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1.
This paper presents a gas-kinetic theory based multidimensional high-order method for the compressible Naiver–Stokes solutions. In our previous study, a spatially and temporally dependent third-order flux scheme with the use of a third-order gas distribution function is employed.However, the third-order flux scheme is quite complicated and less robust than the second-order scheme. In order to reduce its complexity and improve its robustness, the secondorder flux scheme is adopted instead in this paper, while the temporal order of method is maintained by using a two stage temporal discretization. In addition, its CPU cost is relatively lower than the previous scheme. Several test cases in two and three dimensions, containing high Mach number compressible flows and low speed high Reynolds number laminar flows, are presented to demonstrate the method capacity. 相似文献
2.
Jianming Liu Ning Zhao Ou Hu Mikhail Goman Xin Kai Li 《International Journal of Computational Fluid Dynamics》2013,27(3):151-163
This paper presents an immersed boundary method for compressible Navier–Stokes equations in irregular domains, based on a local radial basis function approximation. This approach allows one to define a reconstruction of the radial basis functions on each irregular interface cell to treat both the Dirichlet and Neumann boundary conditions accurately on the immersed interfaces. Several numerical examples, including problems with available analytical solutions and the well-documented flow past an airfoil, are presented to test the proposed method. The numerical results demonstrate that the proposed method provides accurate solutions for viscous compressible flows. 相似文献
3.
The first goal of this paper is to study the large time behavior of solutions to the Cauchy problem for the 3-dimensional incompressible Navier–Stokes system. The Marcinkiewicz space L3, is used to prove some asymptotic stability results for solutions with infinite energy. Next, this approach is applied to the analysis of two classical regularized Navier–Stokes systems. The first one was introduced by J. Leray and consists in mollifying the nonlinearity. The second one was proposed by J.-L. Lions, who added the artificial hyper-viscosity (–)/ 2, > 2 to the model. It is shown in the present paper that, in the whole space, solutions to those modified models converge as t toward solutions of the original Navier–Stokes system. 相似文献
4.
A development is provided showing that for any phase, by not neglecting the macroscopic terms of the deviation from the intensive momentum and of the dispersive momentum, we obtain a macroscopic secondary momentum balance equation coupled with a macroscopic dominant momentum balance equation that is valid at a larger spatial scale. The macroscopic secondary momentum balance equation is in the form of a wave equation that propagates the deviation from the intensive momentum while concurrently, in the case of a Newtonian fluid and under certain assumptions, the macroscopic dominant momentum balance equation may be approximated by Darcys equation to address drag dominant flow. We then develop extensions to the dominant macroscopic Navier–Stokes (NS) equation for saturated porous matrices, to account for the pressure gradient at the microscopic solid-fluid interfaces. At the microscopic interfaces we introduce the exchange of inertia between the phases, accounting for the relative fluid square velocities and the rate of these velocities, interpreted as Forchheimer terms. Conditions are provided to approximate the extended dominant NS equation by Forchheimer quadratic momentum law or by Darcys linear momentum law. We also show that the dominant NS equation can conform into a nonlinear wave equation. The one-dimensional numerical solution of this nonlinear wave equation demonstrates good qualitative agreement with experiments for the case of a highly deformable elasto-plastic matrix. 相似文献
5.
We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier–Stokes
equation with the Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev
space and has only one normal derivative bounded in L
∞. This allows us to obtain the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument. 相似文献
6.
We tackle the issue of the inviscid limit of the incompressible Navier–Stokes equations when the Navier slip-with-friction
conditions are prescribed on impermeable boundaries. We justify an asymptotic expansion which involves a weak amplitude boundary
layer, with the same thickness as in Prandtl’s theory and a linear behavior. This analysis holds for general regular domains,
in both dimensions two and three. 相似文献
7.
Pablo Pedregal 《Journal of Mathematical Fluid Mechanics》2012,14(1):159-176
We introduce a variational approach to treat the regularity of the Navier–Stokes equations both in dimensions 2 and 3. Though
the method allows the full treatment in dimension 2, we seek to precisely stress where it breaks down for dimension 3. The
basic feature of the procedure is to look directly for strong solutions, by minimizing a suitable error functional that measures
the departure of feasible fields from being a solution of the problem. By considering the divergence-free property as part
of feasibility, we are able to avoid the explicit analysis of the pressure. Two main points in our analysis are:
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Coercivity for the error functional is achieved by looking at scaling. 相似文献
8.
We consider the full Navier–Stokes–Fourier system describing the motion of a compressible viscous and heat conducting fluid
driven by a time-periodic external force. We show the existence of at least one weak time periodic solution to the problem
under the basic hypothesis that the system is allowed to dissipate the thermal energy through the boundary. Such a condition
is in fact necessary, as energetically closed fluid systems do not possess non-trivial (changing in time) periodic solutions
as a direct consequence of the Second law of thermodynamics. 相似文献
9.
Michael Renardy 《Archive for Rational Mechanics and Analysis》2009,194(3):877-886
We prove that the linearization of the hydrostatic Euler equations at certain parallel shear flows is ill-posed. The result
also extends to the hydrostatic Navier–Stokes equations with a small viscosity. 相似文献
10.
