokes(RANS)equations are directly applied for turbulent flow and heat transfer of the supercritical fluid,ignoring turbulent effect of the thermal physical properties due to the intense nonlinearity.This paper deduces a set of Reynolds-averaged Navier-Stokes equations for supercritical fluid(SCF-RANS equations)to depict turbulent flow and heat transfer of the supercritical fluid taking all the physical parameters as variables.The SCF-RANS equations include many new correlation terms due to fluctuation of the thermal physical properties.Model methods for the new correlation term have been discussed for closing the SCF-RANS equations.Some of them have relatively mature models,while others are completely new and need profound physical theoretical analysis for proposing reasonable models.This paper provides referable information for these new correlations as far as authors know.The SCF-RANS equations not only provide the formulation special for flow and heat transfer of the supercritical fluid,but also represent the most sophisticate form of the RANS equations,for every involved physical property has been considered as variable without any simplification.
基金supported by the National High-Tech Research and Development Program of China (No.2009AA01A135)the National Natural Science Foundation of China (Nos. 10926080, 10971165, 10871156)Xian Jiaotong University (No. XJJ2008033)
文摘In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations. The authors also prove the existence of the solution of the optimal control problem, the existence of the solution of the Navier-Stokes equations with mixed boundary conditions, the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the Gateaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.
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 Nos. 11871005 and 12271032)。
文摘This paper aims to give a detailed presentation of long-wave instabilities of shear layers for NavierStokes equations,and in particular to give a simple and easy-to-read presentation of the study of the OrrSommerfeld equation and to detail the analysis of its adjoint.Using these analyses,we prove the existence of long-wave instabilities in the cases of slowly rotating fuids,slightly compressible fuids,or fuids with Navier boundary conditions,under smallness conditions.
基金supported by the Joint Funds of National Natural Science Foundation of China(Grant No.U1204103)China Postdoctoral Science Foundation Funded Project(Grant No.2013M530032)the Science and Technology Research Projects of Education Department of Henan Province(Grant No.13A110731)
文摘The combined quasi-neutral and non-relativistic limit of compressible Navier-Stokes-Maxwell equations for plasmas is studied.For well-prepared initial data,it is shown that the smooth solution of compressible Navier-Stokes-Maxwell equations converges to the smooth solution of incompressible Navier-Stokes equations by introducing new modulated energy functional.
基金supported by the Italian MIUR-PRIN Research Project 2008 "Transizioni di fase,isteresi e scale multiple"
文摘Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered.They consist of the 3D incompressible Navier-Stokes equations,subject to time-dependent external forces and coupled with either a convective Allen-Cahn or Cahn-Hilliard equation.Such systems can be viewed as generalizations of the Navier-Stokes equations to two-phase fluids.Using the trajectory approach,the authors prove the existence of the trajectory attractor for both systems.
基金Xin-Guang Yang was partially supported by the Fund of Young Backbone Teacher in Henan Province(No.2018GGJS039)cultivation Fund of Henan Normal University(No.2020PL17)Henan Overseas Expertise Introduction Center for Discipline Innovation(No.CXJD2020003).
文摘This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain.Under appropriate assumption on the delay term,we establish the existence of pullback attractors for the fluid flow model,which is dependent on the past state.Inspired by the idea in Zelati and Gal’s paper(JMFM,2015),the robustness of pullback attractors has been proved via upper semi-continuity in last section.
文摘A mathematical model for unsteady electro-and aerodynamic processes in the presence of a plasma actuator has been elaborated through physical modeling of the dielectric barrier discharge.A specialized computational fluid dynamics package has been developed accordingly in order to calculate steady and unsteady laminar and turbulent flows.For the numerical simulation of the dielectric barrier discharge,in particular,two equations have been added to the Navier-Stokes equations and solved.They describe the distribution of the applied voltage and the charged particles density.The impact of the plasma actuator on air has been accounted for through the Lorentz force,included as a source term in the momentum balance equation.The system of governing equations for the considered hydrodynamics and electrodynamics has been written in an arbitrary curvilinear coordinate system in dimensionless form and integrated in the framework of a finite volume method.A TVD scheme with a third-order ISNAS flow limiter has been chosen for the convective terms approximation.The obtained block-matrix system of linear algebraic equations has been solved by the generalized minimal residual(GMRES)method with ILU(k)preconditioning.Using this approach,the occurrence of a propulsion force,emerging as a result of the action of plasma actuators on a cylinder in quiescent air,has been investigated.The possibility to mitigate the cylinder drag coefficient with the help of the plasma actuators,due to the ensuing suppression of the Karman vortex street,has been demonstrated.
基金supported by the National Key Research and Development Program of China(No.2020YFA0714200)by the National Science Foundation of China(No.12371424).
文摘In this paper we investigate the nonconforming P_(1) finite element ap-proximation to the sequential regularization method for unsteady Navier-Stokes equations.We provide error estimates for a full discretization scheme.Typi-cally,conforming P_(1) finite element methods lead to error bounds that depend inversely on the penalty parameter ∈.We obtain an ∈-uniform error bound by utilizing the nonconforming P_(1) finite element method in this paper.Numerical examples are given to verify theoretical results.
