Status for the two-dimensional Navier-Stokes solver EllipSys2D
DEFF Research Database (Denmark)
Bertagnolio, F.; Sørensen, Niels N.; Johansen, J.
2001-01-01
This report sets up an evaluation of the two-dimensional Navier-Stokes solver EllipSys2D in its present state. This code is used for blade aerodynamics simulations in the Aeroelastic Design group at Risø. Two airfoils are investigated by computing theflow at several angles of attack ranging from...... the linear to the stalled region. The computational data are compared to experimental data and numerical results from other computational codes. Several numerical aspects are studied, as mesh dependency,convective scheme, steady state versus unsteady computations, transition modelling. Some general...... conclusions intended to help in using this code for numerical simulations are given....
Coexistence of chaotic and non-chaotic states in the two-dimensional Gauss-Navier-Stokes dynamics
Giberti, C.; Rondoni, L.; Vernia, C.
2004-01-01
Recently, Gallavotti proposed an Equivalence Conjecture in hydrodynamics, which states that forced-damped fluids can be equally well represented by means of the Navier-Stokes equations (NS) and by means of time reversible modifications of NS called Gauss-Navier-Stokes equations (GNS). This Equivalence Conjecture received numerical support in several recent papers concerning two-dimensional fluid mechanics. The corresponding results rely on the fact that the NS and GNS systems only have one attracting set. Performing similar two-dimensional simulations, we find that there are conditions to be met by the GNS system for this to be the case. In particular, increasing the Reynolds number, while keeping fixed the number of Fourier modes, leads to the coexistence of different attractors. This makes difficult a test of the Equivalence Conjecture, but constitutes a spurious effect due to the insufficient spectral resolution. With sufficiently fine spectral resolution, the steady states are unique and the Equivalence Conjecture can be conveniently established.
EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR TWO-DIMENSIONAL MODIFIED NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
赵才地
2004-01-01
This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further extended to the case of unbounded channel-like domains.
Quadrature-free spline method for two-dimensional Navier-Stokes equation
Institute of Scientific and Technical Information of China (English)
HU Xian-liang; HAN Dan-fu
2008-01-01
In this paper,a quadrature-free scheme of spline method for two-dimensional Navier-Stokes equation is derived,which can dramatically improve the efficiency of spline method for fluid problems proposed by Lai and Wenston(2004). Additionally,the explicit formulation for boundary condition with up to second order derivatives is presented. The numerical simulations on several benchmark problems show that the scheme is very efficient.
Generalized scale-invariant solutions to the two-dimensional stationary Navier-Stokes equations
Guillod, Julien
2014-01-01
New explicit solutions to the incompressible Navier-Stokes equations in $\\mathbb{R}^{2}\\setminus\\left\\{ \\boldsymbol{0}\\right\\}$ are determined, which generalize the scale-invariant solutions found by Hamel. These new solutions are invariant under a particular combination of the scaling and rotational symmetries. They are the only solutions invariant under this new symmetry in the same way as the Hamel solutions are the only scale-invariant solutions. While the Hamel solutions are parameterized by a discrete parameter $n$, the flux $\\Phi$ and an angle $\\theta_{0}$, the new solutions generalize the Hamel solutions by introducing an additional parameter $a$ which produces a rotation. The new solutions decay like $\\left|\\boldsymbol{x}\\right|^{-1}$ as the Hamel solutions, and exhibit spiral behavior. The new variety of asymptotes induced by the existence of these solutions further emphasizes the difficulties faced when trying to establish the asymptotic behavior of the Navier-Stokes equations in a two-dimensional ...
Kuiper, Logan K
2016-01-01
An approximate solution to the two dimensional Navier Stokes equation with periodic boundary conditions is obtained by representing the x any y components of fluid velocity with complex Fourier basis vectors. The chosen space of basis vectors is finite to allow for numerical calculations, but of variable size. Comparisons of the resulting approximate solutions as they vary with the size of the chosen vector space allow for extrapolation to an infinite basis vector space. Results suggest that such a solution, with the full basis vector space and which would give the exact solution, would fail for certain initial velocity configurations when initial velocity and time t exceed certain limits.
Effects of friction on forced two-dimensional Navier-Stokes turbulence
Blackbourn, Luke A. K.; Tran, Chuong V.
2011-10-01
Large-scale dissipation mechanisms have been routinely employed in numerical simulations of two-dimensional turbulence to absorb energy at large scales, presumably mimicking the quasisteady picture of Kraichnan in an unbounded fluid. Here, “side effects” of such a mechanism—mechanical friction—on the small-scale dynamics of forced two-dimensional Navier-Stokes turbulence are elaborated by both theoretical and numerical analysis. Given a positive friction coefficient α, viscous dissipation of enstrophy has been known to vanish in the inviscid limit ν→0. This effectively renders the scale-neutral friction the only mechanism responsible for enstrophy dissipation in that limit. The resulting dynamical picture is that the classical enstrophy inertial range becomes a dissipation range in which the dissipation of enstrophy by friction mainly occurs. For each α>0, there exists a critical viscosity νc, which depends on physical parameters, separating the regimes of predominant viscous and frictional dissipation of enstrophy. It is found that νc=[η'1/3/(Ckf2)]exp[-η'1/3/(Cα)], where η' is half the enstrophy injection rate, kf is the forcing wave number, and C is a nondimensional constant (the Kraichnan-Batchelor constant). The present results have important theoretical and practical implications. Apparently, mechanical friction is a poor choice in numerical attempts to address fundamental issues concerning the direct enstrophy transfer in two-dimensional Navier-Stokes turbulence. Furthermore, as relatively strong friction naturally occurs on the surfaces and at lateral boundaries of experimental fluids as well as at the interfaces of shallow layers in geophysical fluid models, the frictional effects discussed in this study are crucial in understanding the dynamics of these systems.
Fang, Li; Guo, Zhenhua
2016-04-01
The aim of this paper is to establish the global well-posedness and large-time asymptotic behavior of the strong solution to the Cauchy problem of the two-dimensional compressible Navier-Stokes equations with vacuum. It is proved that if the shear viscosity {μ} is a positive constant and the bulk viscosity {λ} is the power function of the density, that is, {λ=ρ^{β}} with {β in [0,1],} then the Cauchy problem of the two-dimensional compressible Navier-Stokes equations admits a unique global strong solution provided that the initial data are of small total energy. This result can be regarded as the extension of the well-posedness theory of classical compressible Navier-Stokes equations [such as Huang et al. (Commun Pure Appl Math 65:549-585, 2012) and Li and Xin (http://arxiv.org/abs/1310.1673) respectively]. Furthermore, the large-time behavior of the strong solution to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations had been also obtained.
CHEBYSHEV SPECTRAL-FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION
Institute of Scientific and Technical Information of China (English)
Benyu Guo; Songnian He; Heping Ma
2002-01-01
A mixed Chebyshev spectral-finite element method is proposed for solving two-dimensionalunsteady Navier-Stokes equation. The generalized stability and convergence are proved.The numerical results show the advantages of this method.
Directory of Open Access Journals (Sweden)
Neng Wan
2014-01-01
Full Text Available In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.
Wang, Zhiheng
2014-12-10
A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.
Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration
Vignal, Philippe
2015-06-01
In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higher- order operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a two- dimensional annulus, and model spinodal decomposition under shear flow.
Fast chemical reaction in two-dimensional Navier-Stokes flow: initial regime.
Ait-Chaalal, Farid; Bourqui, Michel S; Bartello, Peter
2012-04-01
This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional biperiodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one-dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion κ of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution on stratospheric chemistry in climate-chemistry models. Adopting a Lagrangian straining theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it, and of the modulus of the time derivative of the space-average reactant concentrations (here called the chemical speed) to the joint probability density function of the finite-time Lyapunov exponent λ with two times τ and τ[over ̃]. The time 1/λ measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time t, while τ measures it in the recent past before t, and τ[over ̃] in the early part of the trajectory. We show that the chemical speed scales like κ(1/2) and that its time evolution is determined by rare large events in the finite-time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNSs) using a pseudospectral model.
Tamellini, L.
2014-01-01
In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.
Szmelter, J.; Marchant, M. J.; Evans, A.; Weatherill, N. P.
A cell vertex finite volume Jameson scheme is used to solve the 2D compressible, laminar, viscous fluid flow equations on locally embedded multiblock meshes. The proposed algorithm is applicable to both the Euler and Navier-Stokes equations. It is concluded that the adaptivity method is very successful in efficiently improving the accuracy of the solution. Both the mesh generator and the flow equation solver which are based on a quadtree data structure offer good flexibility in the treatment of interfaces. It is concluded that methods under consideration lead to accurate flow solutions.
A TWO-GRID METHOD FOR THE STEADY PENALIZED NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Chun-fengRen; Yi-chenMa
2004-01-01
A two-grid method for the steady penalized incompressible Navier-Stokes equations is presented. Convergence results are proved. If h = O(H3-s) and ε = O(H5-2s) (s = 0(n=2);s=1/2(n=3)are chosen, the convergence order of this two-grid method is the same as that of the usual finite element method. Numerical results show that this method is efficient and can save a lot of computation time.
Persistence of Steady 3D Euler Solutions for 3D Navier-Stokes Equations
Li, Y Charles
2008-01-01
In the classical plane Couette flow, certain 3D steady solution (the so-called lower branch state) of the Navier-Stokes equations has a nontrivial limit as the Reynolds number approaches infinity \\cite{WGW07}. The limit is a shear of the form ($U(y,z), 0, 0$) in velocity variables. On the other hand, all the shears of this form are solutions of the corresponding 3D Euler equations. This note derives a necessary condition for such a shear to be a limit shear. The condition is $\\int \\Dl U f(U) dy dz = 0$ for any function $f$ satisfying certain boundary condition. Similar conditions are also derived for plane Poiseuille flow and pipe Poiseuille flow, which correspond to similar limit shears as revealed in \\cite{Wal03} \\cite{Vis08}.
A Finite-Element Solution of the Navier-Stokes Equations for Two-Dimensional and Axis-Symmetric Flow
Directory of Open Access Journals (Sweden)
Sven Ø. Wille
1980-04-01
Full Text Available The finite element formulation of the Navier-Stokes equations is derived for two-dimensional and axis-symmetric flow. The simple triangular, T6, isoparametric element is used. The velocities are interpolated by quadratic polynomials and the pressure is interpolated by linear polynomials. The non-linear simultaneous equations are solved iteratively by the Newton-Raphson method and the element matrix is given in the Newton-Raphson form. The finite element domain is organized in substructures and an equation solver which works on each substructure is specially designed. This equation solver needs less storage in the computer and is faster than the traditional banded equation solver. To reduce the amount of input data an automatic mesh generator is designed. The input consists of the coordinates of eight points defining each substructure with the corresponding boundary conditions. In order to interpret the results they are plotted on a calcomp plotter. Examples of plots of the velocities, the streamlines and the pressure inside a two-dimensional flow divider and an axis-symmetric expansion of a tube are shown for various Reynolds numbers.
Gkioulekas, Eleftherios
2016-09-01
Using the fusion-rules hypothesis for three-dimensional and two-dimensional Navier-Stokes turbulence, we generalize a previous nonperturbative locality proof to multiple applications of the nonlinear interactions operator on generalized structure functions of velocity differences. We call this generalization of nonperturbative locality to multiple applications of the nonlinear interactions operator "multilocality." The resulting cross terms pose a new challenge requiring a new argument and the introduction of a new fusion rule that takes advantage of rotational symmetry. Our main result is that the fusion-rules hypothesis implies both locality and multilocality in both the IR and UV limits for the downscale energy cascade of three-dimensional Navier-Stokes turbulence and the downscale enstrophy cascade and inverse energy cascade of two-dimensional Navier-Stokes turbulence. We stress that these claims relate to nonperturbative locality of generalized structure functions on all orders and not the term-by-term perturbative locality of diagrammatic theories or closure models that involve only two-point correlation and response functions.
Computation of 3D steady Navier-Stokes flow with free-surface gravity waves
Lewis, M.R.; Koren, B.; Raven, H.C.
2003-01-01
In this paper an iterative method for the computation of stationary gravity-wave solutions is investigated, using a novel formulation of the free-surface (FS) boundary-value problem. This method requires the solution of a sequence of stationary Reynolds-Averaged Navier-Stokes subproblems employing t
Computation of 3D Steady Navier-Stokes Flow with Free-Surface Gravity Waves
Lewis, M.R.; Koren, B.; Raven, H.C.
2003-01-01
In this paper an iterative method for the computation of stationary gravity-wave solutions is investigated, using a novel formulation of the free-surface (FS) boundary-value problem. This method requires the solution of a sequence of stationary Reynolds-Averaged Navier-Stokes subproblems employing t
Institute of Scientific and Technical Information of China (English)
Ying-hui ZHANG; Zhong TAN
2011-01-01
In this paper,we are concerned with the asymptotic behaviour of a weak solution to the NavierStokes equations for compressible barotropic flow in two space dimensions with the pressure function satisfying p(ρ) =a(ρ)logd(ρ) for large (ρ).Here d ＞ 2,a ＞ 0.We introduce useful tools from the theory of Orlicz spaces and construct a suitable function which approximates the density for time going to infinity.Using properties of this function,we can prove the strong convergence of the density to its limit state.The behaviour of the velocity field and kinetic energy is also briefly discussed.
Full Navier-Stokes analysis of a two-dimensional mixer/ejector nozzle for noise suppression
Debonis, James R.
1992-01-01
A three-dimensional full Navier-Stokes (FNS) analysis was performed on a mixer/ejector nozzle designed to reduce the jet noise created at takeoff by a future supersonic transport. The PARC3D computational fluid dynamics (CFD) code was used to study the flow field of the nozzle. The grid that was used in the analysis consisted of approximately 900,000 node points contained in eight grid blocks. Two nozzle configurations were studied: a constant area mixing section and a diverging mixing section. Data are presented for predictions of pressure, velocity, and total temperature distributions and for evaluations of internal performance and mixing effectiveness. The analysis provided good insight into the behavior of the flow.
Hindman, R. G.
1985-09-01
Theoretical background and several basic test cases are presented for a new, time dependent Navier-Stokes solver for two-dimensional and axisymmetric flows. The goal of the effort is to invoke state-of-the-art computational fluid dynamics (CFD) technology to improve modeling of viscous phenomenal and to increase the robustness of CFD analysis. The original motivation was inadequate representation of supersonic ramp-induced separation by existing CFD codes. The present work addresses that inadequacy by using modern numerical methods which accurately model signal propagation in high-speed fluid flow. This technique solves the Navier-Stokes equations in general curvilinear coordinates in a four-sided domain bounded by a wall, and upper boundary opposite the wall, an inflow boundary, and an outflow boundary. The interior algorithm is a flux-difference splitting method similar to that of Yang, Lombard, and Bershader, but is blended into a second order, implicit factored delta form. With implicitly treated boundary conditions, the solution is performed using a block tridiagonal method followed by an explicit updating of the boundaries. The resulting scheme satisfies the global conversation requirement to within the order of accuracy of the algorithm. The grid is generated using a relaxation Poisson solver. A systematic and rigorous development of the complete method is presented. Initial steps in code validation include successful reproduction of Couette and Blasius solutions.
Bailey, Harry E.; Beam, Richard M.
1991-01-01
Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.
Institute of Scientific and Technical Information of China (English)
A.S.J.AL-SAIF; 朱正佑
2003-01-01
The traditional differential quadrature method was improved by using the upwind difference scheme for the convectiveterms to solve the coupled two-dimensional incompressible Navier-stokes equations and heat equation. The new method was comparedwith the conventional differential quadrature method in the aspects of convergence and accuracy. The results show that the newmethod is more accurate, and has better convergence than the conventional differential quadrature method for numerically computingthe steady-state solution.
A one-parameter family of LAD methods for the steady-state Navier-Stokes equations
Mittal, R. C.; Sharma, P. K.
Numerical solutions for the square driven cavity flow problem have been obtained using the Laplacian-Driver Method. The Reynolds number of the driven cavity flow was in the range 1-500 for different values of Theta, the boundary condition parameter. The steps involved in the computational procedure are described, and computed values for primary vortex strength and vorticity at the vortex center are given in a table. On the basis of the numerical results, it is found that: (1) the LAD method developed here is more stable than the method developed by Roache (1975) for steady state Navier-Stokes equations; and (2), at small Reynolds numbers the behavior of CDC and CDD is the same, but for large Reynolds numbers (greater than 20), the accuracy and stability of CDD surpass those of CDC. Computed values for the size of the downstream secondary vortex confirmed the experimental results of Pan and Archivos (1966).
Novo, Sébastien; Novotný, Antonin
2002-01-01
We consider the steady compressible Navier-Stokes equations in the isentropic regime in a bounded domain of $\\mathbb{R}^{3}$. We show that the renormalized continuity equation holds even if the density is not square integrable. We use this result to prove existence of weak solutions under the sole hypothesis $\\gamma > 3/2$ for the adiabatic constant.
Jiang, Song
2011-01-01
We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \\gamma > 1. Generally speaking, the proof is based on the new weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method of weak convergence. Comparing with [12] where the spatially periodic case was studied, here we have to control the additional integral terms of both pressure and kinetic energy involving with the points near the boundary which become degenerate when the points approach the boundary. Such integral terms are estimated using some new techniques, i.e., we use the techniques of the mirror image and boundary straightening to prove that the weighted estimates of both pressure and kinetic energy for the points near the boundary can be controlled by the weighted estimates for the points on the boundary. Moreover, we prove that once the we...
Takagi, S.; Og˜uz, H. N.; Zhang, Z.; Prosperetti, A.
2003-05-01
This paper presents a new approach to the direct numerical simulation of particle flows. The basic idea is to use a local analytic representation valid near the particle to "transfer" the no-slip condition from the particle surface to the adjacent grid nodes. In this way the geometric complexity arising from the irregular relation between the particle boundary and the underlying mesh is avoided and fast solvers can be used. The results suggest that the computational effort increases very slowly with the number of particles so that the method is efficient for large-scale simulations. The focus here is on the two-dimensional case (cylindrical particles), but the same procedure, to be developed in forthcoming papers, applies to three dimensions (spherical particles). Several extensions are briefly discussed.
Efficient numerical solution of steady free-surface Navier-Stokes flow
Brummelen, E.H. van; Raven, H.C.; Koren, B.
2001-01-01
Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. The usual method for solving steady viscous free-surface flow subject to gravitation is alternating time integration of the kinematic cond
Energy Technology Data Exchange (ETDEWEB)
Perez Guerrero, Jesus Salvador
1995-12-31
Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author) 78 refs., 24 figs., 14 tabs.
Directory of Open Access Journals (Sweden)
Hannelore Breckner
2000-01-01
Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
RESIDUAL A POSTERIORI ERROR ESTIMATE OF A NEW TWO-LEVEL METHOD FOR STEADY NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Chunfeng REN; Yichen MA
2006-01-01
Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derived. A posteriori error estimate contains additional terms in comparison to the estimate for the solution obtained by the standard finite element method. The importance of the additional terms in the error estimates is investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than the convergence of discrete solution. The two-level method aims to solve the nonlinear problem on a coarse grid with less computational work,then to solve the linear problem on a fine grid, which is superior to the usual finite element method solving a similar nonlinear problem on the fine grid.
Messaris, G. T.; Papastavrou, C. A.; Loukopoulos, V. C.; Karahalios, G. T.
2009-08-01
A new finite-difference method is presented for the numerical solution of the Navier-Stokes equations of motion of a viscous incompressible fluid in two (or three) dimensions and in the primitive-variable formulation. Introducing two auxiliary functions of the coordinate system and considering the form of the initial equation on lines passing through the nodal point (x0, y0) and parallel to the coordinate axes, we can separate it into two parts that are finally reduced to ordinary differential equations, one for each dimension. The final system of linear equations in n-unknowns is solved by an iterative technique and the method converges rapidly giving satisfactory results. For the pressure variable we consider a pressure Poisson equation with suitable Neumann boundary conditions. Numerical results, confirming the accuracy of the proposed method, are presented for configurations of interest, like Poiseuille flow and the flow between two parallel plates with step under the presence of a pressure gradient.
Some observations on a new numerical method for solving Navier-Stokes equations
Kumar, A.
1981-01-01
An explicit-implicit technique for solving Navier-Stokes equations is described which, is much less complex than other implicit methods. It is used to solve a complex, two-dimensional, steady-state, supersonic-flow problem. The computational efficiency of the method and the quality of the solution obtained from it at high Courant-Friedrich-Lewy (CFL) numbers are discussed. Modifications are discussed and certain observations are made about the method which may be helpful in using it successfully.
Pulliam, Tom; Kwak, Dochan (Technical Monitor)
1997-01-01
Implicit methods have been the workhorse for the Euler and Navier-Stokes equations for the last 25 years. The ground breaking work of Dr. Joe Steger in implementing such techniques in practical Euler and Navier-Stokes codes provided the basis for all the success in this area. This presentation will highlight his contribution and technical excellence in the area of implicit methods for CFD.
An adjoint-based approach for finding invariant solutions of Navier-Stokes equations
Farazmand, Mohammad
2015-01-01
We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and traveling wave solutions of the Navier--Stokes equations. Using the adjoint equations, arbitrary initial conditions evolve to the vicinity of a (relative) equilibrium at which point a few Newton-type iterations yield the desired (relative) equilibrium solution. We apply this adjoint-based method to a chaotic two-dimensional Kolmogorov flow. A convergence rate of 100% is observed, leading to the discovery of 21 new steady state and traveling wave solutions at Reynolds number Re=40. Some of the new invariant solutions have spatially localized structures that were previously believed to only exist on domains with large aspect ratios. We show that one of the newly found steady state solutions underpins the temporal intermittencies, i.e., high energy dissipation episodes of the flo...
Carling; Williams; Bowtell
1998-12-01
Anguilliform swimming has been investigated by using a computational model combining the dynamics of both the creature's movement and the two-dimensional fluid flow of the surrounding water. The model creature is self-propelled; it follows a path determined by the forces acting upon it, as generated by its prescribed changing shape. The numerical solution has been obtained by applying coordinate transformations and then using finite difference methods. Results are presented showing the flow around the creature as it accelerates from rest in an enclosed tank. The kinematics and dynamics associated with the creature's centre of mass are also shown. For a particular set of body shape parameters, the final mean swimming speed is found to be 0.77 times the speed of the backward-travelling wave. The corresponding movement amplitude envelope is shown. The magnitude of oscillation in the net forward force has been shown to be approximately twice that in the lateral force. The importance of allowing for acceleration and deceleration of the creature's body (rather than imposing a constant swimming speed) has been demonstrated. The calculations of rotational movement of the body and the associated moment of forces about the centre of mass have also been included in the model. The important role of viscous forces along and around the creature's body and in the growth and dissolution of the vortex structures has been illustrated.
Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability
Arnaudon, Marc
2010-01-01
We prove a variational principle for stochastic Lagrangian Navier-Stokes trajectories on manifolds. We study the behaviour of such trajectories concerning stability as well as rotation between particles; the two-dimensional torus case is described in detail.
Navier Stokes Theorem in Hydrology
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
Navier-Stokes predictions of multifunction nozzle flows
Wilmoth, Richard G.; Leavitt, Laurence D.
1987-10-01
A two-dimensional, Navier-Stokes code developed by Imlay based on the implicit, finite-volume method of MacCormack has been applied to the prediction of the flow fields and performance of several nonaxisymmetric, convergent-divergent nozzles with and without thrust vectoring. Comparisons of predictions with experiment show that the Navier-Stokes code can accurately predict both the flow fields and performance for nonaxisymmetric nozzles where the flow is predominantly two-dimensional and at nozzle pressure ratios at or above the design values. Discrepancies between predictions and experiment are noted at lower nozzle pressure ratios where separation typically occurs in portions of the nozzle. The overall trends versus parameters such as nozzle pressure ratio, flap angle, and vector angle were generally predicted correctly.
The Navier-Stokes Equations II
Masuda, Kyûya; Rautmann, Reimund; Solonnikov, Vsevolod
1992-01-01
V.A. Solonnikov, A. Tani: Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid.- W. Borchers, T. Miyakawa:On some coercive estimates for the Stokes problem in unbounded domains.- R. Farwig, H. Sohr: An approach to resolvent estimates for the Stokes equations in L(q)-spaces.- R. Rannacher: On Chorin's projection method for the incompressible Navier-Stokes equations.- E. S}li, A. Ware: Analysis of the spectral Lagrange-Galerkin method for the Navier-Stokes equations.- G. Grubb: Initial value problems for the Navier-Stokes equations with Neumann conditions.- B.J. Schmitt, W. v.Wahl: Decomposition of solenoidal fields into poloidal fields, toroidal fields and the mean flow. Applications to the Boussinesq-equations.- O. Walsh: Eddy solutions of the Navier-Stokesequations.- W. Xie: On a three-norm inequality for the Stokes operator in nonsmooth domains.
A study of the efficiency of various Navier-Stokes solvers. [finite difference methods
Atias, M.; Wolfshtein, M.; Israeli, M.
1975-01-01
A comparative study of the efficiency of some finite difference methods for the solution of the Navier-Stokes equations was conducted. The study was restricted to the two-dimensional steady, uniform property vorticity-stream function equations. The comparisons were drawn by recording the CPU time required to obtain a solution as well as the accuracy of this solution using five numerical methods: central differences, first order upwind differences, second order upwind differences, exponential differences, and an ADI solution of the central difference equations. Solutions were obtained for two test cases: a recirculating eddy inside a square cavity with a moving top, and an impinging jet flow. The results show that whenever the central difference method is stable it generates results with a given accuracy for less CPU time than any other method.
On Bifurcating Time-Periodic Flow of a Navier-Stokes Liquid Past a Cylinder
Galdi, Giovanni P.
2016-10-01
We provide general sufficient conditions for the existence and uniqueness of branching out of a time-periodic family of solutions from steady-state solutions to the two-dimensional Navier-Stokes equations in the exterior of a cylinder. By separating the time-independent averaged component of the velocity field from its oscillatory one, we show that the problem can be formulated as a coupled elliptic-parabolic nonlinear system in appropriate and distinct function spaces, with the property that the relevant linearized operators become Fredholm of index 0. In this functional setting, the notorious difficulty of 0 being in the essential spectrum entirely disappears and, in fact, it is even meaningless. Our approach is different and, we believe, more natural and simpler than those proposed by previous authors discussing similar questions. Moreover, the latter all fail, when applied to the problem studied here.
An efficient transient Navier-Stokes solver on compact nonuniform space grids
Kalita, Jiten C.; Dass, Anoop K.; Nidhi, Nimisha
2008-04-01
In this paper, we propose an implicit higher-order compact (HOC) finite difference scheme for solving the two-dimensional (2D) unsteady Navier-Stokes (N-S) equations on nonuniform space grids. This temporally second-order accurate scheme which requires no transformation from the physical to the computational plane is at least third-order accurate in space, which has been demonstrated with numerical experiments. It efficiently captures both transient and steady-state solutions of the N-S equations with Dirichlet as well as Neumann boundary conditions. The proposed scheme is likely to be very useful for the computation of transient viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variation. Numerical results are presented and compared with analytical as well as established numerical data. Excellent comparison is obtained in all the cases.
Efficient solution of two-dimensional steady separated flows
Napolitano, M.
This work is concerned with the numerical solution of 2D incompressible steady laminar separated flows at moderate-to-high values of Re. The vorticity-stream function Navier-Stokes equations, as well as approximate models based upon the boundary-layer theory, will be considered. The main objective of the paper is to present the development of an efficient approach for solving a class of problems usually referred to as high Re weakly separated flows. A description is given of a block-alternating-direction-implicit method, which applies the approximate factorization scheme of Beam and Warming to the vorticity-stream function equations, using the delta form of the deferred correction procedure of Khosla and Rubin to combine the stability of upwind schemes with the accuracy of central differences. The logical steps which led to the development of a more efficient incremental block-line Gauss-Seidel method and to a simple multigrid strategy particularly suited for this kind of numerical scheme are then outlined. Finally, benchmark-quality solutions for separated flows inside diffusers and channels with smooth as well as sudden expansions are presented.
THE NAVIER-STOKES EQUATIONS IN STREAM LAYER AND ON STREAM SURFACE AND A DIMENSION SPLIT METHODS
Institute of Scientific and Technical Information of China (English)
李开泰; 黄艾香
2002-01-01
In this paper,we proposal stream surface and stream layer. By using classical tensor calculus, we derive 3-D Navier-Stokes Equations(NSE) in the stream layer under semigeodesic coordinate system, Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface, a nonlinear initial-boundary value problem satisfies by stream function is obtained, existence and uniqueness of its solution are proven. Based this theory we proposal a new method called "dimension split method" to solve 3D NSE.
Stochastic nonhomogeneous incompressible Navier-Stokes equations
Cutland, Nigel J.; Enright, Brendan
We construct solutions for 2- and 3-D stochastic nonhomogeneous incompressible Navier-Stokes equations with general multiplicative noise. These equations model the velocity of a mixture of incompressible fluids of varying density, influenced by random external forces that involve feedback; that is, multiplicative noise. Weak solutions for the corresponding deterministic equations were first found by Kazhikhov [A.V. Kazhikhov, Solvability of the initial and boundary-value problem for the equations of motion of an inhomogeneous viscous incompressible fluid, Soviet Phys. Dokl. 19 (6) (1974) 331-332; English translation of the paper in: Dokl. Akad. Nauk SSSR 216 (6) (1974) 1240-1243]. A stochastic version with additive noise was solved by Yashima [H.F. Yashima, Equations de Navier-Stokes stochastiques non homogènes et applications, Thesis, Scuola Normale Superiore, Pisa, 1992]. The methods here extend the Loeb space techniques used to obtain the first general solutions of the stochastic Navier-Stokes equations with multiplicative noise in the homogeneous case [M. Capiński, N.J. Cutland, Stochastic Navier-Stokes equations, Applicandae Math. 25 (1991) 59-85]. The solutions display more regularity in the 2D case. The methods also give a simpler proof of the basic existence result of Kazhikhov.
Is Navier-Stokes turbulence chaotic?
Deissler, R. G.
1986-01-01
Whether turbulent solutions of the Navier-Stokes equations are chaotic is considered. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions separate exponentially with time, having a positive Liapunov characteristic exponent. Thus the turbulence is characterized as chaotic.
Energy Technology Data Exchange (ETDEWEB)
Henandez Rosete, Alejandro; Mazur C, Zdzislaw [Instituto de Investigaciones Electricas, Cuernavaca, Morelos (Mexico)
2007-11-15
The results of the simulation by CFD (Computacional Fluid Dynamics) realized to the first stage of a gas turbine GE Frame 7 are presented. The analysis includes the 3D modeling of the flow channel in the nozzle and the movable blade to know the velocities distributions, temperatures and pressures of the main hot gas flow that are developed in the Inter stage. The results are influenced by the imposed border conditions in the properties of the main flow, the rotation of the movable blade, as well as the simulation of cooling air injection in the nozzle. The present study focuses in the validation of the model of the meshes of the ensemble nozzle-blade, for later realize an analysis of conjugated heat transfer in a model with ceramic lining type heat barrier (THB) in the movable blade. The analysis is realized in a CFD commercial code oriented to turbo-machinery using the equations of unstable flows 3D of Navier Stokes. [Spanish] Se presentan los resultados de la simulacion por CFD (Computacional Fluid Dynamics) realizada a la primera etapa de una turbina de gas GE Frame 7. El analisis incluye la modelacion tridimensional del canal de flujo en la tobera y el alabe movil para conocer las distribuciones de las velocidades, temperaturas y presiones del flujo principal de gases calientes que se desarrollan en la inter etapa. Los resultados son influenciados por las condiciones de frontera impuestos en las propiedades del flujo principal, la rotacion del alabe movil, asi como la simulacion de inyeccion de aire de enfriamiento en la tobera. El presente estudio se enfoca en la validacion del modelo de la malla del conjunto tobera-alabe, para posteriormente realizar un analisis de transferencia de calor conjugada en un modelo con recubrimiento ceramico tipo barrera termica (TBC) en el alabe movil. El analisis es realizado en un codigo de CFD comercial orientado a turbomaquinaria utilizando las ecuaciones de flujos inestables 3D de Navier Stokes.
Towards an ideal preconditioner for linearized Navier-Stokes problems
Energy Technology Data Exchange (ETDEWEB)
Murphy, M.F. [Univ. of Bristol (United Kingdom)
1996-12-31
Discretizing certain linearizations of the steady-state Navier-Stokes equations gives rise to nonsymmetric linear systems with indefinite symmetric part. We show that for such systems there exists a block diagonal preconditioner which gives convergence in three GMRES steps, independent of the mesh size and viscosity parameter (Reynolds number). While this {open_quotes}ideal{close_quotes} preconditioner is too expensive to be used in practice, it provides a useful insight into the problem. We then consider various approximations to the ideal preconditioner, and describe the eigenvalues of the preconditioned systems. Finally, we compare these preconditioners numerically, and present our conclusions.
Institute of Scientific and Technical Information of China (English)
D.C. Wan; G.W. Wei
2000-01-01
An efficient discrete singular convolution (DSC) method is introduced to the numerical solutions of incompressible Euler and Navier-Stokes equations with periodic boundary conditions. Two numerical tests of two-dimensional NavierStokes equations with periodic boundary conditions and Euler equations for doubly periodic shear layer flows are carried out by using the DSC method for spatial derivatives and fourth-order Runge-Kutta method for time advancement, respectively. The computational results show that the DSC method is efficient and robust for solving the problems of incompressible flows, and has the potential of being extended to numerically solve much broader problems in fluid dynamics.
Navier-Stokes analysis of turbomachinery blade external heat transfer
Ameri, A. A.; Sockol, P. M.; Gorla, R. S. R.
1992-01-01
The two-dimensional, compressible, thin-layer Navier-Stokes and energy equations were solved numerically to obtain heat transfer rates on turbomachinery blades. The Baldwin-Lomax algebraic model and the q - omega low Reynolds number, two-equation model were used for modeling of turbulence. For the numerical solution of the governing equations a four-stage Runge-Kutta solver was employed. The turbulence model equations were solved using an implicit scheme. Numerical solutions are presented for two-dimensional flow within two vane cascades. The heat transfer results and the pressure distributions were compared with published experimental data. The agreement between the numerical calculations and the experimental values were found to be generally favorable. The position of transition from laminar to turbulent flow was also predicted accurately.
Navier-Stokes computations of separated vortical flows past prolate spheroid at incidence
Wong, Tin-Chee; Kandil, Osama A.; Liu, C. H.
1989-01-01
The problem of steady incompressible viscous flow past prolate spheroids at incidence is formulated using the unsteady incompressible and compressible thin-layer Navier-Stokes equations. The two sets of Navier-Stokes equations are solved using a pseudotime stepping of the implicit flux-difference splitting scheme on a curvilinear grid, which is generated by a transfinite grid generator. The Baldwin and Lomax (1978) algebraic eddy-viscosity model is used to model the turbulent flow. The computational applications cover a 6:1 prolate spheroid at different angles of attack and Reynolds numbers. The results are compared with experimental data.
A MIXED FINITE ELEMENT METHOD ON A STAGGERED MESH FOR NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Houde Han; Ming Yan
2008-01-01
In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 - P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtained for both the velocity and the pressure.Numerical examples are presented to illustrate the effectiveness of the proposed method.
On Kato's Method for Navier Stokes Equations
Haak, Bernhard H.; Kunstmann, Peer Chr.
2009-10-01
We investigate Kato’s method for parabolic equations with a quadratic non-linearity in an abstract form. We extract several properties known from linear systems theory which turn out to be the essential ingredients for the method. We give necessary and sufficient conditions for these conditions and provide new and more general proofs, based on real interpolation. In application to the Navier Stokes equations, our approach unifies several results known in the literature, partly with different proofs. Moreover, we establish new existence and uniqueness results for rough initial data on arbitrary domains in {mathbb{R}}3 and irregular domains in {mathbb{R}}n.
