Global Classical Solutions for One Dimensional Navier Stokes Equations

In this article the author considers Cauchy problem for one dimensional Navier Stokes equations and the global smooth resolvablity for classical solutions is obtained.

MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID

This article is concerned with the existence of maximal attractors in Hi （i = 1, 2, 4） for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn（n = 2,3）. One of the important features is that the metric spaces H（1）, H（2）, and H（4） we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ（4） H（i） （i = 1, 2, 4） is found, and the existence of maximal （universal） attractors in Hδ（i） （i = 1.2.4） is established.

Some Similarity Reduction Solutions to Two-Dimensional Incompressible Navier-Stokes Equation

We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two special cases in [D.K.Ludlow,P.A.Clarkson,and A.P.Bassom,Stud.Appl.Math.103 (1999) 183] and a theoremin [S.Y.Lou,M.Jia,X.Y.Tang,and F.Huang,Phys.Rev.E 75 (2007) 056318] are retrieved.

NONLINEAR STABILITY OF VISCOUS SHOCK WAVES FOR ONE-DIMENSIONAL NONISENTROPIC COMPRESSIBLE NAVIER–STOKES EQUATIONS WITH A CLASS OF LARGE INITIAL PERTURBATION

We study the nonlinear stability of viscous shock waves for the Cauchy problem of one-dimensional nonisentropic compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas. The viscous shock waves are shown to be time asymptotically stable under large initial perturbation with no restriction on the range of the adiabatic exponent provided that the strengths of the viscous shock waves are assumed to be sufficiently small.The proofs are based on the nonlinear energy estimates and the crucial step is to obtain the positive lower and upper bounds of the density and the temperature which are uniformly in time and space.

THE FUNDAMENTAL SOLUTION METHOD FOR INCOMPRESSIBLE NAVIER STOKES EQUATIONS

A complete boundary integral formulation for incompressible Navier Stokes equations with time discretization by operator splitting is developed by using the fundamental solutions of the Helmhotz operator equation with different orders. The numerical results for the lift and the drag hysteresis associated with a NACA0012 aerofoil oscillating in pitch are good in comparison with available experimental data.

A Note on Similarity Solutions of Navier-Stokes Equations

This note looks at the two similarity solutions of the Navier-Stokes equations in polar coordinates. In the second solution an initial value problem is reduced into generalized stationary KDV and hence integrable.

A Two-Grid Technique for the Penalty Method of the Steady Navier-Stokes Equations

A two grid technique for solving the steady incompressible Navier Stokes equations in a penalty method was presented and the convergence of numerical solutions was analyzed. If a coarse size H and a fine size h satisfy H=O(h 13-s )(s=0(n=2);s=12(n=3), where n is a space dimension), this method has the same convergence accuracy as the usual finite element method. But the two grid method can save a lot of computation time for its brief calculation. Moreover, a numerical test was couducted in order to verify the correctness of above theoretical analysis.

TIME ACCURATE 2D NAVIER-STOKES CALCULATIONS WITH A DUAL-TIME STEPPING METHOD

With the cell vertex finite volume discretization in space and second order backward implicit discretization in time, 2D unsteady Navier Stokes equations are solved by a dual time stepping method to simulate compressible viscous flow around rigid airfoils in arbitrary unsteady motion. The selection of physical time step is not restricted by stability condition any more, and most of the successful acceleration techniques used in steady calculations can be implemented to increase the computation efficiency.

Global Mild Solution of Stochastic Generalized Navier–Stokes Equations with Coriolis Force

In this paper, we apply Littlewood-Paley theory and Ito integral to get the global existence of stochastic Navier-Stokes equations with Coriolis force in Fourier-Besov spaces. As a comparison, we also give corresponding results of the deterministic Navier-Stokes equations with Coriolis force.

Stability of Navier–Stokes System with Singular External Force in Fourier–Herz Space

We prove the asymptotic properties of the solutions to the 3D Navier–Stokes system with singular external force, by making use of Fourier localization method, the Littlewood–Paley theory and some subtle estimates in Fourier–Herz space. The main idea of the proof is motivated by that of Cannone et al. [J. Differential Equations, 314, 316–339(2022)]. We deal either with the nonstationary problem or with the stationary problem where solution may be singular due to singular external force. In this paper, the Fourier–Herz space includes the function space of pseudomeasure type used in Cannone et al. [J. Differential Equations, 314, 316–339(2022)]

CONVERGENCE OF CHORIN-MARSDEN FOR MULA FOR THENAVIER-STOKES EQUATIONS ON CONVEX DOMAINS

We prove the convergence of the Chorin-Marsden product formula for solving the initial-boundary value problems of the Navier-Stokes equations on convex domains. As a particular case we consider the case of the half plane.

Higher-order Accurate and High-resolution Implicit Up wind Finite Volume Scheme for Solving Euler/Reynolds-averaged Navier-Stokes Equations

A new type of third\|order upwind finite volume implicit scheme is proposed for solving two/three\|dimensional Euler/Reynolds\|averaged Navier\|Stokes equations for steady flow. The fundamental form of the implicit scheme is based on the LU\|TVD finite volume scheme with the hybrid flux splitting technique. The third\|order ENN scheme's numerical flux is used to calculate the inviscid terms of Navier\|Stokes equations.A fourth\|order accurate symmetric compact difference is applied to its viscous terms. The Baldwin\|Lomax turbulence model is used to calculate the turbulent viscosity. Numerical experiments suggest that the proposed scheme not only has a fairly rapid convergence rate, but also can generate a highly resolved approximation to the numerical solution.