The paper is devoted to a theoretical analysis of a counter-current gas-liquid flow between two inclined plates. We linearized the Navier–Stokes equations and carried out a stability analysis of the basic steady-state solution over a wide variation of the liquid Reynolds number and the gas superficial velocity. As a result, we found two modes of the unstable disturbances and computed the wavelength and phase velocity of their neutral disturbances varying the liquid and gas Reynolds number. The first mode is a “surface mode” that corresponds to the Kapitza's waves at small values of the gas superficial velocity. We found that the dependence of the neutral disturbance wavelength on the liquid Reynolds number strongly depends on the gas superficial velocity, the distance between the plates and the channel inclination angle for this mode. The second mode of the unstable disturbances corresponds to the transition to a turbulent flow in the gas phase and there is a critical value of the gas Reynolds number for this mode. We obtained that this critical Reynolds number weakly depends on both the channel inclination angle, the distance between the plates and the liquid flow parameters for the conditions considered in the paper. Despite a thorough search, we did not find the unstable modes that may correspond to the instability in frame of the viscous (or inviscid) Kelvin–Helmholtz heuristic analysis. 相似文献
11.
We consider the Cauchy problem for incompressible Navier–Stokes equations
with initial data in
, and study in some detail the smoothing effect of the equation. We prove that for T < ∞ and for any positive integers n and m we have
, as long as
stays finite. 相似文献
12.
We investigate the relationship between the time decay of the solutions u of the Navier–Stokes system on a bounded open subset of
and the time decay of the right-hand sides f. In suitable function spaces, we prove that u always inherits at least part of the decay of f, up to exponential, and that the decay properties of u depend only upon the amount and type (e.g., exponential, or power-like) of decay of f. This is done by first making clear what is meant by “type” and “amount” of decay and by next elaborating upon recent abstract
results pointing to the fact that, in linear and nonlinear PDEs, the decay of the solutions is often intimately related to
the Fredholmness of the differential operator.
This work was done while the second author was visiting the Bernoulli Center, EPFL, Switzerland, whose support is gratefully
acknowledged. 相似文献
13.
This paper is devoted to a theoretical analysis of counter-current gas–liquid wavy film flow between vertical plates. We consider two-dimensional nonlinear waves on the interface over a wide variation of parameters. We use the Navier–Stokes equations in their full statement to describe the liquid phase hydrodynamics. For the gas phase equations, we use the Benjamin-Miles approach where the liquid phase is a small disturbance for the turbulent gas flow. We find a region of the superficial velocity where we have two solutions at one set of the problem parameters and where the flooding takes place. We calculate the flooding dependences on the gas/liquid physical properties, on the liquid Reynolds number and on the distance between the plates. These computations allow us to present the correlation for the onset of flooding that based on the fundamental equations and principles. 相似文献
14.
The Navier–Stokes–Fourier system describing the motion of a compressible, viscous and heat conducting fluid is known to possess
global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides with the strong
solution, emanating from the same initial data, as long as the latter exists. In particular, strong solutions are unique within
the class of weak solutions. 相似文献
15.
16.
We consider asymptotic behavior of Leray’s solution which expresses axis-symmetric incompressible Navier–Stokes flow past
an axis-symmetric body. When the velocity at infinity is prescribed to be nonzero constant, Leray’s solution is known to have
optimum decay rate, which is in the class of physically reasonable solution. When the velocity at infinity is prescribed to
be zero, the decay rate at infinity has been shown under certain restrictions such as smallness on the data. Here we find
an explicit decay rate when the flow is axis-symmetric by decoupling the axial velocity and the horizontal velocities.
The first author was supported by KRF-2006-312-C00466. The second author was supported by KRF-2006-531-C00009. 相似文献
17.
Lorenzo Brandolese 《Archive for Rational Mechanics and Analysis》2009,192(3):375-401
We study the solutions of the nonstationary incompressible Navier–Stokes equations in , of self-similar form , obtained from small and homogeneous initial data a(x). We construct an explicit asymptotic formula relating the self-similar profile U(x) of the velocity field to its corresponding initial datum a(x). 相似文献
18.
We establish a Navier–Stokes–Fourier limit for solutions of the Boltzmann equation considered over any periodic spatial domain
of dimension two or more. We do this for a broad class of collision kernels that relaxes the Grad small deflection cutoff
condition for hard potentials and includes for the first time the case of soft potentials. Appropriately scaled families of
DiPerna–Lions renormalized solutions are shown to have fluctuations that are compact. Every limit point is governed by a weak
solution of a Navier–Stokes–Fourier system for all time. 相似文献
19.
Two-phase flows with interface modeled as a Boussinesq–Scriven surface fluid are analysed concerning their fundamental mathematical
properties. This extended form of the common sharp-interface model for two-phase flows includes both surface tension and surface viscosity. For this system of partial differential equations with free interface it is shown that the energy serves
as a strict Ljapunov functional, where the equilibria of the model without boundary contact consist of zero velocity and spheres
for the dispersed phase. The linearizations of the problem are derived formally, showing that equilibria are linearly stable,
but nonzero velocities may lead to problems which linearly are not well-posed. This phenomenon does not occur in absence of
surface viscosity. The present paper aims at initiating a rigorous mathematical study of two-phase flows with surface viscosity. 相似文献
20.
In this paper we deal with the isentropic (compressible) Navier-Stokes equation in one space dimension and we adress the problem of the boundary controllability for this system. We prove that we can drive initial conditions which are sufficiently close to some constant states to those constant states. This is done under some natural hypotheses on the time of control and on the regularity on the initial conditions. 相似文献
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