Some topics of Navier-Stokes solvers
Honma, H.; Nishikawa, N.
1990-03-01
The process of numerical simulation consists of selection of some items: a mathematical model, a numerical scheme, the level of the computer, and post processing. From this point of view, recent numerical studies of viscous flows are described especially for the fluid engineering laboratories in the Chiba University. The examples of simulations are Mach reflection on a wedge using a kinetic model equation and a cylinder-plate juncture flow using incompressible Navier Stokes equation. Some attempts at graphic monitoring of fluid mechanical calculations are also shown for some combinations of computers with Computational Fluid Dynamics (CFD) solvers.
Preconditioners for Incompressible Navier-Stokes Solvers
Institute of Scientific and Technical Information of China (English)
A.Segal; M.ur Rehman; C.Vuik
2010-01-01
In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method. It is shown that block precon- ditioners form an excellent approach for the solution, however if the grids are not to fine preconditioning with a Saddle point ILU matrix (SILU) may be an attractive al- ternative. The applicability of all methods to stabilized elements is investigated. In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.
Perturbation of eigenvalues of preconditioned Navier-Stokes operators
Energy Technology Data Exchange (ETDEWEB)
Elman, H.C. [Univ. of Maryland, College Park, MD (United States)
1996-12-31
We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steady-state Navier-Stokes equations. In particular, for several choices of preconditioners applied to the system of discrete equations, we derive upper bounds on perturbations of eigenvalues as functions of the viscosity and discretization mesh size. The bounds suggest that the sensitivity of the eigenvalues is at worst linear in the inverse of the viscosity and quadratic in the inverse of the mesh size, and that scaling can be used to decrease the sensitivity in some cases. Experimental results supplement these results and confirm the relatively mild dependence on viscosity. They also indicate a dependence on the mesh size of magnitude smaller than the analysis suggests.
Possibility of turbulence from a post-Navier-Stokes equation
Energy Technology Data Exchange (ETDEWEB)
Getreuer, Pascal [Mathematics Department, University of California, Los Angeles, Los Angeles, CA 90095 (United States); Albano, A.M. [Department of Physics, Bryn Mawr College, Bryn Mawr, PA 19010 (United States)]. E-mail: aalbano@brynmawr.edu; Muriel, A. [Data Transport Systems, 347 East 62nd street, New York, NY 10021 (United States)
2007-06-18
We introduce corrections to the Navier-Stokes equation arising from the transitions between molecular states and the injection of external energy. In the simplest application of the proposed post-Navier-Stokes equation, we find a multi-valued velocity field and the immediate possibility of velocity reversal, both features of turbulence.
Possibility of Turbulence from a Post-Navier-Stokes Equation
Getreuer, P; Muriel, A; Getreuer, Pascal
2006-01-01
We introduce corrections to the Navier-Stokes equation arising from the transitions between molecular states and the injection of external energy. In the simplest application of the proposed post Navier-Stokes equation, we find a multi-valued velocity field and the immediate possibility of velocity reversal, both features of turbulence.
COMPARISON OF STABILITY BETWEEN NAVIER-STOKES AND EULER EQUATIONS
Institute of Scientific and Technical Information of China (English)
SHI Wei-hui; WANG Yue-peng; SHEN Chun
2006-01-01
The stability about Navier-Stokes equation and Euler equation was brought into comparison. And by taking their typical initial value problem for example, the reason of leading to the difference in stability between Navier-Stokes equation and Euler equation was also analyzed.
Tip loss correction for actuator / Navier Stokes computations
DEFF Research Database (Denmark)
Shen, Wen Zhong; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming
2004-01-01
The new tip loss correction, initially developed for ID BEM computations [1], is now extended to 2D Actuator Disc / Navier-Stokes (AD/NS) computations and 3D Actuator Line / Navier-Stokes (AL/NS) computations. As shown in the paper, the tip loss correction is an important and necessary step...
Equivalence of dynamical ensembles and Navier-Stokes equations
Gallavotti, G
1996-01-01
A reversible version of the Navier Stokes equation is studied. A conjecture emerges stating the equivalence between the reversible equation and the usual Navier Stokes equation. The latter appears as a statement of ensembles equivalence in the limit of infinite Reynolds number, which plays the role of the thermodynamic limit.
Generalized extended Navier-Stokes theory
DEFF Research Database (Denmark)
Hansen, J. S.; Daivis, Peter J.; Dyre, Jeppe C.
2013-01-01
in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime......The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present...... and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies...
Institute of Scientific and Technical Information of China (English)
Yin-nianHe
2004-01-01
In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a H1-optimal velocity approximation and a L2-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small,nonlinear Navier-Stokes problem on the coarse mesh with mesh size H, one linear Stokes problem on the fine mesh with mesh size h <
A multigrid solver for the vorticity-velocity Navier-Stokes equations
Napolitano, M.; Catalano, L. A.
1991-06-01
This paper provides a multigrid incremental line-Gauss-Seidel method for solving the steady Navier-Stokes equations in two and three dimensions expressed in terms of the vorticity and velocity variables. The system of parabolic and Poisson equations governing the scalar components of the vector unknowns is solved using centered finite differences on a nonstaggered grid. Numerical results for the two-dimensional driven cavity problem indicate that the spatial discretization of the equation defining the value of the vorticity on the boundary is extremely critical to obtaining accurate solutions. In fact, a standard one-sided three-point second-order-accurate approximation produces very inaccurate results for moderate-to-high values of the Reynolds number unless an exceedingly fine mesh is employed. On the other hand, a compact two-point second-order-accurate discretization is found to be always satisfactory and provides accurate solutions for Reynolds number up to 3200, a target impossible heretofore using this formulation and a nonstaggered grid.
Syrakos, Alexandros
2015-01-01
A methodology is proposed for the calculation of the truncation error of finite volume discretisations of the incompressible Navier-Stokes equations on colocated grids. The truncation error is estimated by restricting the solution obtained on a given grid to a coarser grid and calculating the image of the discrete Navier-Stokes operator of the coarse grid on the restricted velocity and pressure field. The proposed methodology is not a new concept but its application to colocated finite volume discretisations of the incompressible Navier-Stokes equations is made possible by the introduction of a variant of the momentum interpolation technique for mass fluxes where the pressure-part of the mass fluxes is not dependent on the coefficients of the linearised momentum equations. The theory presented is supported by a number of numerical experiments. The methodology is developed for two-dimensional flows, but extension to three-dimensional cases should not pose problems.
Turbomachinery blade design using a Navier-Stokes solver and artificial neural network
Energy Technology Data Exchange (ETDEWEB)
Pierret, S.; Van den Braembussche, R.A. [von Karman Inst. for Fluid dynamics, Rhode-Saint-Genese (Belgium). Turbomachinery Dept.
1999-04-01
This paper describes a knowledge-based method for the automatic design of more efficient turbine blades. An Artificial Neural Network (ANN) is used to construct an approximate model (response surface) using a database containing Navier-Stokes solutions for all previous designs. This approximate model is used for the optimization, by means of Simulated Annealing (SA), of the blade geometry, which is then analyzed by a Navier-Stokes solver. This procedure results in a considerable speed-up of the design process by reducing both the interventions of the operator and the computational effort. It is also shown how such a method allows the design of more efficient blades while satisfying both the aerodynamic and mechanical constraints. The method has been applied to different types of two-dimensional turbine blades, of which three examples are presented in this paper.
Chaos Synchronization in Navier-Stokes Turbulence
Lalescu, Cristian; Meneveau, Charles; Eyink, Gregory
2013-03-01
Chaos synchronization (CS) has been studied for some time now (Pecora & Carroll 1990), for systems with only a few degrees of freedom as well as for systems described by partial differential equations (Boccaletti et al 2002). CS in general is said to be present in coupled dynamical systems when a specific property of each system has the same time evolution for all, even though the evolution itself is chaotic. The Navier-Stokes (NS) equations describe the velocity for a wide range of fluids, and their solutions are usually called turbulent if fluctuation amplitudes decrease as a power of their wavenumber. There have been some studies of CS for continuous systems (Kocarev et al 1997), but CS for NS turbulence seems not to have been investigated so far. We focus on the synchronization of the small scales of a turbulent flow for which the time history of large scales is prescribed. Our DNS results show that high-wavenumbers in turbulence are fully slaved to modes with wavenumbers up to a critical fraction of the Kolmogorov dissipation wavenumber. The motivation for our work is to study deeply sub-Kolmogorov scales in fully developed turbulence (Schumacher 2007), which we found to be recoverable even at very high Reynolds number from simulations with moderate resolutions. This work is supported by the National Science Foundation's CDI-II program, project CMMI-0941530
Scaling Navier-Stokes Equation in Nanotubes
Garajeu, Mihail; Saccomandi, Giuseppe
2013-01-01
On one hand, classical Monte Carlo and molecular dynamics (MD) simulations have been very useful in the study of liquids in nanotubes, enabling a wide variety of properties to be calculated in intuitive agreement with experiments. On the other hand, recent studies indicate that the theory of continuum breaks down only at the nanometer level; consequently flows through nanotubes still can be investigated with Navier-Stokes equations if we take suitable boundary conditions into account. The aim of this paper is to study the statics and dynamics of liquids in nanotubes by using methods of non-linear continuum mechanics. We assume that the nanotube is filled with only a liquid phase; by using a second gradient theory the static profile of the liquid density in the tube is analytically obtained and compared with the profile issued from molecular dynamics simulation. Inside the tube there are two domains: a thin layer near the solid wall where the liquid density is non-uniform and a central core where the liquid de...
Scaling properties of Navier-Stokes turbulence
Institute of Scientific and Technical Information of China (English)
Zhao-cun LIU
2009-01-01
The property of the velocity field and the cascade process of the fluid flow are key problems in turbulence research. This study presents the scaling property of the turbulent velocity field and a mathematical description of the cascade process, using the following methods: (1) a discussion of the general self-similarity and scaling invariance of fluid flow from the viewpoint of the physical mechanism of turbulent flow; (2) the development of the relationship between the scaling indices and the key parameters of the She and Leveque (SL) model in the inertial range; (3) an investigation of the basis of the fractal model and the multi-fractal model of turbulence; (4) a demonstration of the physical meaning of the flowing field scaling that is related to the real flowing vortex. The results illustrate that the SL model could be regarded as an approximate mathematical solution of Navier-Stokes (N-S) equations, and that the phenomena of normal scaling and anomalous scaling is the result of the mutual interactions among the physical factors of nonlinearity, dissipation, and dispersion. Finally, a simple turbulent movement conceptional description model is developed to show the local properties and the instantaneous properties of turbulence.
The Actuator Surface Model: A New Navier-Stokes Based Model for Rotor Computations
DEFF Research Database (Denmark)
Shen, Wen Zhong; Zhang, J.H.; Sørensen, Jens Nørkær
2009-01-01
This paper presents a new numerical technique for simulating two-dimensional wind turbine flow. The method, denoted as the 2D actuator surface technique, consists of a two-dimensional Navier-Stokes solver in which the pressure distribution is represented by body forces that are distributed along...... the chord of the airfoils. The distribution of body force is determined from a set of predefined functions that depend on angle of attack and airfoil shape. The predefined functions are curve fitted using pressure distributions obtained either from viscous-inviscid interactive codes or from full Navier...
Existence and properties of the Navier-Stokes equations
Zhirkin, Alexey V.
2016-01-01
A proof of existence, uniqueness and smoothness of the Navier-Stokes equations is an actual problem, which solution is important for different branches of science. The subject of this study is obtaining the smooth and unique solutions of the three-dimension Stokes-Navier equations for the initial and boundary value problem. The analysis shows that there exist no viscous solutions of the Navier-Stokes equations in three dimensions. The reason is the insufficient capability of the divergence-fr...
Compressible Navier-Stokes Equations with Revised Maxwell's Law
Hu, Yuxi; Racke, Reinhard
2017-03-01
We investigate the compressible Navier-Stokes equations where the constitutive law for the stress tensor given by Maxwell's law is revised to a system of relaxation equations for two parts of the tensor. The global well-posedness is proved as well as the compatibility with the classical compressible Navier-Stokes system in the sense that, for vanishing relaxation parameters, the solutions to the Maxwell system are shown to converge to solutions of the classical system.
Reynolds-averaged Navier-Stokes based ice accretion for aircraft wings
Lashkajani, Kazem Hasanzadeh
This thesis addresses one of the current issues in flight safety towards increasing icing simulation capabilities for prediction of complex 2D and 3D glaze ice shapes over aircraft surfaces. During the 1980's and 1990's, the field of aero-icing was established to support design and certification of aircraft flying in icing conditions. The multidisciplinary technologies used in such codes were: aerodynamics (panel method), droplet trajectory calculations (Lagrangian framework), thermodynamic module (Messinger model) and geometry module (ice accretion). These are embedded in a quasi-steady module to simulate the time-dependent ice accretion process (multi-step procedure). The objectives of the present research are to upgrade the aerodynamic module from Laplace to Reynolds-Average Navier-Stokes equations solver. The advantages are many. First, the physical model allows accounting for viscous effects in the aerodynamic module. Second, the solution of the aero-icing module directly provides the means for characterizing the aerodynamic effects of icing, such as loss of lift and increased drag. Third, the use of a finite volume approach to solving the Partial Differential Equations allows rigorous mesh and time convergence analysis. Finally, the approaches developed in 2D can be easily transposed to 3D problems. The research was performed in three major steps, each providing insights into the overall numerical approaches. The most important realization comes from the need to develop specific mesh generation algorithms to ensure feasible solutions in very complex multi-step aero-icing calculations. The contributions are presented in chronological order of their realization. First, a new framework for RANS based two-dimensional ice accretion code, CANICE2D-NS, is developed. A multi-block RANS code from U. of Liverpool (named PMB) is providing the aerodynamic field using the Spalart-Allmaras turbulence model. The ICEM-CFD commercial tool is used for the iced airfoil
Singularity of Navier-Stokes Equations Leading to Turbulent Transition
Dou, Hua-Shu; Fluid Mechanics Research Team
2014-11-01
As is well known, there is discontinuity during the transition from laminar flow to turbulence in the time-averaged Navier-Stokes equations. In other words, singularity may implicitly exist in the Navier-Stokes equations. Transition of a laminar flow to turbulence must be implemented via the singularity. However, how the singularity of Navier-Stokes equations is related to the turbulent transition is not understood. In this study, the singularity possibly hidden in the Navier-Stokes equation is exactly derived by mathematical treatment. Then, it is found that for pressure driven flows, the singularity of Navier-Stokes equations corresponds to the inflection point on the velocity profile. Since the rate of amplification to a disturbance at the inflection point is infinite, the laminar flow is able to involve into turbulence at this point firstly at a sufficient high Reynolds number. This is the reason why turbulent spot is formed at the location of inflection point. It is further demonstrated that the existence of the singularity in the time-averaged Navier-Stokes equations is the necessary and sufficient condition for the turbulent transition in pressure driven flows. These results agrees well with the findings from the recent proposed energy gradient method. Professor in Fluid Mechanics; AIAA Associate Fellow.
Three-dimensional Navier-Stokes heat transfer predictions for turbine blade rows
Boyle, Robert J.; Giel, Paul W.
1992-01-01
Results are shown for a three-dimensional Navier-Stokes analysis of both the flow and the surface heat transfer for turbine applications. Heat transfer comparisons are made with the experimental shock-tunnel data of Dunn and Kim, and with the data of Blair for the rotor of the large scale rotating turbine. The analysis was done using the steady-state, three-dimensional, thin-layer Navier-Stokes code developed by Chima, which uses a multistage Runge-Kutta scheme with implicit residual smoothing. An algebraic mixing length turbulence model is used to calculate turbulent eddy viscosity. The variation in heat transfer due to variations in grid parameters is examined. The effects of rotation, tip clearance, and inlet boundary layer thickness variation on the predicted blade and endwall heat transfer are examined.
Hydrodynamics beyond Navier-Stokes: the slip flow model.
Yudistiawan, Wahyu P; Ansumali, Santosh; Karlin, Iliya V
2008-07-01
Recently, analytical solutions for the nonlinear Couette flow demonstrated the relevance of the lattice Boltzmann (LB) models to hydrodynamics beyond the continuum limit [S. Ansumali, Phys. Rev. Lett. 98, 124502 (2007)]. In this paper, we present a systematic study of the simplest LB kinetic equation-the nine-bit model in two dimensions--in order to quantify it as a slip flow approximation. Details of the aforementioned analytical solution are presented, and results are extended to include a general shear- and force-driven unidirectional flow in confined geometry. Exact solutions for the velocity, as well as for pertinent higher-order moments of the distribution functions, are obtained in both Couette and Poiseuille steady-state flows for all values of rarefaction parameter (Knudsen number). Results are compared with the slip flow solution by Cercignani, and a good quantitative agreement is found for both flow situations. Thus, the standard nine-bit LB model is characterized as a valid and self-consistent slip flow model for simulations beyond the Navier-Stokes approximation.
Some strange numerical solutions of the non-stationary Navier-Stokes equations in pipes
Energy Technology Data Exchange (ETDEWEB)
Rummler, B.
2001-07-01
A general class of boundary-pressure-driven flows of incompressible Newtonian fluids in three-dimensional pipes with known steady laminar realizations is investigated. Considering the laminar velocity as a 3D-vector-function of the cross-section-circle arguments, we fix the scale for the velocity by the L{sub 2}-norm of the laminar velocity. The usual new variables are introduced to get dimension-free Navier-Stokes equations. The characteristic physical and geometrical quantities are subsumed in the energetic Reynolds number Re and a parameter {psi}, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form u=u{sub L}+u, where u{sub L} is the scaled laminar velocity and periodical conditions in center-line-direction are prescribed for u. An autonomous system (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction is got by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u. The finite-dimensional approximations u{sub N({lambda}}{sub )} of u are defined in the usual way. (orig.)
Shockwaves and Local Hydrodynamics; Failure of the Navier-Stokes Equations
Hoover, Wm G
2009-01-01
Shockwaves provide a useful route to the nonequilibrium properties of simple fluids far from equilibrium. For simplicity, we study a strong shockwave in a dense two-dimensional fluid. Here, our study of such nonlinear transport properties makes plain the connection between the observed local hydrodynamic variables (like the various gradients and fluxes) and the chosen recipes for defining (or "measuring") those variables. The range over which hydrodynamic averages are computed turns out to be much more significant than are the other details of the averaging algorithms. The results show clearly the incompatibility of microscopic time-reversible dynamics with macroscopic irreversible models like the Navier-Stokes equations.
Study of blade-tower interaction using a 2D Navier-Stokes solver
Energy Technology Data Exchange (ETDEWEB)
Bertagnolio, F. [Risoe National Lab., Wind Energy and Atmospheric Physics Dept., Roskilde (Denmark)
1999-03-01
The aim of this work is to model and study the dynamic interaction of the fluid flow with the structure which occurs when the blades of a wind turbine are passing in front of (or possibly behind) the tower. In order to capture the whole complexity of this phenomenon, the full unsteady Navier-Stokes equations for an incompressible fluid are used as a model. A new computational technique is described. For the sake of simplicity, we restrict ourselves to two-dimensional cases. The present methodology is illustrated by the computation of a wind turbine-like configuration in a periodic domain. (au)
A Nine-modes Truncation of the Plane Incompressible Navier-Stokes Equations
Institute of Scientific and Technical Information of China (English)
WANG HE-YUAN; CUI YAN; Yin Jing-xue
2011-01-01
In this paper a nine-modes truncation of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained.The stationary solutions,the existence of attractor and the global stability of the equations are firmly proved.What is more,that the force f acts on the mode k3 and k7 respectively produces two systems,which lead to a much richer and varied phenomenon.Numerical simulation is given at last,which shows a.stochastic behavior approached through an involved sequence of bifurcations.
Evaluation of a research circulation control airfoil using Navier-Stokes methods
Shrewsbury, George D.
1987-01-01
The compressible Reynolds time averaged Navier-Stokes equations were used to obtain solutions for flows about a two dimensional circulation control airfoil. The governing equations were written in conservation form for a body-fitted coordinate system and solved using an Alternating Direction Implicit (ADI) procedure. A modified algebraic eddy viscosity model was used to define the turbulent characteristics of the flow, including the wall jet flow over the Coanda surface at the trailing edge. Numerical results are compared to experimental data obtained for a research circulation control airfoil geometry. Excellent agreement with the experimental results was obtained.
Existence and properties of the Navier-Stokes equations
Zhirkin, Alexey V
2016-01-01
A proof of existence, uniqueness and smoothness of the Navier-Stokes equations is an actual problem, which solution is important for different branches of science. The subject of this study is obtaining the smooth and unique solutions of the three-dimension Stokes-Navier equations for the initial and boundary value problem. The analysis shows that there exist no viscous solutions of the Navier-Stokes equations in three dimensions. The reason is the insufficient capability of the divergence-free velocity field. It is necessary to modify the Navier-Stokes equations for obtaining the desirable solutions. The modified equations describe a three-dimension flow of incompressible fluid which sticks to a body surface. The equation solutions show the resonant blowup of the laminar flow, laminar-turbulent transition, the fluid detachment that opens the way to solve the magnetic dynamo problem.
Error estimation and adaptivity in Navier-Stokes incompressible flows
Wu, J.; Zhu, J. Z.; Szmelter, J.; Zienkiewicz, O. C.
1990-07-01
An adaptive remeshing procedure for solving Navier-Stokes incompressible fluid flow problems is presented in this paper. This procedure has been implemented using the error estimator developed by Zienkiewicz and Zhu (1987, 1989) and a semi-implicit time-marching scheme for Navier-Stokes flow problems (Zienkiewicz et al. 1990). Numerical examples are presented, showing that the error estimation and adaptive procedure are capable of monitoring the flow field, updating the mesh when necessary, and providing nearly optimal meshes throughout the calculation, thus making the solution reliable and the computation economical and efficient.
Instability theory of the Navier-Stokes-Poisson equations
Jang, Juhi
2011-01-01
The stability question of the Lane-Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane-Emden solutions in the framework of the Navier-Stokes-Poisson system with adiabatic exponent $6/5 < \\gamma < 4/3$.
ANALYSIS OF SOME ASSUMPTIONS OF NAVIER-STOKES EQUATION
Directory of Open Access Journals (Sweden)
Budarin V.
2010-08-01
Full Text Available Several stages of the derivation of Navier-Stokes equations in coordinate form are analyzed. The purpose of the analysis is the determination of long-term problems of system closure, of reasons for differences of exact solutions for low Reynolds numbers and the appearance of unstable solutions using computer programs.
Algorithmic Enhancements for the VULCAN Navier-Stokes Solver
Edwards, Jack R.
2004-01-01
Work performed over the last three years has resulted in the addition of several new algorithms to the VULCAN code, NASA's standard for Navier-Stokes calculations in high-speed aeropropulsion devices. This final report describes the new techniques in brief and presents sample results from their use.
The Navier-Stokes Equations Theory and Numerical Methods
Masuda, Kyûya; Rautmann, Reimund; Solonnikov, Vsevolod
1990-01-01
These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.
The Proteus Navier-Stokes code. [two and three dimensional computational fluid dynamics
Towne, Charles E.; Schwab, John R.
1992-01-01
An effort is currently underway at NASA Lewis to develop two and three dimensional Navier-Stokes codes, called Proteus, for aerospace propulsion applications. Proteus solves the Reynolds-averaged, unsteady, compressible Navier-Stokes equations in strong conservation law form. Turbulence is modeled using a Baldwin-Lomax based algebraic eddy viscosity model. In addition, options are available to solve thin layer or Euler equations, and to eliminate the energy equation by assuming constant stagnation enthalpy. An extensive series of validation cases have been run, primarily using the two dimensional planar/axisymmetric version of the code. Several flows were computed that have exact solution such as: fully developed channel and pipe flow; Couette flow with and without pressure gradients; unsteady Couette flow formation; flow near a suddenly accelerated flat plate; flow between concentric rotating cylinders; and flow near a rotating disk. The two dimensional version of the Proteus code has been released, and the three dimensional code is scheduled for release in late 1991.
Local null-controllability of the 2-D Vlasov-Navier-Stokes system
Moyano, Iván
2016-01-01
We prove a null controllability result for the Vlasov-Navier-Stokes system, which describes the interaction of a large cloud of particles immersed in a fluid. We show that one can modify both the distribution of particles and the velocity field of the fluid from any initial state to the zero steady state, by means of an internal control. Indeed, we can modify the non-linear dynamics of the system in order to absorb the particles and let the fluid at rest. The proof is achieved thanks to the r...
Institute of Scientific and Technical Information of China (English)
XIE Xiaoqiang
2012-01-01
The goal of this article is to study the boundary layer of Navier-Stokes/Allen-Cahn system in a channel at small viscosity.We prove that there exists a boundary layer at the outlet(down-wind)of thickness v,where v,is the kinematic viscosity.The convergence in L2 of the solutions of the Navier-Stokes/Allen-Cahn equations to that of the Euler/Allen-Cahn equations at the vanishing viscosity was established.In two dimensional case we are able to derive the physically relevant uniform in space and time estimates,which is derived by the idea of better control on the tangential derivative and the use of an anisotropic Sobolve imbedding.
Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation
Directory of Open Access Journals (Sweden)
Mohamed A. El-Beltagy
2013-01-01
Full Text Available A two-dimensional stochastic solver for the incompressible Navier-Stokes equations is developed. The vorticity-stream function formulation is considered. The polynomial chaos expansion was integrated with an unstructured node-centered finite-volume solver. A second-order upwind scheme is used in the convection term for numerical stability and higher-order discretization. The resulting sparse linear system is solved efficiently by a direct parallel solver. The mean and variance simulations of the cavity flow are done for random variation of the viscosity and the lid velocity. The solver was tested and compared with the Monte-Carlo simulations and with previous research works. The developed solver is proved to be efficient in simulating the stochastic two-dimensional incompressible flows.
Navier-Stokes turbine heat transfer predictions using two-equation turbulence
Ameri, Ali A.; Arnone, Andrea
1992-01-01
Navier-Stokes calculations were carried out in order to predict the heat transfer rates on turbine blades. The calculations were performed using TRAF2D which is a two-dimensional, explicit, finite volume mass-averaged Navier-Stokes solver. Turbulence was modeled using q-omega and k-epsilon two-equation models and the Baldwin-Lomax algebraic model. The model equations along with the flow equations were solved explicitly on a non-periodic C grid. Implicit residual smoothing (IRS) or a combination of multigrid technique and IRS was applied to enhance convergence rates. Calculations were performed to predict the Stanton number distributions on the first stage vane and blade row as well as the second stage vane row of the Rocketdyne Space Shuttle Main Engine (SSME) high pressure fuel turbine. The comparison with the experimental results, although generally favorable, serves to highlight the weaknesses of the turbulence models and the possible areas of improving these models for use in turbomachinery heat transfer calculations.
Analysis of one assumption of the Navier-Stokes equations
Budarin, V A
2013-01-01
This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact on the results of the analytical calculation. The connections between equations, causes of discrepancies in exact solutions of the Navier-Stokes equations at low Reynolds numbers and the emergence of unstable solutions using computer programs are also addressed. The necessity to complement the well-known equations of motion in mechanical stress requires other equations are substantive. It is shown that there are three methods of solving such a problem and the requirements for the unknown equations are described. Keywords: Navier-Stokes, approximate equation, closing equations, holonomic system.
Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations
Vorobev, Anatoliy
2010-01-01
We study the interactions between the thermodynamic transition and hydrodynamic flows which would characterise a thermo- and hydro-dynamic evolution of a binary mixture in a dissolution/nucleation process. The primary attention is given to the slow dissolution dynamics. The Cahn-Hilliard approach is used to model the behaviour of evolving and diffusing interfaces. An important peculiarity of the full Cahn-Hilliard-Navier-Stokes equations is the use of the full continuity equation required even for a binary mixture of incompressible liquids, firstly, due to dependence of mixture density on concentration and, secondly, due to strong concentration gradients at liquids' interfaces. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, provide a strict derivation of the Boussinesq approximation for the Cahn-Hilliard-Navier-Stokes equations. This approximation forms a universal theoretical model that can be further employed for a thermo/hydro-dynamic ...
Tysinger, Thomas Lee
1992-07-01
Efficient numerical procedures are developed for the solution of the Navier-Stokes equations. The Navier-Stokes equations are a system of conservation laws which govern the motion of compressible, viscous, heat-conducting fluids. A conservative finite volume formulation is used for spatial discretization of the governing equations, resulting in a system of ordinary differential equations. To advance the system in time, an Alternating Direction Implicit (ADI) procedure suitable for the Navier-Stokes equations is developed. The resulting implicit system is diagonalized to improve the computational efficiency of the scheme. Viscous contributions are added to the scheme implicitly in a way that enhances the stability, yet does not disturb the efficiency of the algorithm. Rapid convergence to a steady state solution is achieved with a recursive multigrid algorithm. The stability and efficiency of the scheme are demonstrated with simulations of flow over wing sections. Furthermore, the algorithm has been implemented within the framework of multiple-block structured grids in which the spatial domain is decomposed into multiple blocks and the solution is advanced in parallel on the different blocks. Generic utilities have been developed to implement such a scheme in distributed computing environments. The multiple-block algorithm is designed so that the explicit residual calculation is identical to that of the single-block scheme, and therefore converged solutions for both schemes must be the same. To accelerate convergence, horizontal, vertical, and asynchronous multigrid algorithms are tested. Significant speedups have been achieved in a multiprocessor environment, while convergence rates similar to those of the single-clock schemes are observed.
Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations
Le Maitre, Olivier
2014-01-06
In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.
A New Conserved Energy for Incompressible Navier-Stokes Equations
García-Casado, Manuel
2010-01-01
Pressure conditions in incompressible Navier-Stokes equations give rise to conservation of total energy. The energy rate getting into a volume is the same energy rate that gets out from it. Suitable choice of pressure counteracts energy disipation of viscosity term in such a way that total energy is preserved. As consequence, this prevents kinetic energy blow-up in a given volume of the fluid.
Stabilization of weak solutions to compressible Navier-Stokes equations
Novotný, Anton’ın; Straškraba, Ivan
2000-01-01
In [17] the present authors investigated the stabilization of the weak solutions to space periodic problem for barotropic compressible Navier-Stokes equations. The main goal of this paper is to show the power of the method introduced in [17] by treating other boundary conditions. In fact, the only limitation of the method is potential external force and the validity of the Poincaré inequality for the velocity.
Two-dimensional nonlinear nonequilibrium kinetic theory under steady heat conduction.
Hyeon-Deuk, Kim
2005-04-01
The two-dimensional steady-state Boltzmann equation for hard-disk molecules in the presence of a temperature gradient has been solved explicitly to second order in density and the temperature gradient. The two-dimensional equation of state and some physical quantities are calculated from it and compared with those for the two-dimensional steady-state Bhatnagar-Gross-Krook equation and information theory. We have found that the same kind of qualitative differences as the three-dimensional case among these theories still appear in the two-dimensional case.
Fast non-symmetric iterations and efficient preconditioning for Navier-Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Silvester, D. [UMIST, Manchester (United Kingdom); Elman, H. [Univ. of Maryland, College Park, MD (United States)
1994-12-31
Discretisation of the steady-state Navier-Stokes equations: (u.grad)u-{nu}{del}{sup 2}u + grad p = 0; div u = 0 [1]. in some flow domain {Omega} {contained_in} IR{sup d}, (d = 2 or 3), gives a system of non-linear algebraic equations for discretised variables u (the velocity), and p (the pressure). The authors assume that appropriate boundary conditions are imposed. The non-linear equation system can be linearised using a fixed-point (Picard) iteration to give a matrix system which must be solved at every iteration. Part of this matrix is block diagonal, and consists of d convection-diffusion operators, one for each component of velocity. Two difficulties arise when solving this matrix equation. Firstly, the block diagonal part is not symmetric, although under certain conditions the symmetric part is positive definite. Secondly, the overall system is indefinite. This makes the design of fast and efficient iterative solvers for discretised Navier-Stokes operators an extremely challenging task.
Navier-Stokes analysis of solid propellant rocket motor internal flows
Sabnis, J. S.; Gibeling, H. J.; Mcdonald, H.
1989-01-01
A multidimensional implicit Navier-Stokes analysis that uses numerical solution of the ensemble-averaged Navier-Stokes equations in a nonorthogonal, body-fitted, cylindrical coordinate system has been applied to the simulation of the steady mean flow in solid propellant rocket motor chambers. The calculation procedure incorporates a two-equation (k-epsilon) turbulence model and utilizes a consistently split, linearized block-implicit algorithm for numerical solution of the governing equations. The code was validated by comparing computed results with the experimental data obtained in cylindrical-port cold-flow tests. The agreement between the computed and experimentally measured mean axial velocities is excellent. The axial location of transition to turbulent flow predicted by the two-equation (k-epsilon) turbulence model used in the computations also agrees well with the experimental data. Computations performed to simulate the axisymmetric flowfield in the vicinity of the aft field joint in the Space Shuttle solid rocket motor using 14,725 grid points show the presence of a region of reversed axial flow near the downstream edge of the slot.
Navier-Stokes analysis of solid propellant rocket motor internal flows
Sabnis, J. S.; Gibeling, H. J.; Mcdonald, H.
1989-01-01
A multidimensional implicit Navier-Stokes analysis that uses numerical solution of the ensemble-averaged Navier-Stokes equations in a nonorthogonal, body-fitted, cylindrical coordinate system has been applied to the simulation of the steady mean flow in solid propellant rocket motor chambers. The calculation procedure incorporates a two-equation (k-epsilon) turbulence model and utilizes a consistently split, linearized block-implicit algorithm for numerical solution of the governing equations. The code was validated by comparing computed results with the experimental data obtained in cylindrical-port cold-flow tests. The agreement between the computed and experimentally measured mean axial velocities is excellent. The axial location of transition to turbulent flow predicted by the two-equation (k-epsilon) turbulence model used in the computations also agrees well with the experimental data. Computations performed to simulate the axisymmetric flowfield in the vicinity of the aft field joint in the Space Shuttle solid rocket motor using 14,725 grid points show the presence of a region of reversed axial flow near the downstream edge of the slot.
Navier-Stokes solution on the CYBER-203 by a pseudospectral technique
Lambiotte, J. J.; Hussaini, M. Y.; Bokhari, S.; Orszag, S. A.
A three-level, time-split, mixed spectral/finite difference method for the numerical solution of the three-dimensional, compressible Navier-Stokes equations has been developed and implemented on the Control Data Corporation (CDC) CYBER-203. This method uses a spectral representation for the flow variables in the streamwise and spanwise coordinates, and central differences in the normal direction. The five dependent variables are interleaved one horizontal plane at a time and the array of their values at the grid points of each horizontal plane is a typical vector in the computation. The code is organized so as to require, per time step, a single forward-backward pass through the entire data base. The one-and two-dimensional Fast Fourier Transforms are performed using software especially developed for the CYBER-203.
On the Navier-Stokes system with the Coulomb friction law boundary condition
Bălilescu, Loredana; San Martín, Jorge; Takahashi, Takéo
2017-02-01
We propose a new model for the motion of a viscous incompressible fluid. More precisely, we consider the Navier-Stokes system with a boundary condition governed by the Coulomb friction law. With this boundary condition, the fluid can slip on the boundary if the tangential component of the stress tensor is too large. We prove the existence and uniqueness of weak solution in the two-dimensional problem and the existence of at least one solution in the three-dimensional case, together with regularity properties and an energy estimate. We also propose a fully discrete scheme of our problem using the characteristic method, and we present numerical simulations in two physical examples.
On the control of the chaotic attractors of the 2-d Navier-Stokes equations.
Smaoui, Nejib; Zribi, Mohamed
2017-03-01
The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, Re. Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.
Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation
Directory of Open Access Journals (Sweden)
Yuncheng You
2008-12-01
Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.
Two Dimensional Steady State Eddy Current Analysis of a Spinning Conducting Cylinder
2017-03-09
UNCLASSIFIED UNCLASSIFIED AD-E403 855 Technical Report ARMET-TR-16045 TWO-DIMENSIONAL STEADY-STATE EDDY CURRENT ANALYSIS OF A ...any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN...August 2014 4. TITLE AND SUBTITLE TWO-DIMENSIONAL STEADY-STATE EDDY CURRENT ANALYSIS OF A SPINNING CONDUCTING CYLINDER 5a. CONTRACT NUMBER 5b
Navier-Stokes computations on full-span wing-body configuration with oscillating control surfaces
Obayashi, Shigeru; Chiu, Ing-Tsau; Guruswamy, Guru P.
1993-01-01
Unsteady Navier-Stokes simulations have been performed for vortical flows over an 'arrow-wing' configuration of a supersonic transport in the transonic regime. Computed steady pressures and integrated force coefficients with and without control surface deflection at a moderate angle of attack are compared with experiment. For unsteady cases, oscillating trailing-edge control surfaces are modeled by using moving grids. Response characteristics between symmetric and anti-symmetric oscillatory motions of the control surfaces on the left and right wings are studied. The anti-symmetric case produces higher lift than the steady case with no deflection, and the unsteady symmetric case produces higher lift than the anti-symmetric case. The detailed analysis of the wake structure revealed a strong interaction between the primary vortex and the wake vortex sheet from the flap region when the flap is deflected up.
Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations
Gomez, Hector
2010-05-01
This paper is devoted to the numerical simulation of the Navier-Stokes-Korteweg equations, a phase-field model for water/water-vapor two-phase flows. We develop a numerical formulation based on isogeometric analysis that permits straightforward treatment of the higher-order partial-differential operator that represents capillarity. We introduce a new refinement methodology that desensitizes the numerical solution to the computational mesh and achieves mesh invariant solutions. Finally, we present several numerical examples in two and three dimensions that illustrate the effectiveness and robustness of our approach. © 2010 Elsevier B.V.
INERTIAL ALGORITHMS FOR THE STATIONARY NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Hou Yanren(侯延仁); R.M.M. Mattheij
2003-01-01
Several kind of new numerical schemes for the stationary Navier-Stokes equa-tions based on the virtue of Inertial Manifold and Approximate Inertial Manifold, whichwe call them inertial algorithms in this paper, together with their error estimations are pre-sented. All these algorithms are constructed under an uniform frame, that is to constructsome kind of new projections for the Sobolev space in which the true solution is sought.It is shown that the proposed inertial algorithms can greatly improve the convergence rateof the standard Galerkin approximate solution with lower computing effort. And somenumerical examples are also given to verify results of this paper.
Dual Variational Principles for 3-D Navier-Stokes Equations
Liu, G. L.
Just recently the exact variational principles (VP) of the full 3-D Navier-Stokes equations of viscous flow have been successfully established for the first time by the present author by means of a systematic reversed deduction method via the undetermined function. As a continuation and further development of that - a pair of new dual (reciprocal)VP is generated herein by means of the Friedrichs involutory transformation. These VP have the advantage over the previous ones that they possess apparent physical meaning of energy, providing a new rigorous theoretical basis for the finite element analysis of 3-D viscous flow.
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.
2017-05-23
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.
Discretizations in isogeometric analysis of Navier-Stokes flow
DEFF Research Database (Denmark)
Nielsen, Peter Nørtoft; Gersborg, Allan Roulund; Gravesen, Jens;
2011-01-01
for the simplified Stokes problem confirm the existence of many stable discretizations of the velocity and pressure spaces, and in particular show that stability may be achieved by means of knot refinement of the velocity space. Error convergence studies for the full Navier-Stokes problem show optimal convergence...... rates for this type of discretizations. Finally, a comparison of the results of the method to data from the literature for the lid-driven square cavity for Reynolds numbers up to 10,000 serves as benchmarking of the discretizations and confirms the robustness of the method. © 2011 Elsevier B.V....
The proper orthogonal decomposition method for the Navier-Stokes equations
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficien...
On the emergence of the Navier-Stokes-α model for turbulent channel flows
Foias, Ciprian; Tian, Jing; Zhang, Bingsheng
2016-08-01
In a series of papers (see Foias et al. [J. Dyn. Differ. Equations 14(1), 1-35 (2002)] and the pertinent references therein), the 3D Navier-Stokes-α model was shown to be a useful complement to the 3D Navier-Stokes equations, and in particular, to be a good Reynolds version of the latter equations. In this work, we introduce a simple Reynolds averaging which, due to the wall roughness, transforms the Navier-Stokes equations into the Navier-Stokes-α model.
QUASI-NEUTRALLIMIT OF THE BIPOLAR NAVIER-STOKES-POISSON SYSTEM
Institute of Scientific and Technical Information of China (English)
Yang Xiuhui
2011-01-01
This paper is concerned with the quasi-neutral limit of the bipolar NavierStokes-Poisson system.It is rigorously proved,by introducing the new modulated energy functional and using the refined energy analysis,that the strong solutions of the bipolar Navier-Stokes-Poisson system converge to the strong solution of the compressible NavierStokes equations as the Debye length goes to zero.Moreover,if we let the viscous coefficients and the Debye length go to zero simultaneously,then we obtain the convergence of the strong solutions of bipolar Navier-Stokes-Poisson system to the strong solution of the compressible Euler equations.
Microscopic statistical description of incompressible Navier-Stokes granular fluids
Tessarotto, Massimo; Mond, Michael; Asci, Claudio
2017-05-01
Based on the recently established Master kinetic equation and related Master constant H-theorem which describe the statistical behavior of the Boltzmann-Sinai classical dynamical system for smooth and hard spherical particles, the problem is posed of determining a microscopic statistical description holding for an incompressible Navier-Stokes fluid. The goal is reached by introducing a suitable mean-field interaction in the Master kinetic equation. The resulting Modified Master Kinetic Equation (MMKE) is proved to warrant at the same time the condition of mass-density incompressibility and the validity of the Navier-Stokes fluid equation. In addition, it is shown that the conservation of the Boltzmann-Shannon entropy can similarly be warranted. Applications to the plane Couette and Poiseuille flows are considered showing that they can be regarded as final decaying states for suitable non-stationary flows. As a result, it is shown that an arbitrary initial stochastic 1-body PDF evolving in time by means of MMKE necessarily exhibits the phenomenon of Decay to Kinetic Equilibrium (DKE), whereby the same 1-body PDF asymptotically relaxes to a stationary and spatially uniform Maxwellian PDF.
Microscopic statistical description of incompressible Navier-Stokes granular fluids
Tessarotto, Massimo; Asci, Claudio
2016-01-01
Based on the recently-established Master kinetic equation and related Master constant H-theorem which describe the statistical behavior of the Boltzmann-Sinai classical dynamical system for smooth and hard spherical particles, the problem is posed of determining a microscopic statistical description holding for an incompressible Navier-Stokes fluid. The goal is reached by introducing a suitable mean-field interaction in the Master kinetic equation. The resulting Modified Master Kinetic Equation (MMKE) is proved to warrant at the same time the condition of mass-density incompressibility and the validity of the Navier-Stokes fluid equation. In addition, it is shown that the conservation of the Boltzmann-Shannon entropy can similarly be warranted. Applications to the plane Couette and Poiseuille flows are considered showing that they can be regarded as final decaying states for suitable non-stationary flows. As a result, it is shown that an arbitrary initial stochastic $1-$body PDF evolving in time by means of M...
Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations.
Vorobev, Anatoliy
2010-11-01
We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.
Modeling Vortex Generators in a Navier-Stokes Code
Dudek, Julianne C.
2011-01-01
A source-term model that simulates the effects of vortex generators was implemented into the Wind-US Navier-Stokes code. The source term added to the Navier-Stokes equations simulates the lift force that would result from a vane-type vortex generator in the flowfield. The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, subsonic flow in an S-duct with 22 corotating vortex generators, and supersonic flow in a rectangular duct with a counter-rotating vortex-generator pair. The model was also used to successfully simulate microramps in supersonic flow by treating each microramp as a pair of vanes with opposite angles of incidence. The validation results indicate that the source-term vortex-generator model provides a useful tool for screening vortex-generator configurations and gives comparable results to solutions computed using gridded vanes.
Pressure moderation and effective pressure in Navier-Stokes flows
Tran, Chuong V.; Yu, Xinwei
2016-10-01
We study the Cauchy problem of the Navier-Stokes equations by both semi-analytic and classical energy methods. The former approach provides a physical picture of how viscous effects may or may not be able to suppress singularity development. In the latter approach, we examine the pressure term that drives the dynamics of the velocity norms \\parallel u{{\\parallel}{{Lq}}} , for q≥slant 3 . A key idea behind this investigation is due to the fact that the pressure p in this term is determined up to a function of both space and |u| , say P(x,|u|) , which may assume relatively broad forms. This allows us to use P as a pressure moderator in the evolution equation for \\parallel u{{\\parallel}{{Lq}}} , whereby optimal regularity criteria can be sought by varying P within its admissible classes. New regularity criteria are derived with and without making use of the moderator. The results obtained in the absence of the moderator feature some improvement over existing criteria in the literature. Several criteria are derived in terms of the moderated (effective) pressure p+P . A simple moderation scheme and the plausibility of the present approach to the problem of Navier-Stokes regularity are discussed.
Algorithmic Enhancements to the VULCAN Navier-Stokes Solver
Litton, D. K.; Edwards, J. R.; White, J. A.
2003-01-01
VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes solver implemented in VULCAN. The first addition is a highly implicit approach that uses subiterations to enhance block to block connectivity between adjacent subdomains. The addition of this scheme allows more efficient solution of viscous flows on highly-stretched meshes. The second algorithm addresses the shortcomings associated with density-based schemes by the addition of a time-derivative preconditioning strategy. High speed, compressible flows are typically solved with density based schemes, which show a high level of degradation in accuracy and convergence at low Mach numbers (M less than or equal to 0.1). With the addition of preconditioning and associated modifications to the numerical discretization scheme, the eigenvalues will scale with the local velocity, and the above problems will be eliminated. With these additions, VULCAN now has improved convergence behavior for multi-block, highly-stretched meshes and also can solve the Navier-Stokes equations for very low Mach numbers.
Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP
Vadyak, Joseph; Shrewsbury, George E.; Narramore, Jim C.; Montry, Gary; Holst, Terry; Kwak, Dochan (Technical Monitor)
1995-01-01
The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time
Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP
Vadyak, Joseph; Shrewsbury, George E.; Narramore, Jim C.; Montry, Gary; Holst, Terry; Kwak, Dochan (Technical Monitor)
1995-01-01
The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time
Directory of Open Access Journals (Sweden)
Aiwen Wang
2012-01-01
Full Text Available We investigate an Oseen two-level stabilized finite-element method based on the local pressure projection for the 2D/3D steady Navier-Stokes equations by the lowest order conforming finite-element pairs (i.e., Q1−P0 and P1−P0. Firstly, in contrast to other stabilized methods, they are parameter free, no calculation of higher-order derivatives and edge-based data structures, implemented at the element level with minimal cost. In addition, the Oseen two-level stabilized method involves solving one small nonlinear Navier-Stokes problem on the coarse mesh with mesh size H, a large general Stokes equation on the fine mesh with mesh size h=O(H2. The Oseen two-level stabilized finite-element method provides an approximate solution (uh,ph with the convergence rate of the same order as the usual stabilized finite-element solutions, which involves solving a large Navier-Stokes problem on a fine mesh with mesh size h. Therefore, the method presented in this paper can save a large amount of computational time. Finally, numerical tests confirm the theoretical results. Conclusion can be drawn that the Oseen two-level stabilized finite-element method is simple and efficient for solving the 2D/3D steady Navier-Stokes equations.
On Exact Solutions of the Navier-Stokes Equations for Uni-directional Flows
Lam, F
2015-01-01
In the present note, we show that the uni-directional flows in a rectangular channel and in a circular pipe are exact spatio-temporal solutions of the Navier-Stokes equations over a short time interval. We assert that the classical plane Poiseuille-Couette flow and Hagen-Poiseuille flow are time-independent approximations of the exact solutions if an appropriate initial velocity distribution at starting location is specified. Conceptually, there do not exist absolute steady flows starting from unspecified initial data. The classic experimental measurements by Poiseuille can be explained in terms of the evolutional solutions. In particular, the pipe flow does not have a time-independent characteristic velocity. The orthodox notion that the parabolic profile exists for arbitrary Reynolds numbers is unwarranted.
A least-squares finite element method for 3D incompressible Navier-Stokes equations
Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.
1993-01-01
The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.
Multigrid-based grid-adaptive solution of the Navier-Stokes equations
Michelsen, Jess
A finite volume scheme for solution of the incompressible Navier-Stokes equations in two dimensions and axisymmetry is described. Solutions are obtained on nonorthogonal, solution adaptive BFC grids, based on the Brackbill-Saltzman generator. Adaptivity is achieved by the use of a single control function based on the local kinetic energy production. Nonstaggered allocation of pressure and Cartesian velocity components avoids the introduction of curvature terms associated with the use of a grid-direction vector-base. A special interpolation of the pressure correction equation in the SIMPLE algorithm ensures firm coupling between velocity and pressure field. Steady-state solutions are accelerated by a full approximation multigrid scheme working on the decoupled grid-flow problem, while an algebraic multigrid scheme is employed for the pressure correction equation.
Investigation of Navier-Stokes Code Verification and Design Optimization
Vaidyanathan, Rajkumar
2004-01-01
With rapid progress made in employing computational techniques for various complex Navier-Stokes fluid flow problems, design optimization problems traditionally based on empirical formulations and experiments are now being addressed with the aid of computational fluid dynamics (CFD). To be able to carry out an effective CFD-based optimization study, it is essential that the uncertainty and appropriate confidence limits of the CFD solutions be quantified over the chosen design space. The present dissertation investigates the issues related to code verification, surrogate model-based optimization and sensitivity evaluation. For Navier-Stokes (NS) CFD code verification a least square extrapolation (LSE) method is assessed. This method projects numerically computed NS solutions from multiple, coarser base grids onto a freer grid and improves solution accuracy by minimizing the residual of the discretized NS equations over the projected grid. In this dissertation, the finite volume (FV) formulation is focused on. The interplay between the xi concepts and the outcome of LSE, and the effects of solution gradients and singularities, nonlinear physics, and coupling of flow variables on the effectiveness of LSE are investigated. A CFD-based design optimization of a single element liquid rocket injector is conducted with surrogate models developed using response surface methodology (RSM) based on CFD solutions. The computational model consists of the NS equations, finite rate chemistry, and the k-6 turbulence closure. With the aid of these surrogate models, sensitivity and trade-off analyses are carried out for the injector design whose geometry (hydrogen flow angle, hydrogen and oxygen flow areas and oxygen post tip thickness) is optimized to attain desirable goals in performance (combustion length) and life/survivability (the maximum temperatures on the oxidizer post tip and injector face and a combustion chamber wall temperature). A preliminary multi-objective optimization
Feireisl, Eduard; Novotny, Antonin
2011-01-01
We introduce the notion of relative entropy for the weak solutions of the compressible Navier-Stokes system. We show that any finite energy weak solution satisfies a relative entropy inequality for any pair of sufficiently smooth test functions. As a corollary we establish weak-strong uniqueness principle for the compressible Navier-Stokes system.
SOLUTION OF 3-D TURBULENCE NAVIER-STOKES EQUATIONS USING HYBRID GRIDS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Hybrid grids are used for the solution of 3D turbulence Navier-Stokes equations. The prismatic grids are generated near the wall, and the tetrahedron grids are generated in the other field. A Navier-Stokes solver using ic Baldwin-Lomax turbulence model is adopted. The numerical tests show that the above method is very efficient.``
On Approximation and Computation of Navier-Stokes Flow
Institute of Scientific and Technical Information of China (English)
VARNHORN Werner; ZANGER Florian
2013-01-01
We present an approximation method for the non-stationary nonlinear incompressible Navier-Stokes equations in a cylindrical domain (0,T)×G,where G （C） IR3is a smoothly bounded domain.Our method is applicable to general three-dimensional flow without any symmetry restrictions and relies on existence,uniqueness and representation results from mathematical fluid dynamics.After a suitable time delay in the nonlinear convective term v·▽v we obtain globally (in time) uniquely solvable equations,which-by using semi-implicit time differences-can be transformed into a finite number of Stokes-type boundary value problems.For the latter a boundary element method based on a corresponding hydrodynamical potential theory is carried out.The method is reported in short outlines ranging from approximation theory up to numerical test calculations.
Navier-Stokes Dynamics by a Discrete Boltzmann Model
Rubinstein, Robet
2010-01-01
This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.
Aerodynamics of thrust vectoring by Navier-Stokes solutions
Tseng, Jing-Biau; Lan, C. Edward
1991-01-01
Induced aerodynamics from thrust vectoring are investigated by a computational fluid dynamic method. A thin-layer Reynolds-averaged Navier-Stokes code with multiblock capability is used. Jet properties are specified on the nozzle exit plane to simulate the jet momentum. Results for a rectangular jet in a cross flow are compared with data to verify the code. Further verification of the calculation is made by comparing the numerical results with transonic data for a wing-body combination. Additional calculations were performed to elucidate the following thrust vectoring effects: the thrust vectoring effect on shock and expansion waves, induced effects on nearby surfaces, and the thrust vectoring effect on the leading edge vortex.
Beyond the Navier-Stokes equations: Burnett hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Garcia-Colin, L.S. [Department of Physics, Universidad Autonoma Metropolitana - Iztapalapa, Mexico D. F. 09340 (Mexico); El Colegio Nacional, Centro Historico, Mexico, 06020 (Mexico)], E-mail: lgcs@xanum.uam.mx; Velasco, R.M. [Department of Physics, Universidad Autonoma Metropolitana - Iztapalapa, Mexico D. F. 09340 (Mexico)], E-mail: rmvb@xanum.uam.mx; Uribe, F.J. [Department of Physics, Universidad Autonoma Metropolitana - Iztapalapa, Mexico D. F. 09340 (Mexico)], E-mail: paco@xanum.uam.mx
2008-08-15
This work is mainly concerned with the extension of hydrodynamics beyond the Navier-Stokes equations, a regime known as Burnett hydrodynamics. The derivation of the Burnett equations is considered from several theoretical approaches. In particular we discuss the Chapman-Enskog, Grad's method, and Truesdell's approach for solving the Boltzmann equation. Also, their derivation using the macroscopic approach given by extended thermodynamics is mentioned. The problems and successes of these equations are discussed and some alternatives proposed to improve them are mentioned. Comparisons of the predictions coming from the Burnett equations with experiments and/or simulations are given in order to have the necessary elements to give a critical assessment of their validity and usefulness.
Iterative methods for compressible Navier-Stokes and Euler equations
Energy Technology Data Exchange (ETDEWEB)
Tang, W.P.; Forsyth, P.A.
1996-12-31
This workshop will focus on methods for solution of compressible Navier-Stokes and Euler equations. In particular, attention will be focused on the interaction between the methods used to solve the non-linear algebraic equations (e.g. full Newton or first order Jacobian) and the resulting large sparse systems. Various types of block and incomplete LU factorization will be discussed, as well as stability issues, and the use of Newton-Krylov methods. These techniques will be demonstrated on a variety of model transonic and supersonic airfoil problems. Applications to industrial CFD problems will also be presented. Experience with the use of C++ for solution of large scale problems will also be discussed. The format for this workshop will be four fifteen minute talks, followed by a roundtable discussion.
The Navier-Stokes equations an elementary functional analytic approach
Sohr, Hermann
2001-01-01
The primary objective of this monograph is to develop an elementary and self-contained approach to the mathematical theory of a viscous, incompressible fluid in a domain of the Euclidean space, described by the equations of Navier-Stokes. Moreover, the theory is presented for completely general domains, in particular, for arbitrary unbounded, nonsmooth domains. Therefore, restriction was necessary to space dimensions two and three, which are also the most significant from a physical point of view. For mathematical generality, however, the linearized theory is expounded for general dimensions higher than one. Although the functional analytic approach developed here is, in principle, known to specialists, the present book fills a gap in the literature providing a systematic treatment of a subject that has been documented until now only in fragments. The book is mainly directed to students familiar with basic tools in Hilbert and Banach spaces. However, for the readers’ convenience, some fundamental properties...
Energy Technology Data Exchange (ETDEWEB)
Almeida, Regina Celia Cerqueira de
1993-12-31
A space-time finite element finite element formulation for the compressible Euler and Navier-Stokes equations is proposed. The present work develops a stable generalized CAU method which represents shocks and boundary-layers accurately. An h-adaptive remeshing refinement, which takes into account directional stretching and stretching ratio, is used leading to a very good way to indicate and refine the flow regions with singularities. Numerical experiment were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) 63 refs., 40 figs.
Energy Technology Data Exchange (ETDEWEB)
Rocha, Jussie Soares da, E-mail: jussie.soares@ifpi.edu.br [Instituto Federal de Educacao, Ciencia e Tecnologia do Piaui (IFPI), Valenca, PI (Brazil); Maciel, Edisson Savio de G., E-mail: edissonsavio@yahoo.com.br [Instituto Tecnologico de Aeronautica (ITA), Sao Paulo, SP (Brazil); Lira, Carlos A.B. de O., E-mail: cabol@ufpe.edu.br [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil)
2015-07-01
Very High Temperature Gas Cooled Reactors - VHTGRs are studied by several research groups for the development of advanced reactors that can meet the world's growing energy demand. The analysis of the flow of helium coolant around the various geometries at the core of these reactors through computational fluid dynamics techniques is an essential tool in the development of conceptual designs of nuclear power plants that provide added safety. This analysis suggests a close analogy with aeronautical cases widely studied using computational numerical techniques to solve systems of governing equations for the flow involved. The present work consists in solving the Navier-Stokes equations in a conservative form, in two-dimensional space employing a finite difference formulation for spatial discretization using the Euler method for explicit marching in time. The physical problem of supersonic laminar flow of helium gas along a ramp configuration is considered. For this, the Jameson and Mavriplis algorithm and the artificial dissipations models linear and nonlinear of Pulliam was implemented. A spatially variable time step is employed aiming to accelerate the convergence to the steady state solution. The main purpose of this work is to study the cited dissipation models and describe their characteristics in relation to the overall quality of the solution, aiming preliminary results for the development of computational tools of dynamic analysis of helium flow for the VHTGR core. (author)
Energy Technology Data Exchange (ETDEWEB)
Chaviaropoulos, P.K. [CRES-Center for Renewable Energy Sources, Pikermi Attiki (Greece)
1997-08-01
The blade element codes provide surprisingly accurate predictions of the aerodynamic loads provided that they are `fed` with proper lift and drag - incidence curves for the profiles mounted on the rotor blades. The evident question is how one can obtain such data. It is common experience that the use of the mostly available steady two-dimensional profile data may lead to serious discrepancies between measured and simulated loads. Although several correction techniques have been proposed as a remedy during the last years, from simplified dynamic stall models suitably tuned for wind turbines to 3-D correction schemes for profile data, the problem is by no means over-passed. Especially for the three-dimensional effects it seems that part of the difficulty is due to our limited understanding of the physical mechanism which is responsible for the extra loading of the inner part of the blades. Recognizing the importance of the above aspects two relevant Joule projects have been launched, the concluded `Dynamic Stall and 3-D Effects` JOU2-CT93-0345 and the ongoing `VISCWIND` JOR3-CT95-0007 project. Part of the activities in the first and all the activities in the second project are devoted to the identification and quantification of the dynamic stall and three-dimensional effects experienced by the wind turbine blades using Navier-Stokes computations. The contribution of CRES in these two projects is briefly presented in this paper. (EG)
On the existence of two-dimensional nonlinear steady states in plane Couette flow
Rincon, Francois
2007-01-01
The problem of two-dimensional steady nonlinear dynamics in plane Couette flow is revisited using homotopy from either plane Poiseuille flow or from plane Couette flow perturbed by a small symmetry-preserving identity operator. Our results show that it is not possible to obtain the nonlinear plane Couette flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids, 14, 667 (1995)] using their Poiseuille-Couette homotopy. We also demonstrate that the steady solutions obtained by Mehta and Healey [Phys. Fluids, 17, 4108 (2005)] for small symmetry-preserving perturbations are influenced by an artefact of the modified system of equations used in their paper. However, using a modified version of their model does not help to find plane Couette flow solution in the limit of vanishing symmetry-preserving perturbations either. The issue of the existence of two-dimensional nonlinear steady states in plane Couette flow remains unsettled.
Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions
Tidriri, M. D.
1995-01-01
One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.
A rigorous justification of the Euler and Navier-Stokes equations with geometric effects
Bella, Peter; Lewicka, Marta; Novotny, Antonin
2015-01-01
We derive the 1D isentropic Euler and Navier-Stokes equations describing the motion of a gas through a nozzle of variable cross section as the asymptotic limit of the 3D isentropic Navier-Stokes system in a cylinder, the diameter of which tends to zero. Our method is based on the relative energy inequality satisfied by any weak solution of the 3D Navier-Stokes system and a variant of Korn-Poincare's inequality on thin channels that may be of independent interest.
Ibrahim, Slim
2011-01-01
We investigate large time existence of solutions of the Navier-Stokes-Boussinesq equations with spatially almost periodic large data when the density stratification is sufficiently large. In 1996, Kimura and Herring \\cite{KH} examined numerical simulations to show a stabilizing effect due to the stratification. They observed scattered two-dimensional pancake-shaped vortex patches lying almost in the horizontal plane. Our result is a mathematical justification of the presence of such two-dimensional pancakes. To show the existence of solutions for large times, we use $\\ell^1$-norm of amplitudes. Existence for large times is then proven using techniques of fast singular oscillating limits and bootstrapping argument from a global-in-time unique solution of the system of limit equations.
Viegas, J. R.; Rubesin, M. W.
1983-01-01
To make computer codes for two-dimensional compressible flows more robust and economical, wall functions for these flows, under adiabatic conditions, have been developed and tested. These wall functions have been applied to three two-equation models of turbulence. The tests consist of comparisons of calculated and experimental results for transonic and supersonic flow over a flat plate and for two-dimensional and axisymmetrical transonic shock-wave/boundary-layer interaction flows with and without separation. The calculations are performed with an implicit algorithm that solves the Reynolds-averaged Navier-Stokes equations. It is shown that results obtained agree very well with the data for the complex compressible flows tested, provided criteria for use of the wall functions are followed. The expected savings in cost of the computations and improved robustness of the code were achieved.
Stability of Filters for the Navier-Stokes Equation
Brett, C E A; Law, K J H; McCormick, D S; Scott, M R; Stuart, A M
2011-01-01
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation algorithms designed to update the estimation of the state in a on-line fashion, as data is acquired sequentially. For linear problems subject to Gaussian noise filtering can be performed exactly using the Kalman filter. For nonlinear systems it can be approximated in a systematic way by particle filters. However in high dimensions these particle filtering methods can break down. Hence, for the large nonlinear systems arising in applications such as weather forecasting, various ad hoc filters are used, mostly based on making Gaussian approximations. The purpose of this work is to study the properties of these ad hoc filters, working in the context of the 2D incompressible Navier-Stokes equation. By working in this infinite dimensional setting we provide an analysis which is useful f...
Disentangling the triadic interactions in Navier-Stokes equations
Sahoo, Ganapati
2015-01-01
We study the role of helicity in the dynamics of energy transfer in a modified version of the Navier-Stokes equations with explicit breaking of the mirror symmetry. We select different set of triads participating in the dynamics on the basis of their helicity content. In particular, we remove the negative helically polarized Fourier modes at all wavenumbers except for those falling on a localized shell of wavenumber, $|{\\bf k}| \\sim k_m$. Changing $k_m$ to be above or below the forcing scale, $k_f$, we are able to assess the energy transfer of triads belonging to different interaction classes. We observe that when the negative helical modes are present only at wavenumber smaller than the forced wavenumbers, an inverse energy cascade develops with an accumulation of energy on a stationary helical condensate. Vice versa, when negative helical modes are present only at wavenumber larger than the forced wavenumbers, a transition from backward to forward energy transfer is observed in the regime when the minority ...
Energy Technology Data Exchange (ETDEWEB)
John, V. [Magdeburg Univ. (Germany). Inst. fuer Analysis und Numerik
2001-07-01
We consider slip with friction and penetration with resistance boundary conditions in the steady state Navier-Stokes equations. This paper describes some aspects of the implementation of these boundary conditions for finite element discretizations. Numerical tests on two and three dimensional channel flows across a step using the slip with friction boundary condition study the influence of the friction parameter on the position of the reattachment point and the reattachment line, respectively, of the recirculating vortex. (orig.)
PARTIAL REGULARITY FOR WEAK SOLUTIONS OF STATIONARY NAVIER-STOKES SYSTEMS
Institute of Scientific and Technical Information of China (English)
Chen Shuhong; Tan Zhong
2008-01-01
This article is concerned with the partial regularity for the weak solutions of stationary Navier-Stokes system under the controllable growth condition. By A-harmonic approximation technique, the optimal regularity is obtained.
Exponential Mixing of the 3D Stochastic Navier-Stokes Equations Driven by Mildly Degenerate Noises
Energy Technology Data Exchange (ETDEWEB)
Albeverio, Sergio [Bonn University, Department of Applied Mathematics (Germany); Debussche, Arnaud, E-mail: arnaud.debussche@bretagne.ens-cachan.fr [ENS Cachan Bretagne and IRMAR Campus de Ker Lann (France); Xu Lihu, E-mail: Lihu.Xu@brunel.ac.uk [Brunel University, Mathematics Department (United Kingdom)
2012-10-15
We prove the strong Feller property and exponential mixing for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes being forced) via a Kolmogorov equation approach.
FOURIER-LEGENDRE PSEUDOSPECTRAL METHOD FOR THE NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Jian Li
2000-01-01
In this paper, we construct a Fourier-Legendre pseudospectral scheme for the unsteady Navier-Stokes equations. This method easily deals with nonlinear terms and saves computational time. The strict error estimations are given.
Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code
Bartels, Robert E.
2005-01-01
A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
@@Suppose Rn, n = 2,3 be a smooth bounded domain, we consider the perturbed Navier-Stokes equationequation ut - ut - u + (u )u + p = F, in ,equationequation div u = 0, in ,equationequation u = 0, on .equation The study of this equation for = 0 has a long and richhistory. In the two-dimensional case, the study is very successful and it iswell known that the solutions of the equation define a C0-semigroupS(t): t 0 inthe space H = PL2() (where P is the projection onto the space ofdivergence-free vector fields) and which has a global attractor A0 on H(see ［1］). But, in the three-dimensional case, things are quitedifference, although some progress has been made recently,there are many problems still open, i.e., the global regularity of thesolutions and the existence of the global attractors (see ［1--7］ andthe references therein). The machanical background ofthe equation in the case of > 0 can be found in ［8］
An addendum to the paper: "Some elementary estimates for the Navier-Stokes system"
Cortissoz, Jean
2009-01-01
In this paper we give a proof of the existence of global regular solutions to the Fourier transformed Navier-Stokes system with small initial data in $\\Phi(2)$ via an iteration argument. The proof of the regularity theorem is a minor modification of the proof given in the paper "Some elementary estimates for the Navier-Stokes system". So this paper is intended to be just a complement to the afore mentioned paper.
Zhang, Ting; Fang, Daoyuan
2008-03-01
In this paper, we study the free boundary problem for 1D compressible Navier-Stokes equations with density-dependent viscosity. We focus on the case where the viscosity coefficient vanishes on vacuum. We prove the global existence and uniqueness for discontinuous solutions to the Navier-Stokes equations when the initial density is a bounded variation function, and give a decay result for the density as t-->+[infinity].
Uniform Regularity and Vanishing Viscosity Limit for the Free Surface Navier-Stokes Equations
Masmoudi, Nader; Rousset, Frederic
2016-09-01
We study the inviscid limit of the free boundary Navier-Stokes equations. We prove the existence of solutions on a uniform time interval by using a suitable functional framework based on Sobolev conormal spaces. This allows us to use a strong compactness argument to justify the inviscid limit. Our approach does not rely on the justification of asymptotic expansions. In particular, we get a new existence result for the Euler equations with free surface from the one for Navier-Stokes.
A FINITE ELEMENT SOLVER FOR NAVIER-STOKES EQUATIONS VIA VORTICITY AND VELOCITY
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The incompressible Navier-Stokes equations are solved via variables of vorticity and velocity. Firstly, a rigorous variational framework with the equivalence between the velocity-pressure and the vorticity-velocity formulations is presented in a Lipschitz domain. Next, a class of Galerkin finite element approximations of the corresponding variational form is introduced, and a convergence analysis is given for the Stokes problem. Finally,an iterative finite element solver for the Navier-Stokes problem is proposed.``
Group classification of steady two-dimensional boundary-layer stagnation-point flow equations
Nadjafikhah, Mehdi; Hejazi, Seyed Reza
2010-01-01
Lie symmetry group method is applied to study the boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.
Boundary Shape Control of the Navier-Stokes Equations and Applications
Institute of Scientific and Technical Information of China (English)
Kaitai LI; Jian SU; Aixiang HUANG
2010-01-01
In this paper,the geometrical design for the blade's surface(s)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 G(a)teaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.
Convergence Acceleration of the Navier-Stokes Equations Through Time-Derivative Preconditioning
Merkle, Charles L.; Venkateswaran, Sankaran; Deshpande, Manish
1996-01-01
Chorin's method of artificial compressibility is extended to both compressible and incompressible fluids by using physical arguments to define artificial fluid properties that make up a local preconditioning matrix. In particular, perturbation expansions are used to provide appropriate temporal derivatives for the equations of motion at both low speeds and low Reynolds numbers. These limiting forms are then combined into a single function that smoothly merges into the physical time derivatives at high speeds so that the equations are left unchanged at transonic, high Reynolds number conditions. The effectiveness of the resulting preconditioning procedures for the Navier-Stokes equations is demonstrated for a wide speed and Reynolds number ranges by means of stability results and computational solutions. Nevertheless, the preconditioned equations sometimes fail to provide a solution for applications for which the non-preconditioned equations converge. Often this is because the reduced dissipation in the preconditioned equations results in an unsteady solution while the more dissipative non-preconditioned equations result in a steady state. Problems of this type represent a computational challenge; it is important to distinguish between non-convergence of algorithms, and the non-existence of steady state solutions.
Global smooth flows for compressible Navier-Stokes-Maxwell equations
Xu, Jiang; Cao, Hongmei
2016-08-01
Umeda et al. (Jpn J Appl Math 1:435-457, 1984) considered a rather general class of symmetric hyperbolic-parabolic systems: A0zt+sum_{j=1}nAjz_{xj}+Lz=sum_{j,k=1}nB^{jk}z_{xjxk} and showed optimal decay rates with certain dissipative assumptions. In their results, the dissipation matrices {L} and {B^{jk}(j,k=1,ldots,n)} are both assumed to be real symmetric. So far there are no general results in case that {L} and {B^{jk}} are not necessarily symmetric, which is left open now. In this paper, we investigate compressible Navier-Stokes-Maxwell (N-S-M) equations arising in plasmas physics, which is a concrete example of hyperbolic-parabolic composite systems with non-symmetric dissipation. It is observed that the Cauchy problem for N-S-M equations admits the dissipative mechanism of regularity-loss type. Consequently, extra higher regularity is usually needed to obtain the optimal decay rate of {L1({mathbb{R}}^3)}-{L^2({mathbb{R}}^3)} type, in comparison with that for the global-in-time existence of smooth solutions. In this paper, we obtain the minimal decay regularity of global smooth solutions to N-S-M equations, with aid of {L^p({mathbb{R}}^n)}-{Lq({mathbb{R}}^n)}-{Lr({mathbb{R}}^n)} estimates. It is worth noting that the relation between decay derivative orders and the regularity index of initial data is firstly found in the optimal decay estimates.