Asymptotics of Stationary Navier Stokes Equations in Higher Dimensions

We show that the asymptotics of solutions to stationary Navier Stokes equations in 4, 5 or 6 dimensions in the whole space with a smooth compactly supported forcing are given by the linear Stokes equation. We do not need to assume any smallness condition. The result is in contrast to three dimensions, where the asymptotics for steady states are different from the linear Stokes equation, even for small data, while the large data case presents an open problem. The case of dimension n = 2 is still harder.

A Note on Time-Decay Estimates for the Compressible Navier–Stokes Equations

In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier-Stokes equations. Those decay rates of Lq-Lr type of the solution and its derivatives are available in the critical regularity framework, which were exactly firstly observed by Matsumura ＆ Nishida, and subsequently generalized by Ponce for solutions with high Sobolev regularity. We would like to mention that our approach is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics. In this paper, a new observation is involved in the high frequency, which enables us to improve decay exponents for the high frequencies of solutions.

WAVE TRANSFORMATION AND BREAKING OVER A RECTANGULAR STEP

An idealized numerical wave flume has been established by finite element method on the bases of Navier Stokes equations through prescribing the appropriate boundary conditions for the open boundary,incident boundary,free surface and solid boundary in this paper.The characteristics of waves propagating over a step have been investigated by this numerical model.The breaker wave height is determined depending on the kinetic criterion.The numerical model is verified by laboratory experiments,and the empirical formula for the damping of wave height due to breaking is also given by experiments.

NUMERICAL SIMULATIONS OF EVOLUTIONS FROM WALL PULSE TO TURBULENT COHE RENT STRUCTURES

The high order compact d if ference method is developed for solving the perturbation equations based on Navi er Stokes equations, and is used in studying complex evolution processes from w all negative pulse to the turbulent coherent structure in the channel flow. Th is method contains three dimensional coupling difference scheme with high accur acy and high resolution, and the high order time splitting methods. Compared with the general spectral method, the method can be used to research turbule nt coherent structure under more general boundary conditions and in flow domains . In this paper, the generation and evolution of the turbulent coherent structur es ind uced by wall pulse in the channel flow are simulated, and the basic characterist ics and rules of the turbulent coherent structure are shown. Computational r esults indicate that a wall negative pulse is more convenient than the resonant three wave model.

Secondary Instability of Large Scale Structure in Free Turbulent Shear Layer

The secondary instability theory is used to study the behavior of spatially growingdisturbance in free turbulent shear layer.The numerical results indicate that secondaryinstability of subharmonic mode shows a strong choice of spanwise wavenumber andthe maximum growth two dimensional case.In contrast to thatsecondary instabilities of the fundamental mode occur in a wide scope of spanwisewavenumber.We have found so called translative atβ=0 and bifurcationphenomenon for an amplitude of the KH wave larger than 0.06.Dey words instability,large scale structure,bifurcation

Time-Periodic Solution to the Compressible Navier–Stokes/Allen–Cahn System

In this paper,we investigate the time-periodic solution to a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of a mixture of two viscous compressible fluids with a time periodic external force in a periodic domain in R^N.The existence of the time-periodic solution to the system is established by using an approach of parabolic regularization and combining with the topology degree theory,and then the uniqueness of the period solution is obtained under some smallness and symmetry assumptions on the external force.

Investigation of Unsteady Flow in a Diffuser Pump

Flow in pumps is essentially three-dimensional and unsteady, and it has much influence on the pump hydraulic performance and structural vibration. This paper presents a numerical methodology developed for modeling such complicated flows. Three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations, together with standard k-Ε equation, describe the unsteady-turbulent flow in the pumps. System characteristics are incorporated into the pump CFD models to allow for fluid acceleration in the piper Arbitrary Sliding Interface (ASI) is used to simulate the relative movement between the impeller and stationary components; a numerical analysis is carried out for the entire circumference to consider the asymmetrical flow physics during the stall condition. Combination of these techniques has captured the realistic unsteady flow physics in the pumps and it permits good prediction for the pump off-design performance.

A Numerical Investigation of the Reduction of Solitary Wave Runup by A Row of Vertical Slotted Piles

To improve the current understanding of the reduction of tsunami-like solitary wave runup by the pile breakwater on a sloping beach, we developed a 3D numerical wave tank based on the CFD tool OpenFOAM in this study. The Navier Stokes equations were applied to solve the two-phase incompressible flow, combined with an LES model to solve the turbulence and a VOF method to capture the free surface. The adopted model was firstly validated with existing empirical formulas for solitary wave runup on the slope without the pile structure. It is then validated using our new laboratory observations of the free surface elevation, the velocity and the pressure around a row of vertical slotted piles subjected to solitary waves, as well as the wave runup on the slope behind the piles. Subsequently, a set of numerical simulations were implemented to analyze the wave reflection, the wave transmission, and the shoreline runup with various offshore wave heights, offshore water depths, adjacent pile spaces and beach slopes. Finally, an improved empirical equation accounting for the maximum wave runup on the slope was proposed by taking the presence of the pile breakwater into consideration.