Edwards, Jack R.; Mcrae, D. S.
1993-01-01
An efficient implicit method for the computation of steady, three-dimensional, compressible Navier-Stokes flowfields is presented. A nonlinear iteration strategy based on planar Gauss-Seidel sweeps is used to drive the solution toward a steady state, with approximate factorization errors within a crossflow plane reduced by the application of a quasi-Newton technique. A hybrid discretization approach is employed, with flux-vector splitting utilized in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes. Convergence histories and comparisons with experimental data are presented for several 3-D shock-boundary layer interactions. Both laminar and turbulent cases are considered, with turbulent closure provided by a modification of the Baldwin-Barth one-equation model. For the problems considered (175,000-325,000 mesh points), the algorithm provides steady-state convergence in 900-2000 CPU seconds on a single processor of a Cray Y-MP.
Liu, N.-S.; Shamroth, S. J.; Mcdonald, H.
1984-01-01
An existing method which solves the multi-dimensional ensemble-averaged compressible time-dependent Navier-Stokes equations in conjunction with mixing length turbulence model and shock capturing technique has been extended to include the shock-tracking adaptive grid systems. The numerical scheme for solving the governing equations is based on a linearized block implicit approach. The effects of grid-motion and grid-distribution on the calculated flow solutions have been studied in relative detail and this is carried out in the context of physically steady, shocked flows computed with non-stationary grids. Subsequently, the unsteady dynamics of the flows occurring in a supercritically operated transonic diffuser and a mixed compression supersonic inlet have been investigated with the adaptive grid systems by solving the Navier-Stokes equations.
Graham, J Pietarila; Mininni, Pablo; Pouquet, Annick
2007-01-01
We test three regularizations of the Navier-Stokes equations, the Lagrangian-Averaged Navier-Stokes alpha-model (LANS-alpha), Leray-alpha, and Clark-alpha, as subgrid scale (SGS) models by comparison with a direct numerical simulation (DNS) on a regular grid of 1024^3 points at a Reynolds number of approximatley 3300 and a Taylor Reynolds number of approximately 790. We use a Taylor-Green forcing which corresponds to a von Karman flow as used in several ongoing laboratory experiments. We also derive the Karman-Howarth equation for both the Clark-alpha and Leray-alpha models. We confirm one of two possible scalings resulting from this equation for Clark-alpha as well as its associated k^(-1) energy spectrum. Clark-alpha reproduces the total dissipation and the time to reach a statistical turbulent steady-state of the DNS. For small values of the filter width alpha it also reproduces the large-scale energy spectrum and intermittency properties of the DNS. As alpha is increased, Clark-alpha exhibits increased in...
Shrewsbury, George D.; Vadyak, Joseph; Schuster, David M.; Smith, Marilyn J.
1989-01-01
A computer analysis was developed for calculating steady (or unsteady) three-dimensional aircraft component flow fields. This algorithm, called ENS3D, can compute the flow field for the following configurations: diffuser duct/thrust nozzle, isolated wing, isolated fuselage, wing/fuselage with or without integrated inlet and exhaust, nacelle/inlet, nacelle (fuselage) afterbody/exhaust jet, complete transport engine installation, and multicomponent configurations using zonal grid generation technique. Solutions can be obtained for subsonic, transonic, or hypersonic freestream speeds. The algorithm can solve either the Euler equations for inviscid flow, the thin shear layer Navier-Stokes equations for viscous flow, or the full Navier-Stokes equations for viscous flow. The flow field solution is determined on a body-fitted computational grid. A fully-implicit alternating direction implicit method is employed for the solution of the finite difference equations. For viscous computations, either a two layer eddy-viscosity turbulence model or the k-epsilon two equation transport model can be used to achieve mathematical closure.
Arteaga, Santiago Egido
1998-12-01
The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the
Navier-Stokes-Fourier analytic solutions for non-isothermal Couette slip gas flow
Directory of Open Access Journals (Sweden)
Milićev Snežana S.
2016-01-01
Full Text Available The explicit and reliable analytical solutions for steady plane compressible non-isothermal Couette gas flow are presented. These solutions for velocity and temperature are developed by macroscopic approach from Navier-Stokes-Fourier system of continuum equations and the velocity slip and the temperature jump first order boundary conditions. Variability of the viscosity and thermal conductivity with temperature is involved in the model. The known result for the gas flow with constant and equal temperatures of the walls (isothermal walls is verified and a new solution for the case of different temperature of the walls is obtained. Evan though the solution for isothermal walls correspond to the gas flow of the Knudsen number Kn≤0.1, i.e. to the slip and continuum flow, it is shown that the gas velocity and related shear stress are also valid for the whole range of the Knudsen number. The deviation from numerical results for the same system is less than 1%. The reliability of the solution is confirmed by comparing with results of other authors which are obtained numerically by microscopic approach. The advantage of the presented solution compared to previous is in a very simple applicability along with high accuracy. [Projekat Ministarstva nauke Republike Srbije, br. 35046 i 174014
A 3-dimensional Navier-Stokes-Euler code for blunt-body flow computations
Li, C. P.
1985-01-01
The shock-layer flowfield is obtained with or without viscous and heat-conducting dissipations from the conservative laws of fluid dynamics equations using a shock-fitting implicity finite-difference technique. The governing equations are cast in curvilinear-orthogonal coordinates and transformed to the domain between the shock and the body. Another set of equations is used for the singular coordinate axis, which, together with a cone generator away from the stagnation point, encloses the computation domain. A time-dependent alternating direction implicit factorization technique is applied to integrate the equations with local-time increment until a steady solution is reached. The shock location is updated after the flowfield computation, but the wall conditions are implemented into the implicit procedure. Innovative procedures are introduced to define the initial flowfield, to treat both perfect and equilibrium gases, to advance the solution on a coarse-to-fine grid sequence, and to start viscous flow computations from their corresponding inviscid solutions. The results are obtained from a grid no greater than 28 by 18 by 7 and converged within 300 integration steps. They are of sufficient accuracy to start parabolized Navier-Stokes or Euler calculations beyond the nose region, to compare with flight and wind-tunnel data, and to evaluate conceptual designs of reentry spacecraft.
Computer modeling of flow and transport interactions for compressible Navier-Stokes equations
Rahman, Mohamed Mizanur
A unified numerical algorithm to simulate viscous flow with heat transfer over a wide range of Mach number and Reynolds number is developed. The governing equations used to model the numerical simulations are the 2-D compressible viscous Navier-Stokes equations. The numerical procedure is based on MacCormack's explicit 'predictor corrector' time dependent finite difference scheme. For an explicit scheme, a great number of iterations is required to get a converged steady solution because of a small time step. Vectorizing and parallelizing the code greatly alleviates this problem by reducing the total job running time manifold. The numerical algorithm, thus developed, is used to simulate such demanding and interacting flow problems as convection heat transfer in a cavity flow heat transfer enhancement by eddy-promoters, laminar/turbulent shock boundary layer interactions and unsteady shock boundary layer interactions over a compression corner. A detailed analysis of all important flow features that characterize such flows and the mechanisms that are involved, is performed for each individual case. The flow physics are discussed and new insights are provided. Results are compared with experimental data where available and the empirical relations between different flow properties or parameters are either established or verified where possible. Apart from these, some algorithm related questions, such as grid sensitivity, boundary conditions, convergence criteria, effects of artificial viscosity and the numerical stability are investigated.
Energy Technology Data Exchange (ETDEWEB)
Roberts, Nathan V.; Demkowiz, Leszek; Moser, Robert
2015-11-15
The discontinuous Petrov-Galerkin methodology with optimal test functions (DPG) of Demkowicz and Gopalakrishnan [18, 20] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. Whereas Bubnov-Galerkin methods use identical trial and test spaces, Petrov-Galerkin methods allow these function spaces to differ. In DPG, test functions are computed on the fly and are chosen to realize the supremum in the inf-sup condition; the method is equivalent to a minimum residual method. For well-posed problems with sufficiently regular solutions, DPG can be shown to converge at optimal rates—the inf-sup constants governing the convergence are mesh-independent, and of the same order as those governing the continuous problem [48]. DPG also provides an accurate mechanism for measuring the error, and this can be used to drive adaptive mesh refinements. We employ DPG to solve the steady incompressible Navier-Stokes equations in two dimensions, building on previous work on the Stokes equations, and focusing particularly on the usefulness of the approach for automatic adaptivity starting from a coarse mesh. We apply our approach to a manufactured solution due to Kovasznay as well as the lid-driven cavity flow, backward-facing step, and flow past a cylinder problems.
Exponential integrators for the incompressible Navier-Stokes equations.
Energy Technology Data Exchange (ETDEWEB)
Newman, Christopher K.
2004-07-01
We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is scalable in the sense that the computational costs grow linearly with problem size. Exponential integrators, used typically to solve systems of ODEs, utilize matrix vector products of the exponential of the Jacobian on a vector. For large systems, this product can be approximated efficiently by Krylov subspace methods. However, in contrast to explicit methods, KBEIs are not restricted by the time step. While implicit methods require a solution of a linear system with the Jacobian, KBEIs only require matrix vector products of the Jacobian. Furthermore, these methods are based on linearization, so there is no non-linear system solve at each time step. Differential-algebraic equations (DAEs) are ordinary differential equations (ODEs) subject to algebraic constraints. The discretized NSE constitute a system of DAEs, where the incompressibility condition is the algebraic constraint. Exponential integrators can be extended to DAEs with linear constraints imposed via a projection onto the constraint manifold. This results in a projected ODE that is integrated by a KBEI. In this approach, the Krylov subspace satisfies the constraint, hence the solution at the advanced time step automatically satisfies the constraint as well. For the NSE, the projection onto the constraint is typically achieved by a projection induced by the L{sup 2} inner product. We examine this L{sup 2} projection and an H{sup 1} projection induced by the H{sup 1} semi-inner product. The H
Renouf, M.; Bonamy, D.; Dubois, F.; Alart, P.
2005-10-01
The rheology of two-dimensional steady surface flow of cohesionless cylinders in a rotating drum is investigated through nonsmooth contact dynamics simulations. Profiles of volume fraction, translational and angular velocity, rms velocity, strain rate, and stress tensor are measured at the midpoint along the length of the surface-flowing layer, where the flow is generally considered as steady and homogeneous. Analysis of these data and their interrelations suggest the local inertial number—defined as the ratio between local inertial forces and local confinement forces—to be the relevant dimensionless parameter to describe the transition from the quasistatic part of the packing to the flowing part at the surface of the heap. Variations of the components of the stress tensor as well as the ones of rms velocity as a function of the inertial number are analyzed within both the quasistatic and the flowing phases. Their implications are discussed.
Secret Hidden in Navier-Stokes Equations: Singularity and Criterion of Turbulent Transition
Dou, Hua-Shu
2014-01-01
As is well known, there is discontinuity from laminar flow to turbulence in the time-averaged Navier-Stokes equations. In other words, singular point may implicitly exist in the Navier-Stokes equations for a given flow configuration. Transition of a laminar flow to a turbulent flow must be via the singular point. However, how the singularity of Navier-Stokes equations is related to the turbulent transition is not understood in the community. In this paper, a new formulation of the Navier-Stokes equation is derived for the time-averaged flows, and the singular point possibly existing in the Navier-Stokes equation is exactly found. For pressure driven flows, this singular point is actually the inflection point on the velocity profile. It is found that the stability of a flow depends on the direction of the gradient of the total mechanical energy for incompressible pressure-driven flow. When this direction is nearer the normal direction of the streamline, the flow is more unstable. It is further demonstrated tha...
Euler/Navier-Stokes Solvers Applied to Ducted Fan Configurations
Keith, Theo G., Jr.; Srivastava, Rakesh
1997-01-01
Due to noise considerations, ultra high bypass ducted fans have become a more viable design. These ducted fans typically consist of a rotor stage containing a wide chord fan and a stator stage. One of the concerns for this design is the classical flutter that keeps occurring in various unducted fan blade designs. These flutter are catastrophic and are to be avoided in the flight envelope of the engine. Some numerical investigations by Williams, Cho and Dalton, have suggested that a duct around a propeller makes it more unstable. This needs to be further investigated. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading be available. Aerodynamic solvers based on unsteady three-dimensional analysis will provide accurate and fast solutions and are best suited for aeroelastic analysis. The Euler solvers capture significant physics of the flowfield and are reasonably fast. An aerodynamic solver Ref. based on Euler equations had been developed under a separate grant from NASA Lewis in the past. Under the current grant, this solver has been modified to calculate the aeroelastic characteristics of unducted and ducted rotors. Even though, the aeroelastic solver based on three-dimensional Euler equations is computationally efficient, it is still very expensive to investigate the effects of multiple stages on the aeroelastic characteristics. In order to investigate the effects of multiple stages, a two-dimensional multi stage aeroelastic solver was also developed under this task, in collaboration with Dr. T. S. R. Reddy of the University of Toledo. Both of these solvers were applied to several test cases and validated against experimental data, where available.
Greenshields, Christopher J
2007-01-01
Howard Brenner has recently proposed modifications to the Navier-Stokes equations that relate to a diffusion of fluid volume that would be significant for flows with high density gradients. In a previous paper (Greenshields & Reese, 2007), we found these modifications gave good predictions of the viscous structure of shock waves in argon in the range Mach 1.0-12.0 (while conventional Navier-Stokes equations are known to fail above about Mach 2). However, some areas of concern with this model were a somewhat arbitrary choice of modelling coefficient, and potentially unphysical and unstable solutions. In this paper, we therefore present slightly different modifications to include molecule mass diffusion fully in the Navier-Stokes equations. These modifications are shown to be stable and produce physical solutions to the shock problem of a quality broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. The modifications primarily add a diffusion term to t...
Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach
Kiris, Cetin; Kwak, Dochan
1999-01-01
A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finite volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5th) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5th-order upwind differencing and a modified production term in the Baldwin-Barth one-equation turbulence model are used with adequate grid resolution.
Uniqueness of weak solutions of the Navier-Stokes equations of compressible flow
Ariane Piovezan Entringer
2009-01-01
Resumo: Este trabalho consiste de uma exposição detalhada do resultado provado no artigo Uniqueness of Weak Solutions of the Navier-Stokes Equations of Multidimensional, Compressible Flow de D. Hoff (SIAM J. Math. Anal - 2006) sobre a unicidade de solução fraca e a dependência contínua da solução fraca nos dados iniciais para as equações de Navier-Stokes para fluídos compressíveis...Observação: O resumo, na integra, podera ser visualizado no texto completo da tese digital Abstract: Uniquen...
Low-dimensional representations of exact coherent states of the Navier-Stokes equations
Sharma, Ati S; McKeon, Beverley J; Park, Jae Sung; Graham, Michael D; Willis, Ashley P
2015-01-01
We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just few modes of the model of McKeon & Sharma J. Fl. Mech. 658, 356 (2010). This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows. This establishes a new link between the exact invariant solutions and the theory of turbulent flow and provides new evidence of the former's continuing organising importance in that regime.
Pipe Flow and Wall Turbulence Using a Modified Navier-Stokes Equation
Institute of Scientific and Technical Information of China (English)
L. Jirkovsky; A. Muriel
2012-01-01
We use a derived incompressible modified Navier-Stokes equation to model pipe flow and wall turbulence. We reproduce the observed flattened paraboloid velocity profiles of turbulence that cannot be obtained directly using standard incompressible Navier-Stokes equation. The solutions found are in harmony with multi-valued velocity fields as a definition of turbulence. Repeating the procedure for the flow of turbulent fluid between two parallel flat plates we find similar flattened velocity profiles. We extend the analysis to the turbulent flow along a single wall and compare the results with experimental data and the established controversial yon Karman logarithmic law of the wall.
The Probabilistic Method and large initial data for Generalized Navier-Stokes systems
Cortissoz, Jean C
2011-01-01
In this paper we introduce a probabilistic approach to show the existence of initial data with arbitrarily large $L^2(\\mathbb{R}^3)$, $\\dot{H}^{1/2}(\\mathbb{R}^3)$ and $\\mathcal{PM}^2$-norms for which a Generalized Navier-Stokes system generate a global regular solution. More precisely, we show that from a certain family of possible large initial data most of them give raise to global regular solutions to a given Generalized Navier-Stokes system.
Navier-Stokes Neutral and Plasma Fluid Modelling in 3D
Energy Technology Data Exchange (ETDEWEB)
Riemann, J; Borchardt, M; Schneider, R; Mutzke, A; Rognlien, T; Umansky, M
2004-05-17
The 3D finite volume transport code BoRiS is applied to a system of coupled plasma and neutral fluid equations in a slab. Demonstrating easy implementation of new equations, a new parallel BoRiS version is tested on three different models for the neutral fluid - diffusive, parallel Navier-Stokes and full Navier-Stokes - and the results are compared to each other. Typical effects like density enhancement by ionization of recycled neutrals in front of a target plate can be seen and differences are linked to the neutral models in use.
Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations
Directory of Open Access Journals (Sweden)
Junbai Ren
2014-01-01
Full Text Available This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with Lp-Lq estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C1(1+t-3/4≤uL2≤C2(1+t-3/4, t>1. The decay rate is optimal since it coincides with that of heat equation.
Lattice Boltzmann Model for The Volume-Averaged Navier-Stokes Equations
Zhang, Jingfeng; Ouyang, Jie
2014-01-01
A numerical method, based on discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged Navier-Stokes equations can be recovered from the lattice Boltzmann equation in the limit of small Mach number by the Chapman-Enskog analysis and Taylor expansion. Due to its advantages such as explicit solver and inherent parallelism, the method appears to be more competitive with traditional numerical techniques. Numerical simulations show that the proposed model can accurately reproduce both the linear and nonlinear drag effects of porosity in the fluid flow through porous media.
Solutions to three-dimensional Navier-Stokes equations for incompressible fluids
Directory of Open Access Journals (Sweden)
Jorma Jormakka
2010-07-01
Full Text Available This article gives explicit solutions to the space-periodic Navier-Stokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions, but the solution cannot be continued to the whole space.
Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C., E-mail: waymire@math.oregonstate.edu [Department of Mathematics, Oregon State University, Corvallis, Oregon 97331 (United States); Michalowski, Nicholas [Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003 (United States)
2015-07-15
The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.
Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains
Brzeźniak, Z.; Caraballo, T.; Langa, J. A.; Li, Y.; Łukaszewicz, G.; Real, J.
We show that the stochastic flow generated by the 2-dimensional Stochastic Navier-Stokes equations with rough noise on a Poincaré-like domain has a unique random attractor. One of the technical problems associated with the rough noise is overcomed by the use of the corresponding Cameron-Martin (or reproducing kernel Hilbert) space. Our results complement the result by Brzeźniak and Li (2006) [10] who showed that the corresponding flow is asymptotically compact and also generalize Caraballo et al. (2006) [12] who proved existence of a unique attractor for the time-dependent deterministic Navier-Stokes equations.
Energy Technology Data Exchange (ETDEWEB)
Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics
1997-02-01
The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.
Energy Technology Data Exchange (ETDEWEB)
Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics
1997-02-01
The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.
Shakib, Farzin; Hughes, Thomas J. R.; Johan, Zdenek
1991-01-01
A space-time element method is presented for solving the compressible Euler and Navier-Stokes equations. The proposed formulation includes the variational equation, predictor multi-corrector algorithms and boundary conditions. The variational equation is based on the time-discontinuous Galerkin method, in which the physical entropy variables are employed. A least-squares operator and a discontinuity-capturing operator are added, resulting in a high-order accurate and unconditionally stable method. Implicit/explicit predictor multi-corrector algorithms, applicable to steady as well as unsteady problems, are presented; techniques are developed to enhance their efficiency. Implementation of boundary conditions is addressed; in particular, a technique is introduced to satisfy nonlinear essential boundary conditions, and a consistent method is presented to calculate boundary fluxes. Numerical results are presented to demonstrate the performance of the method.
An investigation of two dimensional parallel and non-parallel steady mixing layers
Energy Technology Data Exchange (ETDEWEB)
Shabani, A. [Azad Islamic Univ., Faculty of Mechanical Engineering, School of Engineering, Research and Science Inst., Tehran (Iran, Islamic Republic of)]. E-mail: ario.shabani@cic.aut.ac.ir; Basirat Tabrizi, H. [Amirkabir Univ. of Technology, Dept. of Mechanical Engineering, Tehran (Iran, Islamic Republic of)
2004-07-01
A CFD code was generated to simulate the steady state behavior of two dimensional, parallel and nonparallel merging mixing layers. For the free stream velocity ratios of 0.7 and 0.9, the effect of the merging angle of free stream velocities of between 0.0 to 18.0 degrees on the mixing zone's velocity distribution, and on the physical spreading of the turbulent domain was numerically simulated and studied. The results were in good agreement with the available theoretical and experimental results, and indicated that increasing the angle of merging of the two free streams, or increasing their associated free stream velocity ratios increases the spatial growth rate and decreases the turbulent development distance. (author)
Hybridizable discontinuous Galerkin projection methods for Navier-Stokes and Boussinesq equations
Ueckermann, M. P.; Lermusiaux, P. F. J.
2016-02-01
Schemes for the incompressible Navier-Stokes and Boussinesq equations are formulated and derived combining the novel Hybridizable Discontinuous Galerkin (HDG) method, a projection method, and Implicit-Explicit Runge-Kutta (IMEX-RK) time-integration schemes. We employ an incremental pressure correction and develop the corresponding HDG finite element discretization including consistent edge-space fluxes for the velocity predictor and pressure correction. We then derive the proper forms of the element-local and HDG edge-space final corrections for both velocity and pressure, including the HDG rotational correction. We also find and explain a consistency relation between the HDG stability parameters of the pressure correction and velocity predictor. We discuss and illustrate the effects of the time-splitting error. We then detail how to incorporate the HDG projection method time-split within standard IMEX-RK time-stepping schemes. Our high-order HDG projection schemes are implemented for arbitrary, mixed-element unstructured grids, with both straight-sided and curved meshes. In particular, we provide a quadrature-free integration method for a nodal basis that is consistent with the HDG method. To prevent numerical oscillations, we develop a selective nodal limiting approach. Its applications show that it can stabilize high-order schemes while retaining high-order accuracy in regions where the solution is sufficiently smooth. We perform spatial and temporal convergence studies to evaluate the properties of our integration and selective limiting schemes and to verify that our solvers are properly formulated and implemented. To complete these studies and to illustrate a range of properties for our new schemes, we employ an unsteady tracer advection benchmark, a manufactured solution for the steady diffusion and Stokes equations, and a standard lock-exchange Boussinesq problem.
HOMOGENIZATION OF A STATIONARY NAVIER-STOKES FLOW IN POROUS MEDIUM WITH THIN FILM
Institute of Scientific and Technical Information of China (English)
Yao Zhengan; Zhao Hongxing
2008-01-01
The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition. At the end of the article, "Darcy's law" is rigorously derived from this model as the parameter e tends to zero, which is independent of the coordinates towards the thickness.
Biedron, Robert T.; Vatsa, Veer N.; Atkins, Harold L.
2005-01-01
We apply an unsteady Reynolds-averaged Navier-Stokes (URANS) solver for unstructured grids to unsteady flows on moving and stationary grids. Example problems considered are relevant to active flow control and stability and control. Computational results are presented using the Spalart-Allmaras turbulence model and are compared to experimental data. The effect of grid and time-step refinement are examined.
Directory of Open Access Journals (Sweden)
Jian Liu
2013-09-01
Full Text Available In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.
Numerical simulation of compressible Navier-Stokes flow in a double throat nozzle
Scott, James N.; Visbal, Miguel R.
The flow through a double-throat nozzle is computed using the complete time-dependent compressible Navier-Stokes equations. The computations were performed by using an existing working code with no special modifications for this particular application. The computations were performed on a Cyber 845 computer and a CRAY XMP-48 computer using three different grid sizes.
Continuum Navier-Stokes modelling of water ow past fullerene molecules
DEFF Research Database (Denmark)
Walther, J. H.; Popadic, A.; Koumoutsakos, P.;
We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest as ...
Global Well-posedness of Compressible Bipolar Navier-Stokes-Poisson Equations
Institute of Scientific and Technical Information of China (English)
Yi Quan LIN; Cheng Chun HAO; Hai Liang LI
2012-01-01
We consider the initial value problem for multi-dimensional bipolar compressible NavierStokes-Poisson equations,and show the global existence and uniqueness of the strong solution in hybrid Besov spaces with the initial data close to an equilibrium state.
Properties of the Residual Stress of the Temporally Filtered Navier-Stokes Equations
Pruett, C. D.; Gatski, T. B.; Grosch, C. E.; Thacker, W. D.
2002-01-01
The development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, is of current interest. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. Causal time-domain filters, parameterized by a temporal filter width 0 less than Delta less than infinity, are considered. For several reasons, the differential forms of such filters are preferred to their corresponding integral forms; among these, storage requirements for differential forms are typically much less than for integral forms and, for some filters, are independent of Delta. The behavior of the residual stress in the limits of both vanishing and in infinite filter widths is examined. It is shown analytically that, in the limit Delta to 0, the residual stress vanishes, in which case the Navier-Stokes equations are recovered from the temporally filtered equations. Alternately, in the limit Delta to infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger's equation. Finally, finite filter widths are also considered, and a priori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted.
Global solutions of stochastic 2D Navier-Stokes equations with Lévy noise
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper,we prove the global existence and uniqueness of the strong and weak solutions for 2D Navier-Stokes equations on the torus T2 perturbed by a Lévy process.The existence of invariant measure of the solutions are proved also.
Actuator Line/Navier-Stokes Computations for Flows past the Yawed MEXICO Rotor
DEFF Research Database (Denmark)
Shen, Wen Zhong; Sørensen, Jens Nørkær; Yang, H.
2011-01-01
In the paper the Actuator Line/Navier-Stokes model has been used to simulate flows past the yawed MEXICO rotor. The computed loads as well as the velocity field behind the yawed rotor are compared to detailed pressure and PIV measurements which were carried out in the EU funded MEXICO project...
Weak-strong uniqueness for the isothermal Navier-Stokes equations
Yao, Lei; Cui, Haibo
2016-11-01
In this paper, we are concerned with weak-strong uniqueness results for the isothermal Navier-Stokes equations in two space dimension. Using the methods of relative entropy, we obtain some conditions on a weak solution, such as the ones built up by Plotnikov and Weigant [SIAM J. Math. Anal. 47, 626-653 (2015)], so that it is unique.
EXISTENCE AND UNIQUENESS OF THE CAUCHY PROBLEM FOR A GENERALIZED NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
刘晓风
2003-01-01
We consider the Cauchy problem for a generalized Navier-Stokes equations with hyperdissipation, with the initial data in Lpσ. We follow the theme of [1] but with more complicated analysis on the symbol and obtain the existence and uniqueness results.
ON THE REGULARITY CRITERIA OF THE 3D NAVIER-STOKES EQUATIONS IN CRITICAL SPACES
Institute of Scientific and Technical Information of China (English)
Dong Boqing; Sadek Gala; Chen Zhimin
2011-01-01
Regularity criteria of Leray-Hopf weak solutions to the three-dimensional Navier-Stokes equations in some critical spaces such as Lorentz space, Morrey space and multiplier space are derived in terms of two partial derivatives, 1u1, 2u2, of velocity fields.
Mathematical geophysics an introduction to rotating fluids and the Navier-Stokes equations
Chemin, Jean-Yves; Gallagher, Isabelle; Grenier, Emmanuel
2006-01-01
Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.
High Re Separated Flow Solutions Using the Navier-Stokes and Approximate Equations,
1985-01-01
flow field. In the present study the incremental block-line Gauss- Seidel method proposed in Ref. 17 is used as an efficient numerical tool for solving...Incremental Block-Line-Gauss- Seidel Method for the Navier-Stokes Equations", AIAA Paper 85-0033. 18. Beam, R. M. and Warming, R. F., "An Implicit Factored
Remarks on the Regularity Criteria of Three-Dimensional Navier-Stokes Equations in Margin Case
Institute of Scientific and Technical Information of China (English)
ZHANG Xingwei; ZHANG Wenliang; DONG Bo-Qing
2011-01-01
In the study of the regularity criteria for Leray weak solutions to threedimensional Navier-Stokes equations, two sufficient conditions such that the horizontal velocity ú satisfies ú∈L2(0,T;BMO(R3)) or ú ∈ L2/1＋r(0,T;Br∞,∞(R3)) for 0 ＜ r ＜ 1 are considered.
HOMOGENIZATION OF THE INCOMPRESSIBLE NAVIER-STOKES FLUID WITH OSCILLATION COEFFICIENT
Institute of Scientific and Technical Information of China (English)
Hongxing ZHAO
2014-01-01
We study the homogenization of the incompressible Navier-Stokes equations with periodic oscillating coefficient in a bounded non-homogeneous media. To do that, we introduce a generalized compensate compactness result and a suitable class of test function to this problem. By passing the limit, we obtain the homogenized model of this problem.
Fully discrete Jacobi-spherical harmonic spectral method for Navier-Stokes equations
Institute of Scientific and Technical Information of China (English)
HUANG Wei; GUO Ben-yu
2008-01-01
A fully discrete Jacobi-spherical harmonic spectral method is provided for the Navier-Stokes equations in a ball.Its stability and convergence are proved.Numerical results show efficiency of this approach.The proposed method is also applicable to other problems in spherical geometry.
The Concept of Turbulence and Some Aspects of The Navier-stokes Equations
Sivertsen, T. H.
In the first place some features of the concept of turbulence presented in literature are discussed. The Navier-Stokes equations are presented, and the connection of the Navier-Stokes equations to an explicit interpretation of the hypothetico-deductive principle (less restrictive than usual) and the concepts of temporal and spatial scale of the physical phenomena of fluid flow are discussed. Then the concept of turbulence is redefined, and we take a look at the scope of the Navier-Stokes equations as well as the necessity of explicit defining the temporal and spatial scales in order to use this system of equations of Navier-Stokes. Turbulence is redefined as all flow phenomena on temporal and spatial scales less than the scales we are actually modelling. These flow phenomena (eddies) must be presented in our flow system by several special parameters possible to measure or theoretically derive from other measurable param- eters. The concept of parameter is interpreted as a numerical measurable attribute of a physical phenomenon, and a formalization of this concept is presented. The concept of sub-grid model of a numerical mathematical flow system model is discussed in the end of the contribution.
Inviscid incompressible limits of the full Navier-Stokes-Fourier system
Feireisl, Eduard
2012-01-01
We consider the full Navier-Stokes-Fourier system in the singular limit for the small Mach and large Reynolds and Peclet numbers, with ill prepared initial data on the three dimensional Euclidean space. The Euler-Boussinesq approximation is identified as the limit system.
Navier-Stokes on Black Hole Horizons and DC Thermoelectric Conductivity
Donos, Aristomenis
2015-01-01
We consider a general class of black hole solutions of Einstein-Maxwell theory which are holographically dual to CFTs with spatially dependent sources. We show that an averaged DC thermoelectric conductivity matrix can be obtained by solving the forced, linearised, time-independent Navier-Stokes equations on the black hole horizon for an incompressible and charged fluid.
Second-order fully discretized projection method for incompressible Navier-Stokes equations
Directory of Open Access Journals (Sweden)
Daniel X. Guo
2016-03-01
Full Text Available A second-order fully discretized projection method for the incompressible Navier-Stokes equations is proposed. It is an explicit method for updating the pressure field. No extra conditions of immediate velocity fields are needed. The stability and convergence are investigated.
Second-order fully discretized projection method for incompressible Navier-Stokes equations
Daniel X. Guo
2016-01-01
A second-order fully discretized projection method for the incompressible Navier-Stokes equations is proposed. It is an explicit method for updating the pressure field. No extra conditions of immediate velocity fields are needed. The stability and convergence are investigated.
Quasi-steady-state analysis of two-dimensional random intermittent search processes
Bressloff, Paul C.
2011-06-01
We use perturbation methods to analyze a two-dimensional random intermittent search process, in which a searcher alternates between a diffusive search phase and a ballistic movement phase whose velocity direction is random. A hidden target is introduced within a rectangular domain with reflecting boundaries. If the searcher moves within range of the target and is in the search phase, it has a chance of detecting the target. A quasi-steady-state analysis is applied to the corresponding Chapman-Kolmogorov equation. This generates a reduced Fokker-Planck description of the search process involving a nonzero drift term and an anisotropic diffusion tensor. In the case of a uniform direction distribution, for which there is zero drift, and isotropic diffusion, we use the method of matched asymptotics to compute the mean first passage time (MFPT) to the target, under the assumption that the detection range of the target is much smaller than the size of the domain. We show that an optimal search strategy exists, consistent with previous studies of intermittent search in a radially symmetric domain that were based on a decoupling or moment closure approximation. We also show how the decoupling approximation can break down in the case of biased search processes. Finally, we analyze the MFPT in the case of anisotropic diffusion and find that anisotropy can be useful when the searcher starts from a fixed location. © 2011 American Physical Society.
Calhoun, Ronald; Gouveia, Frank; Shinn, Joseph; Chan, Stevens; Stevens, Dave; Lee, Robert; Leone, John
2004-05-01
An experiment investigating flow around a single complex building was performed in 2000. Sonic anemometers were placed around the building, and two-dimensional wind velocities were recorded. An energy-budget and wind-measuring station was located upstream to provide stability and inflow conditions. In general, the sonic anemometers were located in a horizontal plane around the building at a height of 2.6 m above the ground. However, at the upwind wind station, two levels of the wind were measured. The resulting database can be sampled to produce mean wind fields associated with specific wind directions such as 210°, 225°, and 240°. The data are available generally and should be useful for testing computational fluid dynamical models for flow around a building. An in-house Reynolds-averaged Navier Stokes approach was used to compare with the mean wind fields for the predominant wind directions. The numerical model assumed neutral flow and included effects from a complex array of trees in the vicinity of the building. Two kinds of comparisons are presented: 1) direct experimental versus modeled vector comparisons and 2) a numerical metric approach that focuses on wind magnitude and direction errors. The numerical evaluation generally corroborates the vector-to-vector inspection, showing reasonable agreement for the mean wind fields around the building. However, regions with special challenges for the model were identified. In particular, recirculation regions were especially difficult for the model to capture correctly. In the 240° case, there is a tendency for the model to exaggerate the turning effect in the wind caused by the effect of the building. Two different kinds of simulations were performed: 1) predictive calculations with a reasonable but not high-fidelity representation of the building's architectural complexity and 2) postexperiment calculations in which a large number of architectural features were well represented. Although qualitative evidence
2014-09-06
AFRL-RD-PS- AFRL-RD-PS- TR-2014-0029 TR-2014-0029 LARGE - EDDY /REYNOLDS-AVERAGED NAVIER- STOKES SIMULATION OF SHOCK-TRAIN DEVELOPMENT IN A COIL...CONTRACT NUMBER FA9451-13-1-0262 Large - Eddy /Reynolds-Averaged Navier-Stokes Simulation of Shock-Train 5b. GRANT NUMBER Development in a COIL –Laser...NOTES 14. ABSTRACT This report describes the application of a hybrid large - eddy simulation / Reynolds-averaged Navier-Stokes method to predict shock
Operator splitting for two-dimensional incompressible fluid equations
Holden, Helge; Karper, Trygve K
2011-01-01
We analyze splitting algorithms for a class of two-dimensional fluid equations, which includes the incompressible Navier-Stokes equations and the surface quasi-geostrophic equation. Our main result is that the Godunov and Strang splitting methods converge with the expected rates provided the initial data are sufficiently regular.
Two-dimensional simulations of steady perforated-plate stabilized premixed flames
Altay, H. Murat
2010-03-17
The objective of this work is to examine the impact of the operating conditions and the perforated-plate design on the steady, lean premixed flame characteristics. We perform two-dimensional simulations of laminar flames using a reduced chemical kinetics mechanism for methane-air combustion, consisting of 20 species and 79 reactions. We solve the heat conduction problem within the plate, allowing heat exchange between the gas mixture and the solid plate. The physical model is based on a zero-Mach-number formulation of the axisymmetric compressible conservation equations. The results suggest that the flame consumption speed, the flame structure, and the flame surface area depend significantly on the equivalence ratio, mean inlet velocity, the distance between the perforated-plate holes and the plate thermal conductivity. In the case of an adiabatic plate, a conical flame is formed, anchored near the corner of the hole. When the heat exchange between themixture and the plate is finite, the flame acquires a Gaussian shape stabilizing at a stand-off distance, that grows with the plate conductivity. The flame tip is negatively curved; i.e. concave with respect to the reactants. Downstream of the plate, the flame base is positively curved; i.e. convex with respect to the reactants, stabilizing above a stagnation region established between neighboring holes. As the plate\\'s thermal conductivity increases, the heat flux to the plate decreases, lowering its top surface temperature. As the equivalence ratio increases, the flame moves closer to the plate, raising its temperature, and lowering the flame stand-off distance. As the mean inlet velocity increases, the flame stabilizes further downstream, the flame tip becomes sharper, hence raising the burning rate at that location. The curvature of the flame base depends on the distance between the neighboring holes; and the flame there is characterized by high concentration of intermediates, like carbon monoxide. © 2010 Taylor
Two-Level Stabilized Finite Volume Methods for Stationary Navier-Stokes Equations
Directory of Open Access Journals (Sweden)
Anas Rachid
2012-01-01
Full Text Available We propose two algorithms of two-level methods for resolving the nonlinearity in the stabilized finite volume approximation of the Navier-Stokes equations describing the equilibrium flow of a viscous, incompressible fluid. A macroelement condition is introduced for constructing the local stabilized finite volume element formulation. Moreover the two-level methods consist of solving a small nonlinear system on the coarse mesh and then solving a linear system on the fine mesh. The error analysis shows that the two-level stabilized finite volume element method provides an approximate solution with the convergence rate of the same order as the usual stabilized finite volume element solution solving the Navier-Stokes equations on a fine mesh for a related choice of mesh widths.
Continuous data assimilation for the three-dimensional Navier-Stokes-$\\alpha$
Albanez, Débora A F; Titi, Edriss S
2014-01-01
Motivated by the presence of a finite number of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages for dissipative dynamical systems, we present a continuous data assimilation algorithm for the three-dimensional Navier-Stokes-$\\alpha$ model. This algorithm consists of introducing a nudging process through general type of approximation interpolation operator (that is constructed from observational measurements) that synchronizes the large spatial scales of the approximate solutions with those of the unknown solutions the Navier-Stokes-$\\alpha$ equations that corresponds to these measurements. Our main result provides conditions on the finite-dimensional spatial resolution of the collected data, sufficient to guarantee that the approximating solution, that is obtained from these collected data, converges to the unkown reference solution (physical reality) over time. These conditions are given in terms of some physical parameters, such as kinematic viscosity, the size of ...
Holst, T. L.; Thomas, S. D.; Kaynak, U.; Gundy, K. L.; Flores, J.; Chaderjian, N. M.
1985-01-01
Transonic flow fields about wing geometries are computed using an Euler/Navier-Stokes approach in which the flow field is divided into several zones. The flow field immediately adjacent to the wing surface is resolved with fine grid zones and solved using a Navier-Stokes algorithm. Flow field regions removed from the wing are resolved with less finely clustered grid zones and are solved with an Euler algorithm. Computational issues associated with this zonal approach, including data base management aspects, are discussed. Solutions are obtained that are in good agreement with experiment, including cases with significant wind tunnel wall effects. Additional cases with significant shock induced separation on the upper wing surface are also presented.
Zero Dissipation Limit to Rarefaction Waves for the 1-D Compressible Navier-Stokes Equations
Institute of Scientific and Technical Information of China (English)
Feimin HUANG; Xing LI
2012-01-01
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 ε1/4[In ε|.In this paper,Xin's convergence rate is improved to ε1/3|In ε|2 by different scaling arguments.The new scaling has various applications in related problems.
Institute of Scientific and Technical Information of China (English)
Hakho HONG
2016-01-01
The zero dissipation limit to the contact discontinuities for one-dimensional com-pressible Navier-Stokes equations was recently proved for ideal polytropic gas (see Huang et al. [15, 22] and Ma [31]), but there is few result for general gases including ideal polytropic gas. We prove that if the solution to the corresponding Euler system of general gas satisfying (1.4) is piecewise constant with a contact discontinuity, then there exist smooth solutions to Navier-Stokes equations which converge to the inviscid solutions at a rate of κ14 as the heat-conductivity coeff cient κtends to zero. The key is to construct a viscous contact wave of general gas suitable to our proof (see Section 2). Notice that we have no need to restrict the strength of the contact discontinuity to be small.
On the Lamb vector divergence, evolution of pressure fields and Navier-Stokes regularity
Lindgren, Jussi
2012-01-01
This paper analyzes the Lamb vector divergence, also called the hydrodynamic charge density, and its implications to the Navier-Stokes system. It is shown that the pressure field can be always chosen in a way that ensures regularity of the Navier-Stokes system. The abstract pressure field that ensures regularity is defined through two partial differential equations, one of them being of the elliptic kind and the other one being an evolution equation. The pressure field defined such a way can be interpreted as a control potential field that keeps the system regular. The controlling pressure field depends only on the velocity field of the fluid and its derivatives, so that the result is applicable in any general setting where the initial data is divergence free, smooth and square-integrable.
A IPN×IPN Spectral Element Projection Method for the Unsteady Incompressible Navier-Stokes Equations
Institute of Scientific and Technical Information of China (English)
Zhijian Rong; Chuanju Xu
2008-01-01
In this paper, we present a PN×PN spectral element method and a detailed comparison with existing methods for the unsteady incompressible Navier-Stokes equations. The main purpose of this work consists of: (i) detailed comparison and discussion of some recent developments of the temporal discretizations in the frame of spectral element approaches in space; (ii) construction of a stable PN×PN method together with a PN→PN-2 post-filtering. The link of different methods will be clarified. The key feature of our method lies in that only one grid is needed for both velocity and pressure variables, which differs from most well-known solvers for the Navier-Stokes equations. Although not yet proven by rigorous theoretical analysis, the stability and accuracy of this one-grid spectral method are demonstrated by a series of numerical experiments.
Study of the Navier-Stokes regularity problem with critical norms
Ohkitani, Koji
2016-04-01
We study the basic problems of regularity of the Navier-Stokes equations. The blowup criteria on the basis of the critical {H}1/2-norm, is bounded from above by a logarithmic function, (Robinson et al 2012 J. Math. Phys. 53 115618). Assuming that the Cauchy-Schwarz inequality for the {H}1/2-norm is not an overestimate, we replace it by a square-root of a product of the energy and the enstrophy. We carry out a simple asymptotic analysis to determine the time evolution of the energy. This generalises the (already ruled-out) self-similar blowup ansatz. Some numerical results are also presented, which support the above-mentioned replacement. We carry out a similar analysis for the four-dimensional Navier-Stokes equations.
Zhang, Xiangxiong
2017-01-01
We construct a local Lax-Friedrichs type positivity-preserving flux for compressible Navier-Stokes equations, which can be easily extended to multiple dimensions for generic forms of equations of state, shear stress tensor and heat flux. With this positivity-preserving flux, any finite volume type schemes including discontinuous Galerkin (DG) schemes with strong stability preserving Runge-Kutta time discretizations satisfy a weak positivity property. With a simple and efficient positivity-preserving limiter, high order explicit Runge-Kutta DG schemes are rendered preserving the positivity of density and internal energy without losing local conservation or high order accuracy. Numerical tests suggest that the positivity-preserving flux and the positivity-preserving limiter do not induce excessive artificial viscosity, and the high order positivity-preserving DG schemes without other limiters can produce satisfying non-oscillatory solutions when the nonlinear diffusion in compressible Navier-Stokes equations is accurately resolved.
A p-adaptive LCP formulation for the compressible Navier-Stokes equations
Cagnone, J. S.; Vermeire, B. C.; Nadarajah, S.
2013-01-01
This paper presents a polynomial-adaptive lifting collocation penalty (LCP) formulation for the compressible Navier-Stokes equations. The LCP formulation is a high-order nodal scheme in differential form. This format, although computationally efficient, complicates the treatment of non-uniform polynomial approximations. In Cagnone and Nadarajah (2012) [9], we proposed to circumvent this difficulty by employing specially designed elements inserted at the interface where the interpolation degree varies. In the present study we examine the applicability of this approach to the discretization of the Navier-Stokes equations, with focus put on the treatment of the viscous fluxes. The stability of the scheme is analyzed with the scalar diffusion equation and the merits of the approach are demonstrated with various p-adaptive simulations.
Chen, Y. K.; Henline, W. D.
1993-01-01
The general boundary conditions including mass and energy balances of chemically equilibrated or nonequilibrated gas adjacent to ablating surfaces have been derived. A computer procedure based on these conditions was developed and interfaced with the Navier-Stokes solver for predictions of the flow field, surface temperature, and surface ablation rates over re-entry space vehicles with ablating Thermal Protection Systems (TPS). The Navier-Stokes solver with general surface thermochemistry boundary conditions can predict more realistic solutions and provide useful information for the design of TPS. A test case with a proposed hypersonic test vehicle configuration and associated free stream conditions was developed. Solutions with various surface boundary conditions were obtained, and the effect of nonequilibrium gas as well as surface chemistry on surface heating and ablation rate were examined. The solutions of the GASP code with complete ablating surface conditions were compared with those of the ASC code. The direction of future work is also discussed.
The Cauchy problem for the pressureless Euler/isentropic Navier-Stokes equations
Choi, Young-Pil; Kwon, Bongsuk
2016-07-01
We present a new hydrodynamic model consisting of the pressureless Euler equations and the isentropic compressible Navier-Stokes equations where the coupling of two systems is through the drag force. This coupled system can be derived, in the hydrodynamic limit, from the particle-fluid equations that are frequently used to study the medical sprays, aerosols and sedimentation problems. For the proposed system, we first construct the local-in-time classical solutions in an appropriate L2 Sobolev space. We also establish the a priori large-time behavior estimate by constructing a Lyapunov functional measuring the fluctuation of momentum and mass from the averaged quantities, and using this together with the bootstrapping argument, we obtain the global classical solution. The large-time behavior estimate asserts that the velocity functions of the pressureless Euler and the compressible Navier-Stokes equations are aligned exponentially fast as time tends to infinity.
Navier-Stokes equation describes the movement of a special superfluid medium
Sbitnev, Valeriy I
2015-01-01
The Navier-Stokes equation contains two terms which have been subjected to slight modification: (a) the viscosity term depends of time (the viscosity in average on time is zero, but its variance is nonzero); (b) the pressure gradient contains an added term describing the entropy gradient multiplied by the pressure. Owing to these modifications, the Navier-Stokes equation can be reduced to the Schr\\"odinger equation describing behavior of a particle into the vacuum, where the vacuum is a superfluid medium. Vortex structures arising in this medium show infinitely long life owing to zero average viscosity. The nonzero variance describes exchange of the vortex energy with zero-point energy of the vacuum. Radius of the vortex trembles around some average value. This observation sheds the light to the Zitterbewegung phenomenon. The vortex has a non-zero core where the vortex velocity vanishes. Its organization is discussed with the point of view of the Calabi-Yau manifold.
Study of Tip-loss Using an Inverse 3D Navier-Stokes Method
DEFF Research Database (Denmark)
Mikkelsen, Robert; Sørensen, Jens Nørkær; Shen, Wen Zhong;
2003-01-01
The tip-correction for air-screws described by Prandtl (1919) and implemented into the Blade Element Momentum (BEM) theory by Glauert (1930), is founded on certain assumptions which the present analysis seeks to overcome. In the paper we propose a method to derive the tip-correction by solving...... the 3D Navier-Stokes equations combined with the actuator line technique where blade loading is applied using an inverse method. The numerical simulations shows that the method captures the tip-correction when comparing with the theories of Prandtl and Goldstein, however, the accuracy of the obtained...... results reveal that further refinements still is needed. Keywords: Tip-loss; Actuator line; 3D Navier-Stokes methods....
A Solvability criterion for Navier-Stokes equations in high dimensions
Viswanathan, T M
2009-01-01
We define the Ladyzhenskaya-Lions exponent $\\alpha_L(n)=(2+n)/4$ for Navier-Stokes equations with dissipation $-(-\\Delta)^{\\alpha}$ in ${\\Bbb R}^n$, for all $n\\geq 2$. We then prove strong global solvability when $\\alpha\\geq \\alpha_L(n)$, given smooth initial data. If the corresponding Euler equations for $n>2$ were to allow uncontrolled growth of the enstrophy ${1\\over 2} \\|\
On the asymptotic limit of the Navier-Stokes system on domains with rough boundaries
Bucur, Dorin; Feireisl, Eduard; Nečasová, Šárka; Wolf, Joerg
We study the asymptotic behavior of solutions to the incompressible Navier-Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter. Imposing the complete slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary provided the oscillations are non-degenerate, meaning not oriented in a single direction.
Chen, Hui; Fang, Daoyuan; Zhang, Ting
2017-02-01
In this paper, we investigate the global well-posedness for the three dimensional inhomogeneous incompressible Navier-Stokes system with axisymmetric initial data. We obtain the global existence and uniqueness of the axisymmetric solution provided that |a0/r|_{∞} and |u0^{θ}|3 {are sufficiently small}. Furthermore, if {u_0 in L1} and {ru^{θ}0in L1 \\cap L2} , we have the decay estimate |u^{θ}(t)|22 + 0.
Conservation of Total Vorticity for a 2D Stochastic Navier Stokes Equation
Directory of Open Access Journals (Sweden)
Peter M. Kotelenez
2011-01-01
Full Text Available We consider point vortices whose positions satisfy a stochastic ordinary differential equation on ℝ2 perturbed by spatially correlated Brownian noise. The associated signed point measure-valued empirical process turns out to be a weak solution to a stochastic Navier-Stokes equation (SNSE with a state-dependent stochastic term. As the number of vortices tends to infinity, we obtain a smooth solution to the SNSE, and we prove the conservation of total vorticity in this continuum limit.
2008-01-17
length local Knudsen number, KnGLL = λ Q ∣∣∣∣ dQ dl ∣∣∣∣ (3.26) where λ is the mean free-path, Q is some quantity of interest such as density, pressure...Comparisons between DSMC and the Navier-Stokes equations for reentry flows. AIAA Paper 1993– 2810. [65] Ozawa, T., Zhong, J., Levin, D. A., Boger , D
Institute of Scientific and Technical Information of China (English)
KOUKOUVINIS P.; BERGELES G.; GAVAISES M
2015-01-01
The paper proposes a methodology within the Reynolds averaged Navier Stokes (RANS) solvers for cavitating flows capable of predicting the flow regions of bubble collapse and the potential aggressiveness to material damage. An aggressiveness index is introduced, called cavitation aggressiveness index (CAI) based on the total derivative of pressure which identifies surface areas exposed to bubble collapses, the index is tested in two known cases documented in the open literature and seems to identify regions of potential cavitation damage.
Regularity Criteria for a Coupled Navier-Stokes and Q-Tensor System
Directory of Open Access Journals (Sweden)
Jishan Fan
2013-01-01
Full Text Available We study a system describing the evolution of a nematic liquid crystal flow. The system couples a forced Navier-Stokes system describing the flow with a parabolic-type system describing the evolution of the nematic crystal director fields (Q-tensors. We prove some regularity criteria for the local strong solutions. However, we do not provide estimates on the rates of increase of high norms.
Carpenter, Mark H.; Fisher, Travis C.; Nielsen, Eric J.; Frankel, Steven H.
2013-01-01
Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.
Hartmann, Ralf; Houston, Paul
2008-11-01
In this article we propose a new symmetric version of the interior penalty discontinuous Galerkin finite element method for the numerical approximation of the compressible Navier-Stokes equations. Here, particular emphasis is devoted to the construction of an optimal numerical method for the evaluation of certain target functionals of practical interest, such as the lift and drag coefficients of a body immersed in a viscous fluid. With this in mind, the key ingredients in the construction of the method include: (i) an adjoint consistent imposition of the boundary conditions; (ii) an adjoint consistent reformulation of the underlying target functional of practical interest; (iii) design of appropriate interior penalty stabilization terms. Numerical experiments presented within this article clearly indicate the optimality of the proposed method when the error is measured in terms of both the L2-norm, as well as for certain target functionals. Computational comparisons with other discontinuous Galerkin schemes proposed in the literature, including the second scheme of Bassi and Rebay, cf. [F. Bassi, S. Rebay, GMRES discontinuous Galerkin solution of the compressible Navier-Stokes equations, in: B. Cockburn, G. Karniadakis, C.-W. Shu (Eds.), Discontinuous Galerkin Methods, Lecture Notes in Comput. Sci. Engrg., vol. 11, Springer, Berlin, 2000, pp. 197-208; F. Bassi, S. Rebay, Numerical evaluation of two discontinuous Galerkin methods for the compressible Navier-Stokes equations, Int. J. Numer. Methods Fluids 40 (2002) 197-207], the standard SIPG method outlined in [R. Hartmann, P. Houston, Symmetric interior penalty DG methods for the compressible Navier-Stokes equations. I: Method formulation, Int. J. Numer. Anal. Model. 3(1) (2006) 1-20], and an NIPG variant of the new scheme will be undertaken.
Time-Filtered Navier-Stokes Approach and Emulation of Turbulence-Chemistry Interaction
Liu, Nan-Suey; Wey, Thomas; Shih, Tsan-Hsing
2013-01-01
This paper describes the time-filtered Navier-Stokes approach capable of capturing unsteady flow structures important for turbulent mixing and an accompanying subgrid model directly accounting for the major processes in turbulence-chemistry interaction. They have been applied to the computation of two-phase turbulent combustion occurring in a single-element lean-direct-injection combustor. Some of the preliminary results from this computational effort are presented in this paper.
Self-Similar Solutions of Three-Dimensional Navier-Stokes Equation
Institute of Scientific and Technical Information of China (English)
I.F. Barna
2011-01-01
In this article we will present pure three dimensional analytic solutions for the Navier-Stokes and the continuity equations in Cartesian coordinates. The key idea is the three-dimensional generalization of the well-known self-similar Ansatz of Barenblatt. A geometrical interpretation of the Ansatz is given also. The results are the Kummer functions or strongly related. Our final formula is compared with other results obtained from group theoretical approaches.
Weak-strong uniqueness property for the full Navier-Stokes-Fourier system
Feireisl, Eduard
2011-01-01
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.
A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations
Institute of Scientific and Technical Information of China (English)
DANCHIN; Raphaёl
2012-01-01
Fourier analysis methods and in particular techniques based on Littlewood-Paley decomposition and paraproduct have known a growing interest recently for the study of nonlinear evolutionary equations.In this survey paper,we explain how these methods may be implemented so as to study the compresible Navier-Stokes equations in the whole space.We shall investigate both the initial value problem in critical Besov spaces and the low Mach number asymptotics.
PARTIALLY AVERAGED NAVIER-STOKES METHOD FOR TIME DEPENDENT TURBULENT CAVITATING FLOWS
Institute of Scientific and Technical Information of China (English)
HUANG Biao; WANG Guo-yu
2011-01-01
Cavitation typically occurs when the fluid pressure is lower than the vapor pressure in a local thermodynamic state, and the flow is frequently unsteady and turbulent. The Reynolds-Averaged Navier-Stokes (RANS) approach has been popular for turbulent flow computations. The most widely used ones, such as the standard k-ε model, have well-recognized deficiencies when treating time dependent flow field. To identify ways to improve the predictive capability of the current RANS-based engineering turbulence closures, conditional averaging is adopted for the Navier-Stokes equation, and one more parameter, based on the filter size, is introduced into the k-ε model. In the Partially Averaged Navier-Stokes (PANS) model, the filter width is mainly controlled by the ratio of unresolved-to-total kinetic energy f1. This model is assessed in unsteady cavitating flows over a Clark-Y hydrofoil. From the experimental validations regarding the forces, frequencies, cavity visualizations and velocity distributions, the PANS model is shown to improve the predictive capability considerably, in comparison to the standard k-ε model, and also, it is observed the value of f1 in the PANS model has substantial influence on the predicting result. As the filter width f1 is decreased, the PANS model can effectively reduce the eddy viscosity near the closure region which can significantly influence the capture of the detach cavity, and this model can reproduce the time-averaged velocity quantitatively around the hydrofoil.
An approximate Riemann solver for real gas parabolized Navier-Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Urbano, Annafederica, E-mail: annafederica.urbano@uniroma1.it [Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Universita di Roma, Via Eudossiana 18, Roma 00184 (Italy); Nasuti, Francesco, E-mail: francesco.nasuti@uniroma1.it [Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Universita di Roma, Via Eudossiana 18, Roma 00184 (Italy)
2013-01-15
Under specific assumptions, parabolized Navier-Stokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized Navier-Stokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roe's Riemann solver is developed as the core of a Godunov type finite volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roe's Riemann solver for the parabolized Navier-Stokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.
On the Inviscid Limit for the Compressible Navier-Stokes System in an Impermeable Bounded Domain
Sueur, Franck
2014-03-01
In this paper we investigate the issue of the inviscid limit for the compressible Navier-Stokes system in an impermeable fixed bounded domain. We consider two kinds of boundary conditions. The first one is the no-slip condition. In this case we extend the famous conditional result (Kato, T.: Remarks on zero viscosity limit for nonstationary Navier-Stokes flows with boundary. In: Seminar on nonlinear partial differential equations, vol. 2, pp. 85-98. Math. Sci. Res. Inst. Publ., Berkeley 1984) obtained by Kato in the homogeneous incompressible case. Kato proved that if the energy dissipation rate of the viscous flow in a boundary layer of width proportional to the viscosity vanishes then the solutions of the incompressible Navier-Stokes equations converge to some solutions of the incompressible Euler equations in the energy space. We provide here a natural extension of this result to the compressible case. The other case is the Navier condition which encodes that the fluid slips with some friction on the boundary. In this case we show that the convergence to the Euler equations holds true in the energy space, as least when the friction is not too large. In both cases we use in a crucial way some relative energy estimates proved recently by Feireisl et al. in J. Math. Fluid Mech. 14:717-730 (2012).
Carpenter, Mark H.; Parsani, Matteo; Fisher, Travis C.; Nielsen, Eric J.
2015-01-01
Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).
Yang, Xiaoquan; Cheng, Jian; Liu, Tiegang; Luo, Hong
2015-11-01
The direct discontinuous Galerkin (DDG) method based on a traditional discontinuous Galerkin (DG) formulation is extended and implemented for solving the compressible Navier-Stokes equations on arbitrary grids. Compared to the widely used second Bassi-Rebay (BR2) scheme for the discretization of diffusive fluxes, the DDG method has two attractive features: first, it is simple to implement as it is directly based on the weak form, and therefore there is no need for any local or global lifting operator; second, it can deliver comparable results, if not better than BR2 scheme, in a more efficient way with much less CPU time. Two approaches to perform the DDG flux for the Navier- Stokes equations are presented in this work, one is based on conservative variables, the other is based on primitive variables. In the implementation of the DDG method for arbitrary grid, the definition of mesh size plays a critical role as the formation of viscous flux explicitly depends on the geometry. A variety of test cases are presented to demonstrate the accuracy and efficiency of the DDG method for discretizing the viscous fluxes in the compressible Navier-Stokes equations on arbitrary grids.
National Aeronautics and Space Administration — This SBIR project proposes to develop a gas-kinetic Navier-Stokes solver for simulation of hypersonic flows in thermal and chemical non-equilibrium. The...
Dellar, Oliver; Jones, Bryn; ACSE Collaboration
2016-11-01
The use of feedback control is looking increasingly attractive as a means of reducing the pressure drag which acts upon bluff body vehicles such as heavy goods vehicles, and thus reducing both fuel consumption and CO2 emissions. Motivated by the need to efficiently obtain low-order models of such flows in order to utilise model based control theory, we consider the effect on system dynamics of basing the plant model on different formulations of the linearised Navier-Stokes equations. The dynamics of a single computational node's subsystem which arises upon spatial discretisation of the governing equations in both primitive variables and pressure Poisson equation formulations are considered, revealing fundamental differences at the nodal level. The effects of these differences on system dynamics at the full fluid flow system level are exemplified by considering the corresponding formulations of a two-dimensional channel flow, subjected to a number different of boundary conditions. This ultimately reveals which formulations of the governing equations are suitable for feedback control design, and which should be avoided.
Feireisl, Eduard; Hošek, Radim; Maltese, David; Novotný, Antonín
2015-01-01
We derive an a priori error estimate for the numerical solution obtained by time and space discretization by the finite volume/finite element method of the barotropic Navier--Stokes equations. The numerical solution on a convenient polyhedral domain approximating a sufficiently smooth bounded domain is compared with an exact solution of the barotropic Navier--Stokes equations with a bounded density. The result is unconditional in the sense that there are no assumed bounds on the numerical sol...
Perlekar, Prasad; Pandit, Rahul
2015-01-01
We study two-dimensional (2D) binary-fluid turbulence by carrying out an extensive direct numerical simulation (DNS) of the forced, statistically steady turbulence in the coupled Cahn-Hilliard and Navier-Stokes equations. In the absence of any coupling, we choose parameters that lead (a) to spinodal decomposition and domain growth, which is characterized by the spatiotemporal evolution of the Cahn-Hilliard order parameter $\\phi$, and (b) the formation of an inverse-energy-cascade regime in the energy spectrum $E(k)$, in which energy cascades towards wave numbers $k$ that are smaller than the energy-injection scale $k_{inj}$ in the turbulent fluid. We show that the Cahn-Hilliard-Navier-Stokes coupling leads to an arrest of phase separation at a length scale $L_c$, which we evaluate from $S(k)$, the spectrum of the fluctuations of $\\phi$. We demonstrate that (a) $L_c \\sim L_H$, the Hinze scale that follows from balancing inertial and interfacial-tension forces, and (b) $L_c$ is independent, within error bars, o...
Bauer, Petr; Klement, Vladimír; Oberhuber, Tomáš; Žabka, Vítězslav
2016-03-01
We present a complete GPU implementation of a geometric multigrid solver for the numerical solution of the Navier-Stokes equations for incompressible flow. The approximate solution is constructed on a two-dimensional unstructured triangular mesh. The problem is discretized by means of the mixed finite element method with semi-implicit timestepping. The linear saddle-point problem arising from the scheme is solved by the geometric multigrid method with a Vanka-type smoother. The parallel solver is based on the red-black coloring of the mesh triangles. We achieved a speed-up of 11 compared to a parallel (4 threads) code based on OpenMP and 19 compared to a sequential code.
Analysis of wall shear stress around a competitive swimmer using 3D Navier-Stokes equations in CFD.
Popa, C V; Zaidi, H; Arfaoui, A; Polidori, G; Taiar, R; Fohanno, S
2011-01-01
This paper deals with the flow dynamics around a competitive swimmer during underwater glide phases occurring at the start and at every turn. The influence of the head position, namely lifted up, aligned and lowered, on the wall shear stress and the static pressure distributions is analyzed. The problem is considered as 3D and in steady hydrodynamic state. Three velocities (1.4 m/s, 2.2 m/s and 3.1 m/s) that correspond to inter-regional, national and international swimming levels are studied. The flow around the swimmer is assumed turbulent. The Reynolds-averaged Navier-Stokes (RANS) equations are solved with the standard k-ω turbulent model by using the CFD (computational fluid dynamics) numerical method based on a volume control approach. Numerical simulations are carried out with the ANSYS FLUENT® CFD code. The results show that the wall shear stress increases with the velocity and consequently the drag force opposing the movement of the swimmer increases as well. Also, high wall shear stresses are observed in the areas where the body shape, globally rigid in form, presents complex surface geometries such as the head, shoulders, buttocks, heel and chest.
Three-dimensional turbine blade design using a Navier-Stokes solver and Artificial Neural Network
Energy Technology Data Exchange (ETDEWEB)
Pierret, S.; Braembussche, R.A. van den [Von Karman Institute, Rhode-Saint-Genese (Belgium)
1999-07-01
Improving turbine efficiency by applying non-radial stacking and three-dimensional design techniques has received considerable attention in the recent years. A big source of losses is the spanwise non-uniformity of the next stage inlet flow angle resulting form the non-uniformity of the outlet flow angle of the preceding blade row. This non-uniformity can be reduced by adjusting the 2D sections along the span and/or by leaning the blades. The present method describes the design of a 3D blade geometry built by a radial stacking of several 2D blade sections which are provided by a 2D design system. A 3D Navier-Stokes solver is used to check the blade performance and to update the requirements imposed for the next design of the 2D blade sections. The 2D sections are designed using an Artificial Neural Network (ANN). The latter one constructs an approximate model (response surface) using a database containing the 2D Navier-Stokes solutions obtained from previous designs. It is used for the optimisation of the 2D blade geometry by means of Simulated Annealing (SA). The optimum 2D geometry is then verified by a 2D Navier-Stokes solver. This procedure results in a considerable speed-up of the design process by reducing both the interventions of the operator and the computational effort. It also allows the design of more efficient blades, satisfying both the aerodynamic and mechanical constraints. The method has been used to design different types of turbine blades of which one example will be presented. (Author)
Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential requirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.
Generalized extended Navier-Stokes theory: Multiscale spin relaxation in molecular fluids
DEFF Research Database (Denmark)
Hansen, Jesper Schmidt
2013-01-01
This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia...... per unit mass. In the regime of large moment of inertia the fast relaxation is wave-vector independent and dominated by the coupling between spin and the fluid streaming velocity, whereas for small inertia the relaxation is slow and spin diffusion plays a significant role. The fast wave...
Hybrid solution of the averaged Navier-Stokes equations for turbulent flow
Lima, J. A.; Perez-Guerrero, J. S.; Cotta, R. M.
The Generalized Integral Transform Technique (GITT) is utilized in the hybrid numerical-analytical solution of the Reynolds averaged Navier-Stokes equations, for developing turbulent flow inside a parallel-plates channel. An algebraic turbulence model is employed in modelling the turbulent diffusivity. The automatic global error control feature inherent to this approach, permits the determination of fully converged reference results for the validation of purely numerical methods. Therefore, numerical results for different values of Reynolds number are obtained, both for illustrating the convergence characteristics of the integral transform approach, and for critical comparisons with previously reported results through different models and numerical schemes.
Impact of singularity of Navier-Stokes equation upon atmospheric motion equations
Institute of Scientific and Technical Information of China (English)
SHI Wei-hui; WANG Yue-peng
2007-01-01
Some conelusiolib about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navkr-Stokes equation are summarized.On the basis of this,by taking the basic system of equations of atmospheric motion via Bonssinesq approximation as example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion iscaused by the instability of Navier-Stokes equation,thereby,a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations.
Institute of Scientific and Technical Information of China (English)
Guo Zhenhua; He Wen
2011-01-01
In this paper, we study a one-dimensional motion of viscous gas near vacuum. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-dimensional isentropic Navier-Stokes equations, and the free boundaries are the interfaces separating the gas from vacuum, across which the density changes discontinuosly. Smoothness of the solutions and the uniqueness of the weak solutions are also discussed. The present paper extends results in Luo-Xin-Yang [12] to the jump boundary conditions case.
Navier-Stokes Simulation of Homogeneous Turbulence on the CYBER 205
Wu, C. T.; Ferziger, J. H.; Chapman, D. R.; Rogallo, R. S.
1984-01-01
A computer code which solves the Navier-Stokes equations for three dimensional, time-dependent, homogenous turbulence has been written for the CYBER 205. The code has options for both 64-bit and 32-bit arithmetic. With 32-bit computation, mesh sizes up to 64 (3) are contained within core of a 2 million 64-bit word memory. Computer speed timing runs were made for various vector lengths up to 6144. With this code, speeds a little over 100 Mflops have been achieved on a 2-pipe CYBER 205. Several problems encountered in the coding are discussed.
A study of plunging breaker mechanics by PIV measurements and a Navier-Stokes solver
DEFF Research Database (Denmark)
Emarat, Narumon; Forehand, David I. M.; Christensen, Erik Damgaard
2000-01-01
The mechanics of a surf-zone plunging breaker are studied from Particle Image Velocimetry (PIV) measurements and a numerical model based on the Navier-Stokes equations, using a Volume of Fluid (VOF) method. An additional numerical model using a Boundary-Integral Method (BIM) is also used in order...... to generate input conditions for the main numerical model. The PIV measurements were performed at the University of Edinburgh and then compared against the results found by the numerical model developed at DHI Water and Environment. Good agreement is found, throughout the breaking process, between...... the velocity fields of the plunging breaker measured using PIV and those predicted by the numerical model....
Inverse airfoil design procedure using a multigrid Navier-Stokes method
Malone, J. B.; Swanson, R. C.
1991-01-01
The Modified Garabedian McFadden (MGM) design procedure was incorporated into an existing 2-D multigrid Navier-Stokes airfoil analysis method. The resulting design method is an iterative procedure based on a residual correction algorithm and permits the automated design of airfoil sections with prescribed surface pressure distributions. The new design method, Multigrid Modified Garabedian McFadden (MG-MGM), is demonstrated for several different transonic pressure distributions obtained from both symmetric and cambered airfoil shapes. The airfoil profiles generated with the MG-MGM code are compared to the original configurations to assess the capabilities of the inverse design method.
Free boundary value problem to 3D spherically symmetric compressible Navier-Stokes-Poisson equations
Kong, Huihui; Li, Hai-Liang
2017-02-01
In the paper, we consider the free boundary value problem to 3D spherically symmetric compressible isentropic Navier-Stokes-Poisson equations for self-gravitating gaseous stars with γ -law pressure density function for 6/5 <γ ≤ 4/3. For stress-free boundary condition and zero flow density continuously across the free boundary, the global existence of spherically symmetric weak solutions is shown, and the regularity and long time behavior of global solution are investigated for spherically symmetric initial data with the total mass smaller than a critical mass.
Continuum Navier-Stokes modelling of water flow past fullerene molecules
Walther, J. H.; Popadic, A.; Koumoutsakos, P.; Praprotnik, M.
2015-11-01
We present continuum simulations of water flow past fullerene molecules. The governing Navier-Stokes equations are complemented with the Navier slip boundary condition with a slip length that is extracted from related molecular dynamics simulations. We find that several quantities of interest as computed by the present model are in good agreement with results from atomistic and atomistic-continuum simulations at a fraction of the computational cost. We simulate the flow past a single fullerene and an array of fullerenes and demonstrate that such nanoscale flows can be computed efficiently by continuum flow solvers, allowing for investigations into spatiotemporal scales inaccessible to atomistic simulations.
Iterative solvers for Navier-Stokes equations: Experiments with turbulence model
Energy Technology Data Exchange (ETDEWEB)
Page, M. [IREQ - Institut de Recherche d`Hydro-Quebec, Varennes (Canada); Garon, A. [Ecole Polytechnique de Montreal (Canada)
1994-12-31
In the framework of developing software for the prediction of flows in hydraulic turbine components, Reynolds averaged Navier-Stokes equations coupled with {kappa}-{omega} two-equation turbulence model are discretized by finite element method. Since the resulting matrices are large, sparse and nonsymmetric, strategies based on CG-type iterative methods must be devised. A segregated solution strategy decouples the momentum equation, the {kappa} transport equation and the {omega} transport equation. These sets of equations must be solved while satisfying constraint equations. Experiments with orthogonal projection method are presented for the imposition of essential boundary conditions in a weak sense.
An Equal-Order DG Method for the Incompressible Navier-Stokes Equations
Cockburn, Bernardo
2008-12-20
We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings. © 2008 Springer Science+Business Media, LLC.
CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Lian Ruxu; Liu Jian; Li Hailiang; Xiao Ling
2012-01-01
We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient.For regular initial data,we show that the unique strong solution exits globally in time and converges to the equilibrium state time asymptotically.When initial density is piecewise regular with jump discontinuity,we show that there exists a unique global piecewise regular solution. In particular,the jump discontinuity of the density decays exponentially and the piecewise regular solution tends to the equilibrium state as t→ +∞.
Discrete exterior calculus (DEC) for the surface Navier-Stokes equation
Nitschke, Ingo; Voigt, Axel
2016-01-01
We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-04-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
Error Estimates for Finite-Element Navier-Stokes Solvers without Standard Inf-Sup Conditions
Institute of Scientific and Technical Information of China (English)
JianGuo LIU; Jie LIU; Robert L.PEGO
2009-01-01
The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary conditions. The methods arise by discretization of a well-posed extended Navier-Stokes dynamics for which pressure is determined from current velocity and force fields. The methods use C1 elements for velocity and C0 elements for pressure. A stability estimate is proved for a related finite-element projection method close to classical time-splitting methods of Orszag, Israeli, DeVille and Karniadakis.
Modeling digital pulse waveforms by solving one-dimensional Navier-stokes equations.
Fedotov, Aleksandr A; Akulova, Anna S; Akulov, Sergey A
2016-08-01
Mathematical modeling for composition distal arterial pulse wave in the blood vessels of the upper limbs was considered. Formation of distal arterial pulse wave is represented as a composition of forward and reflected pulse waves propagating along the arterial vessels. The formal analogy between pulse waves propagation along the human arterial system and the propagation of electrical oscillations in electrical transmission lines with distributed parameters was proposed. Dependencies of pulse wave propagation along the human arterial system were obtained by solving the one-dimensional Navier-Stokes equations for a few special cases.
A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Shi Dongyang; Ren Jincheng; Gong Wei
2011-01-01
In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.
Complex Singular Solutions of the 3-d Navier-Stokes Equations and Related Real Solutions
Boldrighini, Carlo; Li, Dong; Sinai, Yakov G.
2017-02-01
By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267-313, 2008) proved that there are complex solutions of the Navier-Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267-313, 2008) to the study of the real ones.
A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
Energy Technology Data Exchange (ETDEWEB)
Kupiainen, M; Sjogreen, B
2008-03-21
We here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in [6] and for the Euler equations of compressible fluid flow in [11], to the compressible Navier-Stokes equations. We describe the method and we implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.
CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL FORCES
Institute of Scientific and Technical Information of China (English)
Qian Jianzhen; Yin Hui
2009-01-01
For the viscous and heat-conductive fluids governed by the compressible NavierStokes equations with external force of general form in R~3, there exist nontrivial stationary solutions provided the external forces are small in suitable norms, which was studied in article[15], and there we also proved the global in time stability of the stationary solutions with respect to initial data in H~3-framework. In this article, the authors investigate the rates of convergence of nonstationary solutions to the corresponding stationary solutions when the initial data are small in H~3 and bounded in L_(6/5).
NONLINEAR GALERKIN METHOD FOR THE EXTERIOR NONSTATIONARY NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
何银年; 李开泰
2002-01-01
A new algorithm combining nonlinear Galerkin method and coupling method of finite element and boundary element is introduced to solve the exterior nonstationary Navier-Stokes equations. The regularity of the coupling variational formulation and the convergence of the approximate solution corresponding to the algorithm are proved. If the fine mesh h is choosed as coarse mesh H-sgure, the nonlinear Galerkin method, nonlinearity is only treated on the coarse grid and linearity is treated on the fine grid. Hence, the new algorithm can save a large amount of computational time.
Three-dimensional multigrid Navier-Stokes computations for turbomachinery applications
Subramanian, S. V.
1989-01-01
The fully three-dimensional, time-dependent compressible Navier-Stokes equations in cylindrical coordinates are presently used, in conjunction with the multistage Runge-Kutta numerical integration scheme for solution of the governing flow equations, to simulate complex flowfields within turbomechanical components whose pertinent effects encompass those of viscosity, compressibility, blade rotation, and tip clearance. Computed results are presented for selected cascades, emphasizing the code's capabilities in the accurate prediction of such features as airfoil loadings, exit flow angles, shocks, and secondary flows. Computations for several test cases have been performed on a Cray-YMP, using nearly 90,000 grid points.
Finite volume methods for the incompressible Navier-Stokes equations on unstructured grids
Energy Technology Data Exchange (ETDEWEB)
Meese, Ernst Arne
1998-07-01
Most solution methods of computational fluid dynamics (CFD) use structured grids based on curvilinear coordinates for compliance with complex geometries. In a typical industry application, about 80% of the time used to produce the results is spent constructing computational grids. Recently the use of unstructured grids has been strongly advocated. For unstructured grids there are methods for generating them automatically on quite complex domains. This thesis focuses on the design of Navier-Stokes solvers that can cope with unstructured grids and ''low quality grids'', thus reducing the need for human intervention in the grid generation.
Compressible Navier-Stokes equations: A study of leading edge effects
Hariharan, S. I.; Karbhari, P. R.
1987-01-01
A computational method is developed that allows numerical calculations of the time dependent compressible Navier-Stokes equations.The current results concern a study of flow past a semi-infinite flat plate.Flow develops from given inflow conditions upstream and passes over the flat plate to leave the computational domain without reflecting at the downstream boundary. Leading edge effects are included in this paper. In addition, specification of a heated region which gets convected with the flow is considered. The time history of this convection is obtained, and it exhibits a wave phenomena.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Any weak solution u to the Navier-Stokes equations is showed to be regular under the assumption that ||u|| L 2w (0,T ;L ∞ ( R 3 )) is sufficiently small, which is a limiting case of the regularity criteria derived by Kim and Kozono. Our result gives a positive answer to the question proposed by Kim and Kozono. For the incompressible magnetohydrodynamic equations, we also show the regularity of weak solution only under the assumption that ||u|| L 2w (0,T ;L ∞ ( R 3 )) is sufficiently small.
Energy Technology Data Exchange (ETDEWEB)
Fischer, P.F. [Brown Univ., Providence, RI (United States)
1996-12-31
Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.
Quantum Brownian Motions and Navier-Stokes Weakly Turbulence — a Path Integral Study
Botelho, Luiz C. L.
In this paper, we present a new method to solve exactly the Schrödinger Harmonic oscillator wave equation in the presence of time-dependent parameter. We also apply such technique to solve exactly the problem of random frequency averaged quantum propagator of a harmonic oscillator with white-noise statistics frequency. We still apply our technique to solve exactly the Brownian Quantum Oscillator in the presence of an electric field. Finally, we use these quantum mechanic techniques to solve exactly the Statistical-Turbulence of the Navier-Stokes in a region of fluid random stirring weakly (analytical) coupling through time-dependent Euclidean-Quantum oscillators path-integrals.
Kolmogorov, Dmitry; Zhu, Wei Jun; Sørensen, Niels N.; Sørensen, Jens Nørkær; Shen, Wen Zhong
2014-01-01
Direkte numerisk løsning af Navier-Stokes ligninger ved hjælp af Computational Fluid Dynamics (CFD) er anerkendt som en af de mest avancerede og præcise metoder til forudsigelse af luftstrømninger omkring vindmøller. Evnen af disse metoder til at indfange dynamikken i de komplekse strømninger, som optræder i umiddelbar nærhed af en vindmøllerotor, har gjort dem til uvurderlige værktøjer til forudsigelse af lokale vindfelter. Da direkte beregninger af en fuldt opløst strømning omkring en vindm...
Hydrodynamics for a model of a confined quasi-two-dimensional granular gas.
Brey, J Javier; Buzón, V; Maynar, P; García de Soria, M I
2015-05-01
The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and momentum fluxes are calculated to Navier-Stokes order, and the associated transport coefficients are explicitly determined as functions of the coefficient of normal restitution and the velocity parameter involved in the definition of the model. Also an Euler transport term contributing to the energy transport equation is considered. This term arises from the gradient expansion of the rate of change of the temperature due to the inelasticity of collisions, and it vanishes for elastic systems. The hydrodynamic equations are particularized for the relevant case of a system in the homogeneous steady state. The relationship with previous works is analyzed.
Steady Heat Transfer through a Two-Dimensional Rectangular Straight Fin
Directory of Open Access Journals (Sweden)
Raseelo J. Moitsheki
2011-01-01
Full Text Available Exact solutions for models describing heat transfer in a two-dimensional rectangular fin are constructed. Thermal conductivity, internal energy generation function, and heat transfer coefficient are assumed to be dependent on temperature. We apply the Kirchoff transformation on the governing equation. Exact solutions satisfying the realistic boundary conditions are constructed for the resulting linear equation. Symmetry analysis is carried out to classify the internal heat generation function, and some reductions are performed. Furthermore, the effects of physical parameters such as extension factor (the purely geometric fin parameter and Biot number on temperature are analyzed. Heat flux and fin efficiency are studied.
Directory of Open Access Journals (Sweden)
M. P. Markakis
2010-01-01
Full Text Available Through a suitable ad hoc assumption, a nonlinear PDE governing a three-dimensional weak, irrotational, steady vector field is reduced to a system of two nonlinear ODEs: the first of which corresponds to the two-dimensional case, while the second involves also the third field component. By using several analytical tools as well as linear approximations based on the weakness of the field, the first equation is transformed to an Abel differential equation which is solved parametrically. Thus, we obtain the two components of the field as explicit functions of a parameter. The derived solution is applied to the two-dimensional small perturbation frictionless flow past solid surfaces with either sinusoidal or parabolic geometry, where the plane velocities are evaluated over the body's surface in the case of a subsonic flow.
Incompressible Navier-Stokes equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell theories
Energy Technology Data Exchange (ETDEWEB)
Niu Chao [College of Physical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049 (China); Tian Yu, E-mail: ytian@gucas.ac.cn [College of Physical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049 (China); Wu Xiaoning [Institute of Mathematics, Academy of Mathematics and System Science, CAS, Beijing 100190 (China); Hua Loo-Keng Key Laboratory of Mathematics, CAS, Beijing 100190 (China); Ling Yi [Center for Relativistic Astrophysics and High Energy Physics, Department of Physics, Nanchang University, 330031 (China); Institute of Mathematics, Academy of Mathematics and System Science, CAS, Beijing 100190 (China)
2012-05-23
The dual fluid description for a general cutoff surface at radius r=r{sub c} outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter {epsilon}, the coupled Einstein-Maxwell equations are solved up to O({epsilon}{sup 2}). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density {eta}/s is independent of both the cutoff r{sub c} and the black brane charge. Then, we extend our discussion to the Gauss-Bonnet-Maxwell case, where the incompressible Navier-Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio {eta}/s is independent of the cutoff r{sub c} but dependent on the charge density of the black brane.
A new LES model derived from generalized Navier-Stokes equations with nonlinear viscosity
Rodríguez, José M
2015-01-01
Large Eddy Simulation (LES) is a very useful tool when simulating turbulent flows if we are only interested in its "larger" scales. One of the possible ways to derive the LES equations is to apply a filter operator to the Navier-Stokes equations, obtaining a new equation governing the behavior of the filtered velocity. This approach introduces in the equations the so called subgrid-scale tensor, that must be expressed in terms of the filtered velocity to close the problem. One of the most popular models is that proposed by Smagorinsky, where the subgrid-scale tensor is modeled by introducing an eddy viscosity. In this work, we shall propose a new approximation to this problem by applying the filter, not to the Navier-Stokes equations, but to a generalized version of them with nonlinear viscosity. That is, we shall introduce a nonlinear viscosity, not as a procedure to close the subgrid-scale tensor, but as part of the model itself (see below). Consequently, we shall need a different method to close the subgri...
A Galerkin-free model reduction approach for the Navier-Stokes equations
Shinde, Vilas; Longatte, Elisabeth; Baj, Franck; Hoarau, Yannick; Braza, Marianna
2016-03-01
Galerkin projection of the Navier-Stokes equations on Proper Orthogonal Decomposition (POD) basis is predominantly used for model reduction in fluid dynamics. The robustness for changing operating conditions, numerical stability in long-term transient behavior and the pressure-term consideration are generally the main concerns of the Galerkin Reduced-Order Models (ROM). In this article, we present a novel procedure to construct an off-reference solution state by using an interpolated POD reduced basis. A linear interpolation of the POD reduced basis is performed by using two reference solution states. The POD basis functions are optimal in capturing the averaged flow energy. The energy dominant POD modes and corresponding base flow are interpolated according to the change in operating parameter. The solution state is readily built without performing the Galerkin projection of the Navier-Stokes equations on the reduced POD space modes as well as the following time-integration of the resulted Ordinary Differential Equations (ODE) to obtain the POD time coefficients. The proposed interpolation based approach is thus immune from the numerical issues associated with a standard POD-Galerkin ROM. In addition, a posteriori error estimate and a stability analysis of the obtained ROM solution are formulated. A detailed case study of the flow past a cylinder at low Reynolds numbers is considered for the demonstration of proposed method. The ROM results show good agreement with the high fidelity numerical flow simulation.
Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme
Coirier, William J.; Powell, Kenneth G.
1995-01-01
A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.
A unified multigrid solver for the Navier-Stokes equations on mixed element meshes
Mavriplis, D. J.; Venkatakrishnan, V.
1995-01-01
A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.
Li, Q; He, Y L; Wang, Y; Tao, W Q
2007-11-01
A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.
On L3,∞-stability of the Navier-Stokes system in exterior domains
Koba, Hajime
2017-02-01
This paper studies the stability of a stationary solution of the Navier-Stokes system with a constant velocity at infinity in an exterior domain. More precisely, this paper considers the stability of the Navier-Stokes system governing the stationary solution which belongs to the weak L3-space L 3 , ∞. Under the condition that the initial datum belongs to a solenoidal L 3 , ∞-space, we prove that if both the L 3 , ∞-norm of the initial datum and the L 3 , ∞-norm of the stationary solution are sufficiently small then the system admits a unique global-in-time strong L 3 , ∞-solution satisfying both L 3 , ∞-asymptotic stability and L∞-asymptotic stability. Moreover, we investigate L 3 , r-asymptotic stability of the global-in-time solution. Using Lp-Lq type estimates for the Oseen semigroup and applying an equivalent norm on the Lorentz space are key ideas to establish both the existence of a unique global-in-time strong (or mild) solution of our system and the stability of our solution.
On the inviscid limit for the compressible Navier-Stokes system in an impermeable bounded domain
Sueur, Franck
2012-01-01
In this paper we investigate the issue of the inviscid limit for the compressible Navier-Stokes system in an impermeable fixed bounded domain. We consider two kinds of boundary conditions. The first one is the no-slip condition. In this case we extend the famous conditional result obtained by Kato in the homogeneous incompressible case. Kato proved that if the energy dissipation rate of the viscous flow in a boundary layer of width proportional to the viscosity vanishes then the solutions of the incompressible Navier-Stokes equations converge to some solutions of the incompressible Euler equations in the energy space. We provide here a natural extension of this result to the compressible case. The other case is the Navier condition which encodes that the fluid slips with some friction on the boundary. In this case we show that the convergence to the Euler equations holds true in the energy space, as least when the friction is not too large. In both cases we use in a crucial way some relative energy estimates ...
On the Navier-Stokes Equations for Exothermically Reacting Compressible Fluids
Institute of Scientific and Technical Information of China (English)
Gui-Qiang Chen; David Hoff; Konstantina Trivisa
2002-01-01
We analyze mathematical models governing planar flow of chemical reaction from unburnt gases to burnt gases in certain physical regimes in which diffusive effects such as viscosity and heat conduction are significant. These models can be then formulated as the Navier-Stokes equations for exothermically reacting compressible fluids. We first establish the existence and dynamic behavior, including stability, regularity, and large-time behavior, of global discontinuous solutions of large oscillation to the Navier-Stokes equations with constant adiabatic exponent γ and specific heat Cv. Our approach for the existence and regularity is to combine the difference approximation techniques with the energy methods, total variation estimates, and weak convergence arguments to deal with large jump discontinuities; and for large-time behavior is an a posteriori argument directly from the weak form of the equations. The approach and ideas we develop here can be applied to solving a more complicated model where γ and Cv vary as the phase changes; and we then describe this model in detail and contrast the results on the asymptotic behavior of the solutions of these two different models. We also discuss other physical models describing dynamic combustion.
Kouhi, Mohammad; Oñate, Eugenio
2015-07-01
A new implicit stabilized formulation for the numerical solution of the compressible Navier-Stokes equations is presented. The method is based on the finite calculus (FIC) scheme using the Galerkin finite element method (FEM) on triangular grids. Via the FIC formulation, two stabilization terms, called streamline term and transverse term, are added to the original conservation equations in the space-time domain. The non-linear system of equations resulting from the spatial discretization is solved implicitly using a damped Newton method benefiting from the exact Jacobian matrix. The matrix system is solved at each iteration with a preconditioned GMRES method. The efficiency of the proposed stabilization technique is checked out in the solution of 2D inviscid and laminar viscous flow problems where appropriate solutions are obtained especially near the boundary layer and shock waves. The work presented here can be considered as a follow up of a previous work of the authors Kouhi, Oñate (Int J Numer Methods Fluids 74:872-897, 2014). In that paper, the stabilized Galerkin FEM based on the FIC formulation was derived for the Euler equations together with an explicit scheme. In the present paper, the extension of this work to the Navier-Stokes equations using an implicit scheme is presented.
Dynamical systems characterization of the poor man's Navier--Stokes equations
Polly, J. B.; McDonough, J. M.
2011-11-01
The Navier-Stokes (N.-S.) equations governing fluid flow consist of a system of time-dependent, multi-dimensional, non-linear partial differential equations (PDEs) which cannot be solved in real time using current, or near-term foreseeable, computing hardware. The poor man's Navier-Stokes (PMNS) equations comprise a discrete dynamical system (DDS) that is algebraic--hence, easily (and rapidly) solved--and yet which retains many (possibly all) of the temporal behaviors of the full (PDE) N.-S. system at specific spatial locations. In this investigation we outline the derivation of the PMNS equations beginning with the incompressible N.-S. equations. We then consider common techniques to understand the DDS sensitivity to initial conditions (SIC) through calculation of bifurcation diagrams, Lyapunov exponents, and fractal dimension. These techniques are studied with consideration of their ease of computation, and ability to characterize and describe system behavior. The time series generated by the DDS are used to obtain power spectral densities (PSDs) which can be used to categorize most system behaviors. Some chaotic behaviors, however, can be difficult to distinguish via PSD analysis alone; thus we investigate the ability of other methods to characterize the system response.
Elasto-capillarity Simulations based on the Navier-Stokes-Cahn-Hilliard Equations
van Brummelen, E H; van Zwieten, G J
2015-01-01
We consider a computational model for complex-fluid-solid interaction based on a diffuse-interface model for the complex fluid and a hyperelastic-material model for the solid. The diffuse-interface complex-fluid model is described by the incompressible Navier-Stokes-Cahn-Hilliard equations with preferential-wetting boundary conditions at the fluid-solid interface. The corresponding fluid traction on the interface includes a capillary-stress contribution, and the dynamic interface condition comprises the traction exerted by the non-uniform fluid-solid surface tension. We present a weak formulation of the aggregated complex-fluid-solid-interaction problem, based on an Arbitrary-Lagrangian-Eulerian formulation of the Navier-Stokes-Cahn-Hilliard equations and a proper reformulation of the complex-fluid traction and the fluid-solid surface tension. To validate the presented complex-fluid-solid-interaction model, we present numerical results and conduct a comparison to experimental data for a droplet on a soft subs...
An introduction to the mathematical theory of the Navier-Stokes equations
Galdi, Giovanni P
1994-01-01
Undoubtedly, the Navier-Stokes equations are of basic importance within the context of modern theory of partial differential equations. Although the range of their applicability to concrete problems has now been clearly recognised to be limited, as my dear friend and bright colleague K.R. Ra jagopal has showed me by several examples during the past six years, the mathematical questions that remain open are of such a fascinating and challenging nature that analysts and applied mathematicians cannot help being attracted by them and trying to contribute to their resolution. Thus, it is not a coincidence that over the past ten years more than seventy sig nificant research papers have appeared concerning the well-posedness of boundary and initial-boundary value problems. In this monograph I shall perform a systematic and up-to-date investiga tion of the fundamental properties of the Navier-Stokes equations, including existence, uniqueness, and regularity of solutions and, whenever the region of flow is unbou...
Discontinuous Galerkin solution of the Navier-Stokes equations on deformable domains
Energy Technology Data Exchange (ETDEWEB)
Persson, P.-O.; Bonet, J.; Peraire, J.
2009-01-13
We describe a method for computing time-dependent solutions to the compressible Navier-Stokes equations on variable geometries. We introduce a continuous mapping between a fixed reference configuration and the time varying domain, By writing the Navier-Stokes equations as a conservation law for the independent variables in the reference configuration, the complexity introduced by variable geometry is reduced to solving a transformed conservation law in a fixed reference configuration, The spatial discretization is carried out using the Discontinuous Galerkin method on unstructured meshes of triangles, while the time integration is performed using an explicit Runge-Kutta method, For general domain changes, the standard scheme fails to preserve exactly the free-stream solution which leads to some accuracy degradation, especially for low order approximations. This situation is remedied by adding an additional equation for the time evolution of the transformation Jacobian to the original conservation law and correcting for the accumulated metric integration errors. A number of results are shown to illustrate the flexibility of the approach to handle high order approximations on complex geometries.
A Stable Parametric Finite Element Discretization of Two-Phase Navier--Stokes Flow
Barrett, John W; Nürnberg, Robert
2013-01-01
We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier--Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational formulation for the interface evolution gives rise to a natural discretization of the mean curvature of the interface. The parametric finite element approximation of the evolving interface is then coupled to a standard finite element approximation of the two-phase Navier--Stokes equations in the bulk. Here enriching the pressure approximation space with the help of an XFEM function ensures good volume conservation properties for the two phase regions. In addition, the mesh quality of the parametric approximation of the interface in general does not deteriorate over time, and an equidistribution property can be shown for a semidiscrete continuous-in-time variant of our scheme in two space dimensions. Moreover, our finite element approximation can be shown to be uncondit...
A new full discrete stabilized viscosity method for transient Navier-Stokes equations
Institute of Scientific and Technical Information of China (English)
Yan-mei QIN; Min-fu FENG; Tian-xiao ZHOU
2009-01-01
A new full discrete stabilized viscosity method for the transient Navier-Stokes equations with the high Reynolds number (small viscosity coefficient) is proposed based on the pressure projection and the extrapolated trapezoidal rule.The transient NavierStokes equations are fully discretized by the continuous equal-order finite elements in space and the reduced Crank-Nicolson scheme in time.The new stabilized method is stable and has many attractive properties.First,the system is stable for the equal-order combination of discrete continuous velocity and pressure spaces because of adding a pressure projection term.Second,the artifical viscosity parameter is added to the viscosity coefficient as a stability factor,so the system is antidiffusive.Finally,the method requires only the solution to a linear system at every time step.Stability and convergence of the method is proved.The error estimation results show that the method has a second-order accuracy,and the constant in the estimation is independent of the viscosity coefficient.The numerical results are given,which demonstrate the advantages of the method presented.
A COMPUTATIONAL METHOD FOR THE NAVIER-STOKES EQUATIONS AT ALL SPEEDS
Institute of Scientific and Technical Information of China (English)
赵兴艳; 苏莫明; 苗永淼
2002-01-01
A PLU-SGS method based on a time-derivative preconditioning algorithm and LUSGS method is developed in order to calculate the Navier-Stokes equations at all speeds. The equations were discretized using AUSMPW scheme in conjunction with the third-order MUSCL scheme with Van Leer limiter. The present method was applied to solve the multidimensional compressible Navier-Stokes equations in curvilinear coordinates. Characteristic boundary conditions based on the eigensystem of the preconditioned equations were employed. In order to examine the performance of present method, driven-cavity flow at various Reynolds numbers and viscous flow through a convergent-divergent nozzle at supersonic were selected to test this method. The computed results were compared with the experimental data or the other numerical results available in literature and good agreements between them are obtained. The results show that the present method is accurate, self-adaptive and stable for a wide range of flow conditions from low speed to supersonic flows.
Directory of Open Access Journals (Sweden)
Christianto V.
2008-01-01
Full Text Available In the present article we argue that it is possible to write down Schrodinger representation of Navier-Stokes equation via Riccati equation. The proposed approach, while differs appreciably from other method such as what is proposed by R.M.Kiehn, has an advantage, i.e. it enables us extend further to quaternionic and biquaternionic version of Navier-Stokes equation, for instance via Kravchenko's and Gibbon's route. Further observation is of course recommended in order to refute or verify this proposition.
Obabko, Aleksandr Vladimirovich
Numerical solutions of the unsteady Navier-Stokes equations are considered for the flow induced by a thick-core vortex convecting along an infinite surface in a two-dimensional incompressible flow. The formulation is considered as a model problem of the dynamic-stall vortex and is relevant to other unsteady separation phenomena including vorticity ejections in juncture flows and the vorticity production mechanism in turbulent boundary-layers. Induced by an adverse streamwise pressure gradient due to the presence of the vortex above the wall, a primary recirculation region forms and evolves toward a singular solution of the unsteady non-interacting boundary-layer equations. The resulting eruptive spike provokes a small-scale viscous-inviscid interaction in the high-Reynolds-number regime. In the moderate-Reynolds-numbers regime, the growing recirculation region initiates a large-scale interaction in the form of local changes in the streamwise pressure gradient accelerating the spike formation and resulting small-scale interaction through development of a region of streamwise compression. It also was found to induce regions of streamwise expansion and "child" recirculation regions that contribute to ejections of near-wall vorticity and splitting of the "parent" region into multiple co-rotating eddies. These eddies later merge into a single amalgamated eddy that is observed to pair with the detaching vortex similar to the low-Reynolds-number regime where the large-scale interaction occurs, but there is no spike or subsequent small-scale interaction. It is also found that increasing the wall speed or vortex convection velocity toward a critical value results in solutions that are indicative of flows at lower Reynolds numbers eventually leading to suppression of unsteady separation and vortex detachment processes.
Wang, Yong
2016-09-01
In the present paper, we study the uniform regularity and vanishing dissipation limit for the full compressible Navier-Stokes system whose viscosity and heat conductivity are allowed to vanish at different orders. The problem is studied in a three dimensional bounded domain with Navier-slip type boundary conditions. It is shown that there exists a unique strong solution to the full compressible Navier-Stokes system with the boundary conditions in a finite time interval which is independent of the viscosity and heat conductivity. The solution is uniformly bounded in {W^{1,infty}} and is a conormal Sobolev space. Based on such uniform estimates, we prove the convergence of the solutions of the full compressible Navier-Stokes to the corresponding solutions of the full compressible Euler system in {L^infty(0,T; L^2)}, {L^infty(0,T; H1)} and {L^infty([0,T]×Ω)} with a rate of convergence.
McDuffee, Ryan
2016-01-01
Recent observations of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory (LIGO) has confirmed one of the last outstanding predictions in general relativity and in the process opened up a new frontier in astronomy and astrophysics. Additionally the observation of gravitational waves has also given us the data needed to deduce the physical properties of space time. Bredberg et al have shown in their 2011 paper titled From Navier-Stokes to Einstein, that for every solution of the incompressible Navier-Stokes equation in p + 1 dimensions, there is a uniquely associated dual" solution of the vacuum Einstein equations in p + 2 dimensions. The author shows that the physical properties of space time can be deduced using the recent measurements from the Laser Interferometer Gravitational-Wave Observatory and solutions from the incompressible Navier-Stokes equation.
Coirier, William John
1994-01-01
A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a
Energy Technology Data Exchange (ETDEWEB)
Blanchard, M., E-mail: mathieu.blanchard@ladhyx.polytechnique.fr [LadHyX, CNRS and Ecole Polytechnique, 91128 Palaiseau (France); Schuller, T. [CNRS, UPR 288, Laboratoire d’Energétique Moléculaire et Macroscopique Combustion (EM2C), Grande Voie des Vignes, 92290 Châtenay-Malabry (France); Centrale-Supélec, Grande Voie des Vignes, 92290 Châtenay-Malabry (France); Sipp, D. [ONERA-DAFE, 8 rue des Vertugadins, 92190 Meudon (France); Schmid, P. J. [Department of Mathematics, Imperial College London, London SW7 2AZ (United Kingdom)
2015-04-15
The response of a laminar premixed methane-air flame subjected to flow perturbations around a steady state is examined experimentally and using a linearized compressible Navier-Stokes solver with a one-step chemistry mechanism to describe combustion. The unperturbed flame takes an M-shape stabilized both by a central bluff body and by the external rim of a cylindrical nozzle. This base flow is computed by a nonlinear direct simulation of the steady reacting flow, and the flame topology is shown to qualitatively correspond to experiments conducted under comparable conditions. The flame is then subjected to acoustic disturbances produced at different locations in the numerical domain, and its response is examined using the linearized solver. This linear numerical model then allows the componentwise investigation of the effects of flow disturbances on unsteady combustion and the feedback from the flame on the unsteady flow field. It is shown that a wrinkled reaction layer produces hydrodynamic disturbances in the fresh reactant flow field that superimpose on the acoustic field. This phenomenon, observed in several experiments, is fully interpreted here. The additional perturbations convected by the mean flow stem from the feedback of the perturbed flame sheet dynamics onto the flow field by a mechanism similar to that of a perturbed vortex sheet. The different regimes where this mechanism prevails are investigated by examining the phase and group velocities of flow disturbances along an axis oriented along the main direction of the flow in the fresh reactant flow field. It is shown that this mechanism dominates the low-frequency response of the wrinkled shape taken by the flame and, in particular, that it fully determines the dynamics of the flame tip from where the bulk of noise is radiated.
An Exact Mapping from Navier-Stokes Equation to Schördinger Equation via Riccati Equation
Directory of Open Access Journals (Sweden)
Christianto V.
2008-01-01
Full Text Available In the present article we argue that it is possible to write down Schrödinger representation of Navier-Stokes equation via Riccati equation. The proposed approach, while differs appreciably from other method such as what is proposed by R. M. Kiehn, has an advantage, i.e. it enables us extend further to quaternionic and biquaternionic version of Navier-Stokes equation, for instance via Kravchenko’s and Gibbon’s route. Further observation is of course recommended in order to refute or verify this proposition.
Berselli, Luigi C.; Spirito, Stefano
2017-03-01
In this paper we consider the Navier-Stokes equations supplemented with either the Dirichlet or vorticity-based Navier slip boundary conditions. We prove that weak solutions obtained as limits of solutions of the Navier-Stokes-Voigt model satisfy the local energy inequality, and we also prove certain regularity results for the pressure. Moreover, in the periodic setting we prove that if the parameters are chosen in an appropriate way, then we can construct suitable weak solutions through a Fourier-Galerkin finite-dimensional approximation in the space variables.
Institute of Scientific and Technical Information of China (English)
Qing-ping Deng; Xue-jun Xu; Shu-min Shen
2000-01-01
This paper deals with Crouzeix-Raviart nonconforming finite element approxi mation of Navier-Stokes equation in a plane bounded domain, by using the so-called velocity-pressure mixed formulation. The quasi-optimal maximum norm error es timates of the velocity and its first derivatives and of the pressure are derived for nonconforming C-R scheme of stationary Navier-Stokes problem. The analysis is based on the weighted inf-sup condition and the technique of weighted Sobolev norm. By the way, the optimal L2-error estimate for nonconforming finite element approximation is obtained.
Institute of Scientific and Technical Information of China (English)
Wang Yi
2008-01-01
The zero dissipation limit of the compressible heat-conducting Navier-Stokes equations in the presence of the shock is investigated. It is shown that when the heat ε→ 0 (see (1.3)), if the solution of the corresponding Euler equations is piecewise smooth with shock wave satisfying the Lax entropy condition, then there exists a smooth solution to the Navier-Stokes equations, which converges to the piecewise smooth shock solution of the Euler equations away from the shock discontinuity at a rate of ε. The proof is given by a combination of the energy estimates and the matched asymptotic analysis introduced in [3].
A two-dimensional MHD global coronal model - Steady-state streamers
Wang, A.-H.; Wu, S. T.; Suess, S. T.; Poletto, G.
1992-01-01
A 2D, time-dependent, numerical, MHD model for the simulation of coronal streamers from the solar surface to 15 solar is presented. Three examples are given; for dipole, quadrupole and hexapole (Legendre polynomials P1, P2, and P3) initial field topologies. The computed properties are density, temperature, velocity, and magnetic field. The calculation is set up as an initial-boundary value problem wherein a relaxation in time produces the steady state solution. In addition to the properties of the solutions, their accuracy is discussed. Besides solutions for dipole, quadrupole, and hexapole geometries, the model use of realistic values for the density and Alfven speed while still meeting the requirement that the flow speed be super-Alfvenic at the outer boundary by extending the outer boundary to 15 solar radii.
Mohamed, Mamdouh S; Samtaney, Ravi
2015-01-01
A conservative discretization of incompressible Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the contraction operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second ord...
Boundary Layer for the Navier-Stokes-alpha Model of Fluid Turbulence
Cheskidov, A.
We study boundary-layer turbulence using the Navier-Stokes-alpha model obtaining an extension of the Prandtl equations for the averaged flow in a turbulent boundary layer. In the case of a zero pressure gradient flow along a flat plate, we derive a nonlinear fifth-order ordinary differential equation, which is an extension of the Blasius equation. We study it analytically and prove the existence of a two-parameter family of solutions satisfying physical boundary conditions. Matching these parameters with the skin-friction coefficient and the Reynolds number based on momentum thickness, we get an agreement of the solutions with experimental data in the laminar and transitional boundary layers, as well as in the turbulent boundary layer for moderately large Reynolds numbers.
A PARTIALLY-AVERAGED NAVIER-STOKES MODEL FOR HILL AND CURVED DUCT FLOW
Institute of Scientific and Technical Information of China (English)
MA Jia-mei; WANG Fu-jun; YU Xin; LIU Zhu-qing
2011-01-01
Turbulent flows past hill and curved ducts exist in many engineering applications.Simulations of the turbulent flow are carried out based on a newly developed technique,the Partially-Averaged Navier-Stokes(PANS)model,including separation,recirculation,reattachment,turbulent vortex mechanism.The focus is on how to accurately predict typical separating,reattaching and secondary motion at a reasonable computational expense.The effect of the parameter,the unresolved-to-total ratio of kinetic energy (fk),is examined with a given unresolved-to-total ratio of dissipation(fε)for the hill flow with a much coarser grid system than required by the LES.An optimal value of fk can be obtained to predict the separation and reattachment locations and for more accurate simulation of the resolved turbulence.In addition,the turbulent secondary motions are captured by a smaller fk as compared with the RANS method with the same grid.
Towards a Navier Stokes-Darcy Upscaling Based on Permeability Tensor Computation
Lieb, M.
2012-06-02
The micro scale simulation of CO2 sequestration involves complex, porous-like geometries. For the generation of such geometries, we present two approaches: In 2D, we construct a fractured domain by channel networks. In 3D, we approximate sand grain-like scenarios by dense sphere packings. The ﬂow through these structures is simulated with the incompressible Navier-Stokes solver of the PDE framework Peano. Using an upscaling scheme, the results of the micro scale are used as input data for a Darcy solver on the coarse scales. The coupling concept and the scenario generators are presented together with ﬁrst simulation results showing the validity of the approach.
Entropy stable wall boundary conditions for the compressible Navier-Stokes equations
Parsani, Matteo; Nielsen, Eric J
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary...
Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review
Directory of Open Access Journals (Sweden)
Bermejo Rodolfo
2016-09-01
Full Text Available We review in this paper the development of Lagrange-Galerkin (LG methods to integrate the incompressible Navier-Stokes equations (NSEs for engineering applications. These methods were introduced in the computational fluid dynamics community in the early eighties of the past century, and at that time they were considered good methods for both their theoretical stability properties and the way of dealing with the nonlinear terms of the equations; however, the numerical experience gained with the application of LG methods to different problems has identified drawbacks of them, such as the calculation of specific integrals that arise in their formulation and the calculation of the ow trajectories, which somehow have hampered the applicability of LG methods. In this paper, we focus on these issues and summarize the convergence results of LG methods; furthermore, we shall briefly introduce a new stabilized LG method suitable for high Reynolds numbers.
On the use of the incompressibility condition in the Euler and Navier-Stokes equations
Stubbe, Peter
2016-01-01
The Euler and Navier-Stokes equations both belong to a closed system of three transport equations, describing the particle number density N, the macroscopic velocity v and the temperature T. These sytems are complete, leaving no room for any additional equation. Nonetheless, it is common practice in parts of the literature to replace the thermal equation by the incompressibility condition div v = 0, motivated by the wish to obtain simpler equations. It is shown that this procedure is physically inconsistent in several ways, with the consequence that incompressibility is not a property that can be enforced by an external condition. Incompressible behaviour, if existing, will have to follow self-consistently from the full set of transport equations.
A molecular dynamics test of the Navier-Stokes-Fourier paradigm for compressible gaseous continua
Brenner, Howard; Reese, Jason M
2013-01-01
Knudsen's pioneering experimental and theoretical work performed more than a century ago pointed to the fact that the Navier-Stokes-Fourier (NSF) paradigm is inapplicable to compressible gases at Knudsen numbers (Kn) beyond the continuum range, namely to noncontinua. However, in the case of continua, wherein Kn approaches zero asymptotically, it is nevertheless (implicitly) assumed in the literature that the compressible NSF equations remain applicable. Surprisingly, this belief appears never to have been critically tested; rather, most tests of the viability of the NSF equations for continuum flows have, to date, effectively been limited to incompressible fluids, namely liquids. Given that bivelocity hydrodynamic theory has recently raised fundamental questions about the validity of the NSF equations for compressible continuum gas flows, we deemed it worthwhile to test the validity of the NSF paradigm for the case of continua. Although our proposed NSF test does not, itself, depend upon the correctness of th...
A Split-Step Scheme for the Incompressible Navier-Stokes
Energy Technology Data Exchange (ETDEWEB)
Henshaw, W; Petersson, N A
2001-06-12
We describe a split-step finite-difference scheme for solving the incompressible Navier-Stokes equations on composite overlapping grids. The split-step approach decouples the solution of the velocity variables from the solution of the pressure. The scheme is based on the velocity-pressure formulation and uses a method of lines approach so that a variety of implicit or explicit time stepping schemes can be used once the equations have been discretized in space. We have implemented both second-order and fourth-order accurate spatial approximations that can be used with implicit or explicit time stepping methods. We describe how to choose appropriate boundary conditions to make the scheme accurate and stable. A divergence damping term is added to the pressure equation to keep the numerical dilatation small. Several numerical examples are presented.
Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations.
Bell, John B; Garcia, Alejandro L; Williams, Sarah A
2007-07-01
The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.
Unsteady rotating laminar flow: analytical solution of relevant Navier-Stokes equations
Bocci, Alessio; Ritelli, Daniele
2016-01-01
We provide a integration of Navier-Stokes equations concerning the unsteady-state laminar flow of an incompressible, isothermal (newtonian) fluid in a cylindrical vessel spinning about its symmetry axis, say $z$, and inside which the liquid velocity starts with a non-zero axial component as well. Basic physical assumptions are that the pressure axial gradient keeps itself on its hydrostatic value and that no radial velocity exists. In such a way the PDEs become uncoupled and can be faced separately from each other. We succeed in computing both the unsteady velocities, i.e. the axial $v_z$ and the circumferential $v_\\theta$ as well, by means of infinite series expansions of Fourier-Bessel type under time exponential damping. Following this, we also find the unsteady surfaces of dynamical equilibrium, the wall shear stress and the Stokesian streamlines
Euler/Navier-Stokes flow computations on flexible configurations for stability analysis
Guruswamy, G.; Tu, E.
1995-01-01
Longitudinal dynamic stability derivatives required for design of aircraft are computed by using the state-of-the-art numerical methods for wing-body configurations. The flow is modeled using the Euler/Navier-Stokes equations with turbulence models and solved using an efficient finite-difference scheme suitable for patched structured grids. Computations are made at a flow regime that is beyond the limits of the current linear methods mostly used for computing stability derivatives. Flow conditions include shockwaves and viscous dominated vortical flows. Effect of Mach number and angle-of-attack on stability derivatives are demonstrated for a typical wing-body configuration. For the same configuration the effects of wing flexibility on the magnitude and phase angles of stability derivatives are also demonstrated.
Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations
Prohl, Andreas
1997-01-01
Projection methods had been introduced in the late sixties by A. Chorin and R. Teman to decouple the computation of velocity and pressure within the time-stepping for solving the nonstationary Navier-Stokes equations. Despite the good performance of projection methods in practical computations, their success remained somewhat mysterious as the operator splitting implicitly introduces a nonphysical boundary condition for the pressure. The objectives of this monograph are twofold. First, a rigorous error analysis is presented for existing projection methods by means of relating them to so-called quasi-compressibility methods (e.g. penalty method, pressure stabilzation method, etc.). This approach highlights the intrinsic error mechanisms of these schemes and explains the reasons for their limitations. Then, in the second part, more sophisticated new schemes are constructed and analyzed which are exempted from most of the deficiencies of the classical projection and quasi-compressibility methods. "... this book ...
VIRTUAL GRID AND NAVIER-STOKES COMPUTATION FOR CONTROL-SURFACE
Institute of Scientific and Technical Information of China (English)
李孝伟; 范绪箕
2002-01-01
The virtual grid method used in the embedding technique to solve the problem of finding interpolatingcells of the inner and outer boundary points near joint regions was developed for calculating the viscous flowsaround a wing with control-surface.The main purpose of the virtual grid is to effectively treat the geometry of thecrossed facial pIanes at the interface,and to convert a solid wall boundary condition into an interface condition,however,no fluid flow computations are conducted within the virtual grid.Navier-Stokes computations were per-formed for transonic flow over a clipped delta wing with control surface,and the computed results compare wellwith the experimental data.
Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries
Williams-Rioux, Bertrand
2012-01-12
Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.
Navier-Stokes calculation of solid-propellant rocket motor internal flowfields
Hsieh, Kwang-Chung; Yang, Vigor; Tseng, Jesse I. S.
1988-01-01
A comprehensive numerical analysis has been carried out to study the detailed physical and chemical processes involved in the combustion of homogeneous propellant in a rocket motor. The formulation is based on the time-dependent full Navier-Stokes equations, with special attention devoted to the chemical reactions in both gas and condensed phases. The turbulence closure is achieved using both the Baldwin-Lomax algebraic model and a modified k-epsilon two-equation scheme with a low Reynolds number and near-wall treatment. The effects of variable thermodynamic and transport properties are also included. The system of governing equations are solved using a multi-stage Runge-Kutta shceme with the source terms treated implicitly. Preliminary results clearly demonstrate the presence of various combustion regimes in the vicinity of propellant surface. The effects of propellant combustion on the motor internal flowfields are investigated in detail.
FINITE ELEMENT METHODS FOR THE NAVIER-STOKES EQUATIONS BY H(div) ELEMENTS
Institute of Scientific and Technical Information of China (English)
Junping Wang; Xiaoshen Wang; Xiu Ye
2008-01-01
We derived and analyzed a new numerical scheme for the Navier-Stokes equations by using H(div) conforming finite elements. A great deal of effort was given to an establishment of some Sobolev-type inequalities for piecewise smooth functions. In particular, the newly derived Sobolev inequalities were employed to provide a mathematical theory for the H(div) finite element scheme. For example, it was proved that the new finite element scheme has solutions which admit a certain boundedness in terms of the input data. A solution uniqueness was also possible when the input data satisfies a certain smallness condition. Optimal-order error estimates for the corresponding finite element solutions were established in various Sobolev norms. The finite element solutions from the new scheme feature a full satisfaction of the continuity equation which is highly demanded in scientific computing.
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Validation of the actuator line/Navier Stokes technique using mexico measurements
DEFF Research Database (Denmark)
Shen, Wen Zhong; Zhu, Wei Jun; Sørensen, Jens Nørkær
2010-01-01
This paper concerns the contribution of DTU MEK in the international research collaboration project (MexNext) within the framework of IEA Annex 29 to validate aerodynamic models or CFD codes using the existing measurements made in the previous EU funded projectMEXICO (Model Experiments in Control......This paper concerns the contribution of DTU MEK in the international research collaboration project (MexNext) within the framework of IEA Annex 29 to validate aerodynamic models or CFD codes using the existing measurements made in the previous EU funded projectMEXICO (Model Experiments...... in Controlled Conditions). The Actuator Line/Navier Stokes (AL/NS) technique developed at DTU is validated against the detailed MEXICO measurements. The AL/NS computations without the DNW wind tunnel with speeds of 10m/s, 15m/s and 24m/s. Comparisons of blade loading between computations and measurements show...
Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas.
Kolvin, Itamar; Livne, Eli; Meerson, Baruch
2010-08-01
We show that, in dimension higher than one, heat diffusion and viscosity cannot arrest thermal collapse in a freely evolving dilute granular gas, even in the absence of gravity. Thermal collapse involves a finite-time blowup of the gas density. It was predicted earlier in ideal, Euler hydrodynamics of dilute granular gases in the absence of gravity, and in nonideal, Navier-Stokes granular hydrodynamics in the presence of gravity. We determine, analytically and numerically, the dynamic scaling laws that characterize the gas flow close to collapse. We also investigate bifurcations of a freely evolving dilute granular gas in circular and wedge-shaped containers. Our results imply that, in general, thermal collapse can only be arrested when the gas density becomes comparable with the close-packing density of grains. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.
Kiris, Cetin; Kwak, Dochan
1995-01-01
The fractional step and the pseudocompressibility methods for the solution of the incompressible Navier-Stokes equations are outlined. The fractional step method is based on finite-volume formulation and uses the pressure and the volume fluxes across the faces of each cell as dependent variables. The momentum equations are solved implicitly and the Poisson equation for the pressure is solved by using the multigrid method. The pseudocompressibility approach uses an implicit-higher-order-upwind differencing scheme for the convective terms together with the Gauss-Seidel line relaxation method. The dependent variables in the pseudocompressibility approach are the pressure and the cartesian velocity components in unstaggered mesh orientation. The 90-degree square duct flow, the wing-tip vortex wake flow and unsteady turbulent flows over an oscillating NACA 0015 airfoil are computed using both the fractional step and the pseudocompressibility methods. The results obtained from two different schemes are compared against experimental measurements.
A comparison of two incompressible Navier-Stokes algorithms for unsteady internal flow
Wiltberger, N. Lyn; Rogers, Stuart E.; Kwak, Dochan
1993-01-01
A comparative study of two different incompressible Navier-Stokes algorithms for solving an unsteady, incompressible, internal flow problem is performed. The first algorithm uses an artificial compressibility method coupled with upwind differencing and a line relaxation scheme. The second algorithm uses a fractional step method with a staggered grid, finite volume approach. Unsteady, viscous, incompressible, internal flow through a channel with a constriction is computed using the first algorithm. A grid resolution study and parameter studies on the artificial compressibility coefficient and the maximum allowable residual of the continuity equation are performed. The periodicity of the solution is examined and several periodic data sets are generated using the first algorithm. These computational results are compared with previously published results computed using the second algorithm and experimental data.
Recovering Navier-Stokes Equations from Asymptotic Limits of the Boltzmann Gas Mixture Equation
Bianca, Carlo; Dogbe, Christian
2016-05-01
This paper is devoted to the derivation of macroscopic fluid dynamics from the Boltzmann mesoscopic dynamics of a binary mixture of hard-sphere gas particles. Specifically the hydrodynamics limit is performed by employing different time and space scalings. The paper shows that, depending on the magnitude of the parameters which define the scaling, the macroscopic quantities (number density, mean velocity and local temperature) are solutions of the acoustic equation, the linear incompressible Euler equation and the incompressible Navier-Stokes equation. The derivation is formally tackled by the recent moment method proposed by [C. Bardos, et al., J. Stat. Phys. 63 (1991) 323] and the results generalize the analysis performed in [C. Bianca, et al., Commun. Nonlinear Sci. Numer. Simulat. 29 (2015) 240].
Qualitative Behaviour of Solutions for the Two-Phase Navier-Stokes Equations with Surface Tension
Köhne, Matthias; Wilke, Mathias
2010-01-01
The two-phase free boundary value problem for the isothermal Navier-Stokes system is studied for general bounded geometries in absence of phase transitions, external forces and boundary contacts. It is shown that the problem is well-posed in an Lp-setting, and that it generates a local semiflow on the induced phase manifold. If the phases are connected, the set of equilibria of the system forms a (n+1)-dimensional manifold, each equilibrium is stable, and it is shown that global solutions which do not develop singularities converge to an equilibrium as time goes to infinity. The latter is proved by means of the energy functional combined with the generalized principle of linearized stability.
Aeroacoustic Calculations of Wind Turbine Noise with the Actuator Line/ Navier-Stokes Technique
DEFF Research Database (Denmark)
Debertshäuser, Harald; Shen, Wen Zhong; Zhu, Wei Jun
2016-01-01
Noise regulations in many countries are becoming extremely strict and wind turbine noise is thus becoming a barrier for further development of onshore wind turbines. Low noise wind turbine airfoil and blade design is an important technique for noise reduction. However, the ow situation of a wind...... turbine in wind farms is very complicated. In order to accurately model the noise generation and propagation from wind turbines in wind farms,it is urgent to develop a high-fidelity noise model to predict the noise features in complex situations. In the present study, we develop a flow-acoustic splitting...... technique where the wind turbine flow is calculated by using the in-house actuator line/LES/Navier-Stokes technique and the acoustics is obtained by solving the acoustic perturbation equations. In the flow solver, the wind turbine blades are modelled by rotating lines with body forces determined according...
Projection of the rotation form Navier-Stokes equation onto the half-staggered grid
Energy Technology Data Exchange (ETDEWEB)
Cho, Ji Ryong [Inje University, Kimhae (Korea, Republic of)
2016-07-15
A projection method for computing incompressible fluid flow is proposed. For the method, the rotation form Navier-Stokes equation (NSE), for which the velocity and the total pressure are employed, is discretized on the half-staggered, finite difference spatial grid. The total pressure couples the static pressure gradient and the convection of momentum in the continuous NSE while the half-staggered grid provides weak pressure-velocity coupling in discrete space. These two features interact synergistically for the discretized NSE to produce smooth pressure fields without additional numerical artifacts such as the momentum interpolation. The method preserves the kinetic energy at the inviscid limit condition. Numerical solutions of the decaying Taylor vortex, the inviscid Taylor vortex, the sudden expansion channel and the square-prism wake are presented.
Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.
Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo
2012-07-01
We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.
A multigrid method for the Navier-Stokes and Boussinesq equations
Shi, Zeng; Wesseling, P.
A nonlinear multigrid method is developed for the Navier-Stokes and Boussinesq equations using a discretization of finite volume type on Cartesian staggered grids and a nonlinear collective Gauss-Seidel method for smoothing. A simple multigrid algorithm incorporating the cycles V, F, W and an adaptive multigrid cycle (A cycle) is presented. Numerical experiments are described for a driven square cavity problem and a free convection problem in a rectangular cavity. Of the three cycles tested, namely V, W and A, the A cycle is found to be most efficient. The rate of convergence is shown to improve slightly when the mesh size is decreased. The multigrid method is found to be very much faster than single grid iteration with the smoother.
Pore-Scale Modeling of Navier-Stokes Flow in Distensible Networks and Porous Media
Sochi, Taha
2013-01-01
In this paper, a pore-scale network modeling method, based on the flow continuity residual in conjunction with a Newton-Raphson non-linear iterative solving technique, is proposed and used to obtain the pressure and flow fields in a network of interconnected distensible ducts representing, for instance, blood vasculature or deformable porous media. A previously derived analytical expression correlating boundary pressures to volumetric flow rate in compliant tubes for a pressure-area constitutive elastic relation has been used to represent the underlying flow model. Comparison to a preceding equivalent method, the one-dimensional Navier-Stokes finite element, was made and the results were analyzed. The advantages of the new method have been highlighted and practical computational issues, related mainly to the rate and speed of convergence, have been discussed.
Stochastic Navier-Stokes Equation with Colored Noise: Renormalization Group Analysis
Antonov, N. V.; Gulitskiy, N. M.; Malyshev, A. V.
2016-11-01
In this work we study the fully developed turbulence described by the stochastic Navier-Stokes equation with finite correlation time of random force. Inertial-range asymptotic behavior is studied in one-loop approximation and by means of the field theoretic renormalization group. The inertial-range behavior of the model is described by limiting case of vanishing correlation time that corresponds to the nontrivial fixed point of the RG equation. Another fixed point is a saddle type point, i.e., it is infrared attractive only in one of two possible directions. The existence and stability of fixed points depends on the relation between the exponents in the energy spectrum ɛ ∝ k1-y and the dispersion law ω ∝ k2-η.
A relaxation technique for the parabolized Navier-Stokes (PNS) equations
Kaul, Upender K.
1986-01-01
A rapidly converging relaxation technique for the parabolized Navier-Stokes equations has been devised. The scheme is applicable in both supersonic and subsonic flows, but it is discussed here in the context of supersonic flows. The upstream propagating acoustic influence in the subsonic part of the flow is introduced semi-implicitly through the streamwise momentum equation applied on the body, and through a forward-differencing on the streamwise pressure gradient term in the interior. This procedure yields a new boundary condition on the energy in the total energy equation. The pressure-velocity system in the subsonic layer is coupled, but the positive time-like marching characteristic of the governing equations is still maintained. The relaxation technique is demontrated to work for a three-dimensional flow over a cone-flare in supersonic flight.
Isogeometric Divergence-conforming B-splines for the Steady Navier-Stokes Equations
2012-04-01
geometrical mapping meeting our criteria could be defined utilizing B-splines or Non- Uniform Rational B-Splines ( NURBS ) on the coarsest mesh Mh0 . For...examples of such mappings, see Chapter 2 of [13]. NURBS mappings are especially useful as they can represent many geometries of scientific and...complications that are beyond the scope of this work. We would like to note that all four assumptions hold if we employ a conforming NURBS multi-patch
DEFF Research Database (Denmark)
Yang, Yang; Kær, Søren Knudsen
2012-01-01
The flow structure of one isothermal swirling case in the Sydney swirl flame database was studied using two numerical methods. Results from the Reynolds-averaged Navier-Stokes (RANS) approach and large eddy simulation (LES) were compared with experimental measurements. The simulations were applied...
Implementation for blow up of tornado-type solutions for complex version of 3D Navier-Stokes system
Arnold, M D
2008-01-01
We consider Cauchy problem for Fourier transformation of 3-dimensional Navier-Stokes system with zero external force. Using initial data purposed by Dong Li and Ya.G.Sinai we implement self-similar regime producing fast growing behavior of the energy of solution while time tends to critical value.
Sabetghadam, Fereidoun
2014-01-01
The incompressible Navier-Stokes equations are re-formulated to involve an arbitrary time dilation; and in this manner, the modified Navier-Stokes equations are obtained which have some penalization terms in the right hand side. Then, the solid rigid bodies are modeled as the regions where time is dilated infinitely. The physical and mathematical properties of the modified equations and the penalization terms are investigated, and it is shown that the modified equations satisfy the no-slip, no-diffusion, no-advection, and no-pressure coupling conditions. The modified equations can be used in exact imposition of the solid rigid bodies on the incompressible Navier-Stokes equations. To show the capability of the modified equations, three classical exact solutions of the Navier-Stokes equations, that is, the Stokes first problem, the plane stagnation point flow, and the stokes flow over a sphere are re-solved exactly, this time in the presence of a solid region.
DEFF Research Database (Denmark)
Hesthaven, Jan
1997-01-01
This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a res...... for quasi-one-dimensional transonic nozzle flows and for flows around an infinitely long circular cylinder....
Institute of Scientific and Technical Information of China (English)
陈刚; 冯民富; 何银年
2013-01-01
A unified analysis is presented for the stabilized methods including the pres-sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa-tions. The existence and uniqueness of the solution and the optimal error estimates are proved.
TIME-ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR GENERAL NAVIER-STOKES EQUATIONS IN EVEN SPACE-DIMENSION
Institute of Scientific and Technical Information of China (English)
Xu Hongmei
2001-01-01
We study the time-asymptotic behavior of solutions to general NavierStokes equations in even and higher than two space-dimensions. Through the pointwise estimates of the Green function of the linearized system, we obtain explicit expressions of the time-asymptotic behavior of the solutions. The result coincides with weak Huygan's principle.
Guermond, Jean-Luc
2012-01-01
We provide a convergence analysis for a new fractional timestepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization. © 2012 American Mathematical Society.
Yoon, Seokkwan; Kwak, Dochan
1991-01-01
A numerical method based on the pseudocompressibility concept is developed for solving the three-dimensional incompressible Navier-Stokes equations using the lower-upper symmetric-Gauss-Seidel implicit scheme. Very high efficiency is achieved in a new flow solver, INS3D-LU code, by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.
Institute of Scientific and Technical Information of China (English)
DUAN Huoyuan; LIANG Guoping
2001-01-01
Following Part I., we study the stabilized finite element method for the incom pressible Navier-Stokes equations. It is shown that this new methodology is stable and has an optimal error estimates for all mesh Peclet number, allowing any combination of velocity and pressure interpolation.
Statistical study of approximations to two dimensional inviscid turbulence
Energy Technology Data Exchange (ETDEWEB)
Glaz, H.M.
1977-09-01
A numerical technique is developed for studying the ergodic and mixing hypotheses for the dynamical systems arising from the truncated Fourier transformed two-dimensional inviscid Navier-Stokes equations. This method has the advantage of exactly conserving energy and entropy (i.e., total vorticity) in the inviscid case except for numerical error in solving the ordinary differential equations. The development of the mathematical model as an approximation to a real physical (turbulent) flow and the numerical results obtained are discussed.
Zech, Alraune; Attinger, Sabine
2016-05-01
A new method is presented which allows interpreting steady-state pumping tests in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. An effective description of transmissivity is required, being a function of the radial distance to the well and including the parameters of log-transmissivity: mean, variance, and correlation length. Such a model is provided by the upscaling procedure radial coarse graining, which describes the transition of near-well to far-field transmissivity effectively. Based on this approach, an analytical solution for a steady-state pumping test drawdown is deduced. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown within an individual heterogeneous transmissivity field. The analytical form of the solution allows inversely estimating the parameters of aquifer heterogeneity. For comparison with the effective well flow solution, virtual pumping tests are performed and analysed for both cases, the ensemble mean drawdown and pumping tests at individual transmissivity fields. Interpretation of ensemble mean drawdowns showed proof of the upscaling method. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media in contrast to Thiem's solution for homogeneous media. Multiple pumping tests conducted at different locations within an individual transmissivity field are analysed, making use of the effective well flow solution to show that all statistical parameters of aquifer heterogeneity can be inferred under field conditions. Thus, the presented method is a promising tool with which to estimate parameters of aquifer heterogeneity, in particular variance and horizontal correlation length of log-transmissivity fields from steady-state pumping test measurements.
Energy Technology Data Exchange (ETDEWEB)
Fike, Jeffrey A.
2013-08-01
The construction of stable reduced order models using Galerkin projection for the Euler or Navier-Stokes equations requires a suitable choice for the inner product. The standard L2 inner product is expected to produce unstable ROMs. For the non-linear Navier-Stokes equations this means the use of an energy inner product. In this report, Galerkin projection for the non-linear Navier-Stokes equations using the L2 inner product is implemented as a first step toward constructing stable ROMs for this set of physics.
Advancing the theoretical foundation of the partially-averaged Navier-Stokes approach
Reyes, Dasia Ann
The goal of this dissertation is to consolidate the theoretical foundation of variable-resolution (VR) methods in general and the partially-averaged Navier-Stokes (PANS) approach in particular. The accurate simulation of complex turbulent flows remains an outstanding challenge in modern computational fluid dynamics. High-fidelity approaches such as direct numerical simulations (DNS) and large-eddy simulation (LES) are not typically feasible for complex engineering simulations with current computational technologies. Low-fidelity approaches such as Reynolds-averaged Navier-Stokes (RANS), although widely used, are inherently inadequate for turbulent flows with complex flow features. VR bridging methods fill the gap between DNS and RANS by allowing a tunable degree of resolution ranging from RANS to DNS. While the utility of VR methods is well established, the mathematical foundations and physical characterization require further development. This dissertation focuses on the physical attributes of fluctuations in partially-resolved simulations of turbulence. The specific objectives are to: (i) establish a framework for assessing the physical fidelity of VR methods to examine PANS fluctuations; (ii) investigate PANS simulations subject to multiple resolution changes; (iii) examine turbulent transport closure modeling for partially-resolved fields; (iv) examine the effect of filter control parameters in the limit of spectral cut-off in the dissipative region; and (v) validate low-Reynolds number corrections with RANS for eventual implementation with PANS. While the validation methods are carried out in the context of PANS, they are considered appropriate for all VR bridging methods. The key findings of this dissertation are summarized as follows. The Kolmogorov hypotheses are suitably adapted to describe fluctuations of partially-resolved turbulence fields, and the PANS partially-resolved field is physically consistent with the adapted Kolmogorov hypotheses. PANS
Automated Euler and Navier-Stokes Database Generation for a Glide-Back Booster
Chaderjian, Neal M.; Rogers, Stuart E.; Aftosmis, Mike J.; Pandya, Shishir A.; Ahmad, Jasim U.; Tejnil, Edward
2004-01-01
The past two decades have seen a sustained increase in the use of high fidelity Computational Fluid Dynamics (CFD) in basic research, aircraft design, and the analysis of post-design issues. As the fidelity of a CFD method increases, the number of cases that can be readily and affordably computed greatly diminishes. However, computer speeds now exceed 2 GHz, hundreds of processors are currently available and more affordable, and advances in parallel CFD algorithms scale more readily with large numbers of processors. All of these factors make it feasible to compute thousands of high fidelity cases. However, there still remains the overwhelming task of monitoring the solution process. This paper presents an approach to automate the CFD solution process. A new software tool, AeroDB, is used to compute thousands of Euler and Navier-Stokes solutions for a 2nd generation glide-back booster in one week. The solution process exploits a common job-submission grid environment, the NASA Information Power Grid (IPG), using 13 computers located at 4 different geographical sites. Process automation and web-based access to a MySql database greatly reduces the user workload, removing much of the tedium and tendency for user input errors. The AeroDB framework is shown. The user submits/deletes jobs, monitors AeroDB's progress, and retrieves data and plots via a web portal. Once a job is in the database, a job launcher uses an IPG resource broker to decide which computers are best suited to run the job. Job/code requirements, the number of CPUs free on a remote system, and queue lengths are some of the parameters the broker takes into account. The Globus software provides secure services for user authentication, remote shell execution, and secure file transfers over an open network. AeroDB automatically decides when a job is completed. Currently, the Cart3D unstructured flow solver is used for the Euler equations, and the Overflow structured overset flow solver is used for the
A Parallel Newton-Krylov-Schur Algorithm for the Reynolds-Averaged Navier-Stokes Equations
Osusky, Michal
Aerodynamic shape optimization and multidisciplinary optimization algorithms have the potential not only to improve conventional aircraft, but also to enable the design of novel configurations. By their very nature, these algorithms generate and analyze a large number of unique shapes, resulting in high computational costs. In order to improve their efficiency and enable their use in the early stages of the design process, a fast and robust flow solution algorithm is necessary. This thesis presents an efficient parallel Newton-Krylov-Schur flow solution algorithm for the three-dimensional Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model. The algorithm employs second-order summation-by-parts (SBP) operators on multi-block structured grids with simultaneous approximation terms (SATs) to enforce block interface coupling and boundary conditions. The discrete equations are solved iteratively with an inexact-Newton method, while the linear system at each Newton iteration is solved using the flexible Krylov subspace iterative method GMRES with an approximate-Schur parallel preconditioner. The algorithm is thoroughly verified and validated, highlighting the correspondence of the current algorithm with several established flow solvers. The solution for a transonic flow over a wing on a mesh of medium density (15 million nodes) shows good agreement with experimental results. Using 128 processors, deep convergence is obtained in under 90 minutes. The solution of transonic flow over the Common Research Model wing-body geometry with grids with up to 150 million nodes exhibits the expected grid convergence behavior. This case was completed as part of the Fifth AIAA Drag Prediction Workshop, with the algorithm producing solutions that compare favourably with several widely used flow solvers. The algorithm is shown to scale well on over 6000 processors. The results demonstrate the effectiveness of the SBP-SAT spatial discretization, which can
Convergence of a Vector Penalty Projection Scheme for the Navier-Stokes Equations with moving body
Bruneau, Vincent; Fabrie, Pierre
2016-01-01
In this paper, we analyse a Vector Penalty Projection Scheme (see [1]) to treat the displacement of a moving body in incompressible viscous flows in the case where the interaction of the fluid on the body can be neglected. The presence of the obstacle inside the computational domain is treated with a penalization method introducing a parameter $\\eta$. We show the stability of the scheme and that the pressure and velocity converge towards a limit when the penalty parameter $\\epsilon$, which induces a small divergence and the time step $\\delta$t tend to zero with a proportionality constraint $\\epsilon$ = $\\lambda$$\\delta$t. Finally, when $\\eta$ goes to 0, we show that the problem admits a weak limit which is a weak solution of the Navier-Stokes equations with no-sleep condition on the solid boundary. R{\\'e}sum{\\'e} Dans ce travail nous analysons un sch{\\'e}ma de projection vectorielle (voir [1]) pour traiter le d{\\'e}placement d'un corps solide dans un fluide visqueux incompressible dans le cas o` u l'interacti...
One-way spatial integration of Navier-Stokes equations: stability of wall-bounded flows
Rigas, Georgios; Colonius, Tim; Towne, Aaron; Beyar, Michael
2016-11-01
For three-dimensional flows, questions of stability, receptivity, secondary flows, and coherent structures require the solution of large partial-derivative eigenvalue problems. Reduced-order approximations are thus required for engineering prediction since these problems are often computationally intractable or prohibitively expensive. For spatially slowly evolving flows, such as jets and boundary layers, a regularization of the equations of motion sometimes permits a fast spatial marching procedure that results in a huge reduction in computational cost. Recently, a novel one-way spatial marching algorithm has been developed by Towne & Colonius. The new method overcomes the principle flaw observed in Parabolized Stability Equations (PSE), namely the ad hoc regularization that removes upstream propagating modes. The one-way method correctly parabolizes the flow equations based on estimating, in a computationally efficient way, the local spectrum in each cross-stream plane and an efficient spectral filter eliminates modes with upstream group velocity. Results from the application of the method to wall-bounded flows will be presented and compared with predictions from the full linearized compressible Navier-Stokes equations and PSE.
An h-adaptive local discontinuous Galerkin method for the Navier-Stokes-Korteweg equations
Tian, Lulu; Xu, Yan; Kuerten, J. G. M.; van der Vegt, J. J. W.
2016-08-01
In this article, we develop a mesh adaptation algorithm for a local discontinuous Galerkin (LDG) discretization of the (non)-isothermal Navier-Stokes-Korteweg (NSK) equations modeling liquid-vapor flows with phase change. This work is a continuation of our previous research, where we proposed LDG discretizations for the (non)-isothermal NSK equations with a time-implicit Runge-Kutta method. To save computing time and to capture the thin interfaces more accurately, we extend the LDG discretization with a mesh adaptation method. Given the current adapted mesh, a criterion for selecting candidate elements for refinement and coarsening is adopted based on the locally largest value of the density gradient. A strategy to refine and coarsen the candidate elements is then provided. We emphasize that the adaptive LDG discretization is relatively simple and does not require additional stabilization. The use of a locally refined mesh in combination with an implicit Runge-Kutta time method is, however, non-trivial, but results in an efficient time integration method for the NSK equations. Computations, including cases with solid wall boundaries, are provided to demonstrate the accuracy, efficiency and capabilities of the adaptive LDG discretizations.
GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yin-nian He; Yan-ren Hou; Li-quan Mei
2001-01-01
A global finite element nonlinear Galerkin method for the penalized Navier-Stokes equations is presented. This method is based on two finite element spaces XH and Xh,defined respectively on one coarse grid with grid size H and one fine grid with grid size h ＜＜ H. Comparison is also made with the finite element Galerkin method. If we choose H = O(ε-1/4h1/2), ε＞ 0 being the penalty parameter, then two methods are of the same order of approximation. However, the global finite element nonlinear Galerkin method is much cheaper than the standard finite element Galerkin method. In fact, in the finite element Galerkin method the nonlinearity is treated on the fine grid finite element space Xh and while in the global finite element nonlinear Galerkin method the similar nonlinearity is treated on the coarse grid finite element space XH and only the linearity needs to be treated on the fine grid increment finite element space Wh. Finally, we provide numerical test which shows above results stated.
Enhancing finite differences with radial basis functions: Experiments on the Navier-Stokes equations
Flyer, Natasha; Barnett, Gregory A.; Wicker, Louis J.
2016-07-01
Polynomials are used together with polyharmonic spline (PHS) radial basis functions (RBFs) to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial discretizations that can be viewed as enhancements of the classical finite differences (FD). The presented method replicates the convergence properties of FD but for arbitrary node layouts. It is tested on the 2D compressible Navier-Stokes equations at low Mach number, relevant to atmospheric flows. Test cases are taken from the numerical weather prediction community and solved on bounded domains. Thus, attention is given on how to handle boundaries with the RBF-FD method, as well as a novel implementation for hyperviscosity. Comparisons are done on Cartesian, hexagonal, and quasi-uniform node layouts. Consideration and guidelines are given on PHS order, polynomial degree and stencil size. The main advantages of the present method are: 1) capturing the basic physics of the problem surprisingly well, even at very coarse resolutions, 2) high-order accuracy without the need of tuning a shape parameter, and 3) the inclusion of polynomials eliminates stagnation (saturation) errors. A MATLAB code is given to calculate the differentiation weights for this novel approach.
Reynolds-averaged Navier-Stokes and Large-Eddy Simulation Over and Inside Inhomogeneous Forests
DEFF Research Database (Denmark)
Boudreault, Louis-Etienne
the performance of wind models in such environment.A systematic method to acquire gridded input of canopy structure from aircraft based LiDAR scans of heterogeneous forests is defined. An extensive validation against ground-based measurements of the vertically summed frontal area density(or plant area index......) and tree height is performed. The method is optimized both in terms of plant area index magnitude and spatial variability. A forest grid is generated from the LiDAR method using airplane scans of a 5×5 km2 forested site in Sweden. The grid serves as the basis for Reynolds-averaged Navier-Stokes (RANS...... an important influence of the smaller heterogeneities on the flow when the site is complex. A second helicopter-based LiDAR scan of high resolution is used to create a highly detailed forest grid at the site of a previous forest edge experiment on the island of Falster in Denmark. This input is used in a large...
Energy Technology Data Exchange (ETDEWEB)
Xiaodong Liu; Lijun Xuan; Hong Luo; Yidong Xia
2001-01-01
A reconstructed discontinuous Galerkin (rDG(P1P2)) method, originally introduced for the compressible Euler equations, is developed for the solution of the compressible Navier- Stokes equations on 3D hybrid grids. In this method, a piecewise quadratic polynomial solution is obtained from the underlying piecewise linear DG solution using a hierarchical Weighted Essentially Non-Oscillatory (WENO) reconstruction. The reconstructed quadratic polynomial solution is then used for the computation of the inviscid fluxes and the viscous fluxes using the second formulation of Bassi and Reay (Bassi-Rebay II). The developed rDG(P1P2) method is used to compute a variety of flow problems to assess its accuracy, efficiency, and robustness. The numerical results demonstrate that the rDG(P1P2) method is able to achieve the designed third-order of accuracy at a cost slightly higher than its underlying second-order DG method, outperform the third order DG method in terms of both computing costs and storage requirements, and obtain reliable and accurate solutions to the large eddy simulation (LES) and direct numerical simulation (DNS) of compressible turbulent flows.
Error transport equation boundary conditions for the Euler and Navier-Stokes equations
Phillips, Tyrone S.; Derlaga, Joseph M.; Roy, Christopher J.; Borggaard, Jeff
2017-02-01
Discretization error is usually the largest and most difficult numerical error source to estimate for computational fluid dynamics, and boundary conditions often contribute a significant source of error. Boundary conditions are described with a governing equation to prescribe particular behavior at the boundary of a computational domain. Boundary condition implementations are considered sufficient when discretized with the same order of accuracy as the primary governing equations; however, careless implementations of boundary conditions can result in significantly larger numerical error. Investigations into different numerical implementations of Dirichlet and Neumann boundary conditions for Burgers' equation show a significant impact on the accuracy of Richardson extrapolation and error transport equation discretization error estimates. The development of boundary conditions for Burgers' equation shows significant improvements in discretization error estimates in general and a significant improvement in truncation error estimation. The latter of which is key to accurate residual-based discretization error estimation. This research investigates scheme consistent and scheme inconsistent implementations of inflow and outflow boundary conditions up to fourth order accurate and a formulation for a slip wall boundary condition for truncation error estimation are developed for the Navier-Stokes and Euler equations. The scheme consistent implementation resulted in much smoother truncation error near the boundaries and more accurate discretization error estimates.
Study of time-accurate integration of the variable-density Navier-Stokes equations
Lu, Xiaoyi; Pantano, Carlos
2015-11-01
We present several theoretical elements that affect time-consistent integration of the low-Mach number approximation of variable-density Navier-Stokes equations. The goal is for velocity, pressure, density, and scalars to achieve uniform order of accuracy, consistent with the time integrator being used. We show examples of second-order (using Crank-Nicolson and Adams-Bashforth) and third-order (using additive semi-implicit Runge-Kutta) uniform convergence with the proposed conceptual framework. Furthermore, the consistent approach can be extended to other time integrators. In addition, the method is formulated using approximate/incomplete factorization methods for easy incorporation in existing solvers. One of the observed benefits of the proposed approach is improved stability, even for large density difference, in comparison with other existing formulations. A linearized stability analysis is also carried out for some test problems to better understand the behavior of the approach. This work was supported in part by the Department of Energy, National Nuclear Security Administration, under award no. DE-NA0002382 and the California Institute of Technology.
Energy Technology Data Exchange (ETDEWEB)
Gjesdal, Thor
1997-12-31
This thesis discusses the development and application of efficient numerical methods for the simulation of fluid flows, in particular the flow of incompressible fluids. The emphasis is on practical aspects of algorithm development and on application of the methods either to linear scalar model equations or to the non-linear incompressible Navier-Stokes equations. The first part deals with cell centred multigrid methods and linear correction scheme and presents papers on (1) generalization of the method to arbitrary sized grids for diffusion problems, (2) low order method for advection-diffusion problems, (3) attempt to extend the basic method to advection-diffusion problems, (4) Fourier smoothing analysis of multicolour relaxation schemes, and (5) analysis of high-order discretizations for advection terms. The second part discusses a multigrid based on pressure correction methods, non-linear full approximation scheme, and papers on (1) systematic comparison of the performance of different pressure correction smoothers and some other algorithmic variants, low to moderate Reynolds numbers, and (2) systematic study of implementation strategies for high order advection schemes, high-Re flow. An appendix contains Fortran 90 data structures for multigrid development. 160 refs., 26 figs., 22 tabs.
Energy conservation in explicit time integrators for the Navier-Stokes equations
Capuano, Francesco; Coppola, Gennaro; Luis, Rández; Luigi, De Luca
2016-11-01
Discrete conservation of kinetic energy is a fundamental requirement in the numerical solution of the incompressible Navier-Stokes equations. A fully conservative algorithm requires that both the spatial and temporal discretizations do not spuriously contribute to the discrete global energy balance. While various methods are available to accomplish spatial conservation, algorithms that preserve kinetic energy exactly in time are necessarily implicit and might be not applicable in practical situations. In this work, explicit Runge-Kutta methods with optimal energy conservation properties are investigated. The proposed methods are designed to be accurate to order p and to preserve kinetic energy to order q, with q > p . The beneficial effects of the proposed methods have been assessed in terms of a properly defined effective Reynolds number, taking into account both numerical and physical viscosity. Numerical simulations of the three-dimensional Taylor-Green Vortex at high Reynolds number have shown that the proposed methods are able to keep the effective Reynolds number of the flow very close to the nominal one, while classical explicit schemes show large discrepancies.
A Convergent Staggered Scheme for the Variable Density Incompressible Navier-Stokes Equations
Latché, Jean-Claude
2016-01-01
In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the so-called Rannacher-Turek element. The convection term in the momentum balance equation is discretized by a finite volume technique, in such a way that a solution obeys a discrete kinetic energy balance, and the mass balance is approximated by an upwind finite volume method. We first show that the scheme preserves the stability properties of the continuous problem (L $\\infty$-estimate for the density, L $\\infty$ (L 2)-and L 2 (H 1)-estimates for the velocity), which yields, by a topological degree technique, the existence of a solution. Then, invoking compactness arguments and passing to the limit in the scheme, we prove that any sequence of solutions (obtained with a sequence of discretizations the space and time step of which tend to zero) converges up to the extraction of a subs...
A High Order, Locally-Adaptive Method for the Navier-Stokes Equations
Chan, Daniel
1998-11-01
I have extended the FOSLS method of Cai, Manteuffel and McCormick (1997) and implemented it within the framework of a spectral element formulation using the Legendre polynomial basis function. The FOSLS method solves the Navier-Stokes equations as a system of coupled first-order equations and provides the ellipticity that is needed for fast iterative matrix solvers like multigrid to operate efficiently. Each element is treated as an object and its properties are self-contained. Only C^0 continuity is imposed across element interfaces; this design allows local grid refinement and coarsening without the burden of having an elaborate data structure, since only information along element boundaries is needed. With the FORTRAN 90 programming environment, I can maintain a high computational efficiency by employing a hybrid parallel processing model. The OpenMP directives provides parallelism in the loop level which is executed in a shared-memory SMP and the MPI protocol allows the distribution of elements to a cluster of SMP's connected via a commodity network. This talk will provide timing results and a comparison with a second order finite difference method.
Simulation of Rotary-Wing Near-Wake Vortex Structures Using Navier-Stokes CFD Methods
Kenwright, David; Strawn, Roger; Ahmad, Jasim; Duque, Earl; Warmbrodt, William (Technical Monitor)
1997-01-01
This paper will use high-resolution Navier-Stokes computational fluid dynamics (CFD) simulations to model the near-wake vortex roll-up behind rotor blades. The locations and strengths of the trailing vortices will be determined from newly-developed visualization and analysis software tools applied to the CFD solutions. Computational results for rotor nearwake vortices will be used to study the near-wake vortex roll up for highly-twisted tiltrotor blades. These rotor blades typically have combinations of positive and negative spanwise loading and complex vortex wake interactions. Results of the computational studies will be compared to vortex-lattice wake models that are frequently used in rotorcraft comprehensive codes. Information from these comparisons will be used to improve the rotor wake models in the Tilt-Rotor Acoustic Code (TRAC) portion of NASA's Short Haul Civil Transport program (SHCT). Accurate modeling of the rotor wake is an important part of this program and crucial to the successful design of future civil tiltrotor aircraft. The rotor wake system plays an important role in blade-vortex interaction noise, a major problem for all rotorcraft including tiltrotors.
On one-dimensional compressible Navier-Stokes equations for a reacting mixture in unbounded domains
Li, Siran
2017-10-01
In this paper we consider the one-dimensional Navier-Stokes system for a heat-conducting, compressible reacting mixture which describes the dynamic combustion of fluids of mixed kinds on unbounded domains. This model has been discussed on bounded domains by Chen (SIAM J Math Anal 23:609-634, 1992) and Chen-Hoff-Trivisa (Arch Ration Mech Anal 166:321-358, 2003), among others, in which the reaction rate function is a discontinuous function obeying the Arrhenius' law of thermodynamics. We prove the global existence of weak solutions to this model on one-dimensional unbounded domains with large initial data in H^1. Moreover, the large-time behaviour of the weak solution is identified. In particular, the uniform-in-time bounds for the temperature and specific volume have been established via energy estimates. For this purpose we utilise techniques developed by Kazhikhov-Shelukhin (cf. Kazhikhov in Siber Math J 23:44-49, 1982; Solonnikov and Kazhikhov in Annu Rev Fluid Mech 13:79-95, 1981) and refined by Jiang (Commun Math Phys 200:181-193, 1999, Proc R Soc Edinb Sect A 132:627-638, 2002), as well as a crucial estimate in the recent work by Li-Liang (Arch Ration Mech Anal 220:1195-1208, 2016). Several new estimates are also established, in order to treat the unbounded domain and the reacting terms.
Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier-Stokes equations
Birken, Philipp; Gassner, Gregor; Haas, Mark; Munz, Claus-Dieter
2013-05-01
We compare different block preconditioners in the context of parallel time adaptive higher order implicit time integration using Jacobian-free Newton-Krylov (JFNK) solvers for discontinuous Galerkin (DG) discretizations of the three dimensional time dependent Navier-Stokes equations. A special emphasis of this work is the performance for a relative high number of processors, i.e. with a low number of elements on the processor. For high order DG discretizations, a particular problem that needs to be addressed is the size of the blocks in the Jacobian. Thus, we propose a new class of preconditioners that exploits the hierarchy of modal basis functions and introduces a flexible order of the off-diagonal Jacobian blocks. While the standard preconditioners 'block Jacobi' (no off-blocks) and full symmetric Gauss-Seidel (full off-blocks) are included as special cases, the reduction of the off-block order results in the new scheme ROBO-SGS. This allows us to investigate the impact of the preconditioner's sparsity pattern with respect to the computational performance. Since the number of iterations is not well suited to judge the efficiency of a preconditioner, we additionally consider CPU time for the comparisons. We found that both block Jacobi and ROBO-SGS have good overall performance and good strong parallel scaling behavior.
Non-linear simulations of combustion instabilities with a quasi-1D Navier-Stokes code
Haugen, Nils Erland L; Sannan, Sigurd
2010-01-01
As lean premixed combustion systems are more susceptible to combustion instabilities than non-premixed systems, there is an increasing demand for improved numerical design tools that can predict the occurrence of combustion instabilities with high accuracy. The inherent non-linearities in combustion instabilities can be of crucial importance, and we here propose an approach in which the one-dimensional Navier-Stokes and scalar transport equations are solved for geometries of variable cross-section. The focus is on attached flames, and for this purpose a new phenomenological model for the unsteady heat release from a flame front is introduced. In the attached flame method (AFM) the heat release occurs over the full length of the flame. The non-linear code with the use of the AFM approach is validated against results from an experimental study of thermoacoustic instabilities in oxy-fuel flames by Ditaranto and Hals [Combustion and Flame, 146, 493-512 (2006)]. The numerical simulations are in accordance with the...
Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver
Paige, Cody
The use of adjoint methods is common in computational fluid dynamics to reduce the cost of the sensitivity analysis in an optimization cycle. The forward mode ADjoint is a combination of an adjoint sensitivity analysis method with a forward mode automatic differentiation (AD) and is a modification of the reverse mode ADjoint method proposed by Mader et al.[1]. A colouring acceleration technique is presented to reduce the computational cost increase associated with forward mode AD. The forward mode AD facilitates the implementation of the laminar Navier-Stokes (NS) equations. The forward mode ADjoint method is applied to a three-dimensional computational fluid dynamics solver. The resulting Euler and viscous ADjoint sensitivities are compared to the reverse mode Euler ADjoint derivatives and a complex-step method to demonstrate the reduced computational cost and accuracy. Both comparisons demonstrate the benefits of the colouring method and the practicality of using a forward mode AD. [1] Mader, C.A., Martins, J.R.R.A., Alonso, J.J., and van der Weide, E. (2008) ADjoint: An approach for the rapid development of discrete adjoint solvers. AIAA Journal, 46(4):863-873. doi:10.2514/1.29123.
Reynolds Averaged Navier-Stokes (RANS) equation solutions of wind turbine wakes
Energy Technology Data Exchange (ETDEWEB)
Ludwig, Daniel Evandro; Horn, Diego Anderson; Petry, Adriane Prisco [Thermal and Energy Study Group, Mechanical Engeneering Department, Federal University of Rio Grande do Sul, Porto Alegre (Brazil)], E-mail: adrianep@mecanica.ufrgs.br
2010-07-01
This paper aims to evaluate the influence of three different turbulence models in the study of a wind turbine wake. Numerical Simulation is used as working tool to characterize the flow through the wind turbines, it is used the numeric simulation. The numerical analysis is based on the finite volume method and the Reynolds Averaged Navier-Stokes (RANS) equations. Three turbulence models are used to represent the total effects of turbulence in the flow: the two equations k-classical and the RNG k- models, based on the turbulent viscosity; and the Shear Stress Transport (SST) model, based on the transport of the Reynolds tensor. The results of the 'u' velocity profiles are compared to experimental data from Vermeer (2003) at distances equivalent to 2, 4, 6, 8, 10 and 16 diameters downstream from the turbine. Results shows that the SST model gives better results until 6 diameters, beyond this distance there is no significant differences between the compared models. (author)
Institute of Scientific and Technical Information of China (English)
WANG Liang; FU Song
2009-01-01
Based on Reynolds-averaged Navier-Stokes approach, a laminar-turbulence transition model is proposed in this study that takes into account the effects of different instability modes associated with the variations in Mach numbers of compressible boundary layer flows. The model is based on k-ω-γ three-equation eddy-viscosity concept with k representing the fluctuating kinetic energy, ωthe specific dissipation rate and the intermittency factor γ.The particular features of the model are that: 1) k includes the non-turbulent, as well as turbulent fluctuations; 2) a transport equation for the intermittency factor γis proposed here with a source term set to trigger the transition onset; 3) through the introduction of a new length scale normal to wall, the present model employs the local variables only avoiding the use of the integral parameters, like the boundary layer thickness δ,which are often cost-ineffective with the modern CFD (Computational Fluid Dynamics) methods; 4) in the fully turbulent region, the model retreats to the well-known k-ωSST (Shear Stress Transport) model. This model is validated with a number of available experiments on boundary layer transitions including the incompressible, supersonic and hypersonic flows past flat plates, straight/flared cones at zero incidences, etc. It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Based on Reynolds-averaged Navier-Stokes approach,a laminar-turbulence transition model is proposed in this study that takes into account the effects of different instability modes associated with the variations in Mach numbers of compressible boundary layer flows.The model is based on k-ω-γ three-equation eddy-viscosity concept with k representing the fluctuating kinetic energy,ωthe specific dissipation rate and the intermittency factorγ.The particular features of the model are that:1)k includes the non-turbulent,as well as turbulent fluctuations;2)a transport equation for the intermittency factorγis proposed here with a source term set to trigger the transition onset;3)through the introduction of a new length scale normal to wall,the present model employs the local variables only avoiding the use of the integral parameters,like the boundary layer thicknessδ,which are often cost-ineffective with the modern CFD(Computational Fluid Dynamics)methods;4)in the fully turbulent region,the model retreats to the well-known k-ωSST(Shear Stress Transport)model.This model is validated with a number of available experiments on boundary layer transitions including the incompressible,supersonic and hypersonic flows past flat plates,straight/flared cones at zero incidences,etc.It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition.
A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics.
Hageman, Nathan S; Toga, Arthur W; Narr, Katherine L; Shattuck, David W
2009-03-01
We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.
Yamaleev, Nail K.; Carpenter, Mark H.
2017-02-01
High-order numerical methods that satisfy a discrete analog of the entropy inequality are uncommon. Indeed, no proofs of nonlinear entropy stability currently exist for high-order weighted essentially nonoscillatory (WENO) finite volume or weak-form finite element methods. Herein, a new family of fourth-order WENO spectral collocation schemes is developed, that are nonlinearly entropy stable for the one-dimensional compressible Navier-Stokes equations. Individual spectral elements are coupled using penalty type interface conditions. The resulting entropy stable WENO spectral collocation scheme achieves design order accuracy, maintains the WENO stencil biasing properties across element interfaces, and satisfies the summation-by-parts (SBP) operator convention, thereby ensuring nonlinear entropy stability in a diagonal norm. Numerical results demonstrating accuracy and nonoscillatory properties of the new scheme are presented for the one-dimensional Euler and Navier-Stokes equations for both continuous and discontinuous compressible flows.
Lanzafame, Giuseppe
2012-01-01
Physical damping, regarding the nonlinear Navier-Stokes viscous flow dynamics, refers to a tensorial turbulent dissipation term, attributed to adjacent moving macroscopic flow components. Mutual dissipation among these parts of fluid is described by a braking term in the momentum equation together with a heating term in the energy equation, both responsible of the damping of the momentum variation and of the viscous conversion of mechanical energy into heat. A macroscopic mixing scale length is currently the only characteristic length needed in the nonlinear modelling of viscous fluid dynamics describing the nonlinear eddy viscosity through the kinematic viscosity coefficient in the viscous stress tensor, without any reference to the chemical composition and to the atomic dimensions. Therefore, in this paper, we write a new formulation for the kinematic viscosity coefficient to the turbulent viscous physical dissipation in the Navier-Stokes equations, where molecular parameters are also included. Results of 2...
Institute of Scientific and Technical Information of China (English)
LI Jun; LIU Li-jun; FENG Zhen-ping
2004-01-01
Hydrodynamic optimization design of the bend pipe from pump using the Navier-Stokes solver and evolutionary algorithms was conducted. The minimization of the total pressure loss of the bend pipe was chosen as the design object in order to obtain the uniform exit flows through suppressing the secondary flows. The 3-D Navier-Stokes solver was applied to evaluate the hydrodynamic performance of the bend-pipe flows. A 7th-order Bezier curve was used to parameterize the meridional section and elliptic representation was adopted to represent the cross-section profiles of the bend pipe. Evolutionary algorithms were applied in optimization. The obtained results show that the designed bend pipe shape has much more uniform exit flows compared with the initial one and much weaker secondary flows, and that the evolutionary algorithms and CFD technique are the powerful optimization tools for the fluid machinery design.
On the quasi-unconditional stability of BDF-ADI solvers for the compressible Navier-Stokes equations
Bruno, Oscar
2015-01-01
The companion paper "Higher-order in time quasi-unconditionally stable ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains", which is referred to as Part I in what follows, introduces ADI (Alternating Direction Implicit) solvers of higher orders of temporal accuracy (orders $s = 2$ to $6$) for the compressible Navier-Stokes equations in two- and three-dimensional space. The proposed methodology employs the backward differentiation formulae (BDF) together with a quasilinear-like formulation, high-order extrapolation for nonlinear components, and the Douglas-Gunn splitting. A variety of numerical results presented in Part I demonstrate in practice the theoretical convergence rates enjoyed by these algorithms, as well as their excellent accuracy and stability properties for a wide range of Reynolds numbers. In particular, the proposed schemes enjoy a certain property of "quasi-unconditional stability": for small enough (problem-dependent) fixed values of the time-step $\\Delt...
Institute of Scientific and Technical Information of China (English)
Yuxin Ren; Yuxi Jiang; Miao'er Liu; Hanxin Zhang
2005-01-01
In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.
Labeur, Robert Jan
2010-01-01
An interface stabilised finite element method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilising mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. In contrast with discontinuous Galerkin methods, the number of global degrees of freedom is the same as for a continuous method on the same mesh. Different from earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for the appropriate choice of finite element spaces, momentum conservation. Also, in this work a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a point-wise solenoidal velocity field. Mass...
Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla
2010-02-01
Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.
Sifounakis, Adamandios; Lee, Sangseung; You, Donghyun
2016-12-01
A second-order-accurate finite-volume method is developed for the solution of incompressible Navier-Stokes equations on locally refined nested Cartesian grids. Numerical accuracy and stability on locally refined nested Cartesian grids are achieved using a finite-volume discretization of the incompressible Navier-Stokes equations based on higher-order conservation principles - i.e., in addition to mass and momentum conservation, kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithms. Hanging nodes at the interface are virtually slanted to improve the pressure-velocity projection, while the other parts of the grid maintain an orthogonal Cartesian grid topology. The present method is straight-forward to implement and shows superior conservation of mass, momentum, and kinetic energy compared to the conventional methods employing interpolation at the interface between coarse and fine grids.
The Vlasov-Navier-Stokes system in a 2D pipe: existence and stability of regular equilibria
Glass, Olivier; Han-Kwan, Daniel; Moussa, Ayman
2016-01-01
In this paper, we study the Vlasov-Navier-Stokes system in a 2D pipe with partially absorbing boundary conditions. We show the existence of stationary states for this system near small Poiseuille flows for the fluid phase, for which the kinetic phase is not trivial. We prove the asymptotic stability of these states with respect to appropriately compactly supported perturbations. The analysis relies on geometric control conditions which help to avoid any concentration phenomenon for the kineti...
Institute of Scientific and Technical Information of China (English)
Junping YIN; Zhong TAN
2008-01-01
The authors prove two global existence results of strong solutions of the isen- tropic compressible Navier-Stokes-Poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. In this paper the initial vacuum is allowed, and T is bounded.
Bardina, J. E.
1994-01-01
A new computational efficient 3-D compressible Reynolds-averaged implicit Navier-Stokes method with advanced two equation turbulence models for high speed flows is presented. All convective terms are modeled using an entropy satisfying higher-order Total Variation Diminishing (TVD) scheme based on implicit upwind flux-difference split approximations and arithmetic averaging procedure of primitive variables. This method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent Navier-Stokes procedures to solve flows with mixed supersonic and subsonic zones, including streamwise separated flows. Its robust stability derives from a combination of conservative implicit upwind flux-difference splitting with Roe's property U to provide accurate shock capturing capability that non-conservative schemes do not guarantee, alternating symmetric Gauss-Seidel 'method of planes' relaxation procedure coupled with a three-dimensional two-factor diagonal-dominant approximate factorization scheme, TVD flux limiters of higher-order flux differences satisfying realizability, and well-posed characteristic-based implicit boundary-point a'pproximations consistent with the local characteristics domain of dependence. The efficiency of the method is highly increased with Newton Raphson acceleration which allows convergence in essentially one forward sweep for supersonic flows. The method is verified by comparing with experiment and other Navier-Stokes methods. Here, results of adiabatic and cooled flat plate flows, compression corner flow, and 3-D hypersonic shock-wave/turbulent boundary layer interaction flows are presented. The robust 3-D method achieves a better computational efficiency of at least one order of magnitude over the CNS Navier-Stokes code. It provides cost-effective aerodynamic predictions in agreement with experiment, and the capability of predicting complex flow structures in
Duan, Ran; Guo, Ai; Zhu, Changjiang
2017-04-01
We obtain existence and uniqueness of global strong solution to one-dimensional compressible Navier-Stokes equations for ideal polytropic gas flow, with density dependent viscosity and temperature dependent heat conductivity under stress-free and thermally insulated boundary conditions. Here we assume viscosity coefficient μ (ρ) = 1 +ρα and heat conductivity coefficient κ (θ) =θβ for all α ∈ [ 0 , ∞) and β ∈ (0 , + ∞).
Boudin, Laurent; Grandmont, Céline; Moussa, Ayman
2017-02-01
In this article, we prove the existence of global weak solutions for the incompressible Navier-Stokes-Vlasov system in a three-dimensional time-dependent domain with absorption boundary conditions for the kinetic part. This model arises from the study of respiratory aerosol in the human airways. The proof is based on a regularization and approximation strategy designed for our time-dependent framework.
Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration
Institute of Scientific and Technical Information of China (English)
SHEN Yu-jing; HAN Dan-fu; SHAO Xin-ping
2015-01-01
A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h=H2. Both theoretical analysis and numerical experiments illustrate the eﬃ ciency of the algorithm for solving the coupled problem.
Steijl, R.; Hoeijmakers, H. W. M.
2004-09-01
A fourth-order accurate solution method for the three-dimensional Helmholtz equations is described that is based on a compact finite-difference stencil for the Laplace operator. Similar discretization methods for the Poisson equation have been presented by various researchers for Dirichlet boundary conditions. Here, the complicated issue of imposing Neumann boundary conditions is described in detail. The method is then applied to model Helmholtz problems to verify the accuracy of the discretization method. The implementation of the solution method is also described. The Helmholtz solver is used as the basis for a fourth-order accurate solver for the incompressible Navier-Stokes equations. Numerical results obtained with this Navier-Stokes solver for the temporal evolution of a three-dimensional instability in a counter-rotating vortex pair are discussed. The time-accurate Navier-Stokes simulations show the resolving properties of the developed discretization method and the correct prediction of the initial growth rate of the three-dimensional instability in the vortex pair.
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.
2014-02-01
A Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel continuous boundary force (CBF) method is proposed for solving the Navier-Stokes equations subject to the Robin boundary condition. In the CBF method, the Robin boundary condition is replaced by the homogeneous Neumann boundary condition and a volumetric force term added to the momentum conservation equation. Smoothed particle hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two- and three-dimensional flows subject to various forms of the Robin boundary condition in domains bounded by flat and curved boundaries. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite-element method. Considering the no-slip boundary condition as a special case of the slip boundary condition, we demonstrate that the SPH-CBF method accurately describes both the no-slip and slip conditions.
Parsani, Matteo
2016-10-04
Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for the compressible Euler and Navier--Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [M. H. Carpenter, T. C. Fisher, E. J. Nielsen, and S. H. Frankel, SIAM J. Sci. Comput., 36 (2014), pp. B835--B867, M. Parsani, M. H. Carpenter, and E. J. Nielsen, J. Comput. Phys., 292 (2015), pp. 88--113], extends the applicable set of points from tensor product, Legendre--Gauss--Lobatto (LGL), to a combination of tensor product Legendre--Gauss (LG) and LGL points. The new semidiscrete operators discretely conserve mass, momentum, energy, and satisfy a mathematical entropy inequality for the compressible Navier--Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly from a theoretical point of view. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinear stability proof for the compressible Navier--Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).
Gupta, R. N.; Simmonds, A. L.
1986-01-01
Solutions of the Navier-Stokes equations with chemical nonequilibrium and multicomponent surface slip are presented along the stagnation streamline under low-density hypersonic flight conditions. The conditions analyzed are those encountered by the nose region of the Space Shuttle Orbiter during reentry. A detailed comparison of the Navier-Stokes (NS) results is made with the viscous shock-layer (VSL) and Direct Simulation Monte Carlo (DSMC) predictions. With the inclusion of surface-slip boundary conditions in NS calculations, the surface heat transfer and other flow field quantities adjacent to the surface are predicted favorably with the DSMC calculations from 75 km to 115 km in altitude. Therefore, the practical range for the applicability of Navier-Stokes solutions is much wider than previously thought. This is appealing because the continuum (NS and VSL) methods are commonly used to solve the fluid flow problems and are less demanding in terms of computer resource requirements than the noncontinuum (DSMC) methods. The NS solutions agree well with the VSL results for altitudes less than 92 km. An assessment is made of the frozen flow approximation employed in the VSL calculations.
Ha, Sanghyun; You, Donghyun
2015-11-01
Utility of the computational power of Graphics Processing Units (GPUs) is elaborated for solutions of both incompressible and compressible Navier-Stokes equations. A semi-implicit ADI finite-volume method for integration of the incompressible and compressible Navier-Stokes equations, which are discretized on a structured arbitrary grid, is parallelized for GPU computations using CUDA (Compute Unified Device Architecture). In the semi-implicit ADI finite-volume method, the nonlinear convection terms and the linear diffusion terms are integrated in time using a combination of an explicit scheme and an ADI scheme. Inversion of multiple tri-diagonal matrices is found to be the major challenge in GPU computations of the present method. Some of the algorithms for solving tri-diagonal matrices on GPUs are evaluated and optimized for GPU-acceleration of the present semi-implicit ADI computations of incompressible and compressible Navier-Stokes equations. Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning Grant NRF-2014R1A2A1A11049599.
Richter, Christiane; Kotz, Frederik; Giselbrecht, Stefan; Helmer, Dorothea; Rapp, Bastian E
2016-06-01
The fluid mechanics of microfluidics is distinctively simpler than the fluid mechanics of macroscopic systems. In macroscopic systems effects such as non-laminar flow, convection, gravity etc. need to be accounted for all of which can usually be neglected in microfluidic systems. Still, there exists only a very limited selection of channel cross-sections for which the Navier-Stokes equation for pressure-driven Poiseuille flow can be solved analytically. From these equations, velocity profiles as well as flow rates can be calculated. However, whenever a cross-section is not highly symmetric (rectangular, elliptical or circular) the Navier-Stokes equation can usually not be solved analytically. In all of these cases, numerical methods are required. However, in many instances it is not necessary to turn to complex numerical solver packages for deriving, e.g., the velocity profile of a more complex microfluidic channel cross-section. In this paper, a simple spreadsheet analysis tool (here: Microsoft Excel) will be used to implement a simple numerical scheme which allows solving the Navier-Stokes equation for arbitrary channel cross-sections.
Institute of Scientific and Technical Information of China (English)
LU Chang-gen; CAO Wei-dong; QIAN Jian-hua
2006-01-01
A new method for direct numerical simulation of incompressible Navier-Stokes equations is studied in the paper. The compact finite difference and the non-linear terms upwind compact finite difference schemes on non-uniform meshes in x and y directions are developed respectively. With the Fourier spectral expansion in the spanwise direction, three-dimensional N-S equation are converted to a system of two-dimensional equations. The third-order mixed explicit-implicit scheme is employed for time integration. The treatment of the three-dimensional non-reflecting outflow boundary conditions is presented, which is important for the numerical simulations of the problem of transition in boundary layers, jets, and mixing layer. The numerical results indicate that high accuracy, stabilization and efficiency are achieved by the proposed numerical method. In addition, a theory model for the coherent structure in a laminar boundary layer is also proposed, based on which the numerical method is implemented to the non-linear evolution of coherent structure. It is found that the numerical results of the distribution of Reynolds stress, the formation of high shear layer, and the event of ejection and sweeping, match well with the observed characteristics of the coherent structures in a turbulence boundary layer.
Mihaescu, Mihai; Murugappan, Shanmugam; Kalra, Maninder; Khosla, Sid; Gutmark, Ephraim
2008-07-19
Computational fluid dynamics techniques employing primarily steady Reynolds-Averaged Navier-Stokes (RANS) methodology have been recently used to characterize the transitional/turbulent flow field in human airways. The use of RANS implies that flow phenomena are averaged over time, the flow dynamics not being captured. Further, RANS uses two-equation turbulence models that are not adequate for predicting anisotropic flows, flows with high streamline curvature, or flows where separation occurs. A more accurate approach for such flow situations that occur in the human airway is Large Eddy Simulation (LES). The paper considers flow modeling in a pharyngeal airway model reconstructed from cross-sectional magnetic resonance scans of a patient with obstructive sleep apnea. The airway model is characterized by a maximum narrowing at the site of retropalatal pharynx. Two flow-modeling strategies are employed: steady RANS and the LES approach. In the RANS modeling framework both k-epsilon and k-omega turbulence models are used. The paper discusses the differences between the airflow characteristics obtained from the RANS and LES calculations. The largest discrepancies were found in the axial velocity distributions downstream of the minimum cross-sectional area. This region is characterized by flow separation and large radial velocity gradients across the developed shear layers. The largest difference in static pressure distributions on the airway walls was found between the LES and the k-epsilon data at the site of maximum narrowing in the retropalatal pharynx.
Source Term Model for Vortex Generator Vanes in a Navier-Stokes Computer Code
Waithe, Kenrick A.
2004-01-01
A source term model for an array of vortex generators was implemented into a non-proprietary Navier-Stokes computer code, OVERFLOW. The source term models the side force created by a vortex generator vane. The model is obtained by introducing a side force to the momentum and energy equations that can adjust its strength automatically based on the local flow. The model was tested and calibrated by comparing data from numerical simulations and experiments of a single low profile vortex generator vane on a flat plate. In addition, the model was compared to experimental data of an S-duct with 22 co-rotating, low profile vortex generators. The source term model allowed a grid reduction of about seventy percent when compared with the numerical simulations performed on a fully gridded vortex generator on a flat plate without adversely affecting the development and capture of the vortex created. The source term model was able to predict the shape and size of the stream-wise vorticity and velocity contours very well when compared with both numerical simulations and experimental data. The peak vorticity and its location were also predicted very well when compared to numerical simulations and experimental data. The circulation predicted by the source term model matches the prediction of the numerical simulation. The source term model predicted the engine fan face distortion and total pressure recovery of the S-duct with 22 co-rotating vortex generators very well. The source term model allows a researcher to quickly investigate different locations of individual or a row of vortex generators. The researcher is able to conduct a preliminary investigation with minimal grid generation and computational time.
Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre
2014-12-14
We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formation of the so-called "giant fluctuations" of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power -4 of the wavenumber-except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.
Dynamics of vortex interactions in two-dimensional flows
DEFF Research Database (Denmark)
Juul Rasmussen, J.; Nielsen, A.H.; Naulin, V.
2002-01-01
a critical value, a(c). Using the Weiss-field, a(c) is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 a(c) ...The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier-Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R-0l. is below...
Energy Technology Data Exchange (ETDEWEB)
Maita, S.; Ando, J.; Nakatake, K. [Kyushu University, Fukuoka (Japan). Faculty of Engineering
1996-10-01
A simple panel method, the source and quasi continuous vortex lattice method (SQCM) was expanded to two-dimensional non-steady hydrofoil problems. Discussions were given on the results of calculations on two-dimensional hydrofoils making a simple non-steady motion. In calculating hydrofoils which move suddenly from a still state with angle of elevation {alpha} at a velocity U, the following results were obtained: the time differential item in a pressure equation gives a considerably strong effect on lifting power; and the lifting power converges to a steady state with lapse of time, and the lifting power coefficient in that state shows that the lifting power increases as hydrofoil thickness increases. This result agrees with the hydrofoil thickness effect in the two-dimensional steady problem, proving the reasonability of this calculation method. In the calculations of time history of the lifting power acting on hydrofoils passing a sinusoidal gust and hydrofoils in a pitching motion, the calculated values from the SQCM were found to approach analysis solution to thin hydrofoils as the hydrofoil thickness becomes thinner for both cases. This result also proves the result of calculations on non-steady state by using the SQCM reasonable. 11 refs., 10 figs.
Large Eddy/Reynolds-Averaged Navier-Stokes Simulations of CUBRC Base Heating Experiments
Salazar, Giovanni; Edwards, Jack R.; Amar, Adam J.
2012-01-01
ven with great advances in computational techniques and computing power during recent decades, the modeling of unsteady separated flows, such as those encountered in the wake of a re-entry vehicle, continues to be one of the most challenging problems in CFD. Of most interest to the aerothermodynamics community is accurately predicting transient heating loads on the base of a blunt body, which would result in reduced uncertainties and safety margins when designing a re-entry vehicle. However, the prediction of heat transfer can vary widely depending on the turbulence model employed. Therefore, selecting a turbulence model which realistically captures as much of the flow physics as possible will result in improved results. Reynolds Averaged Navier Stokes (RANS) models have become increasingly popular due to their good performance with attached flows, and the relatively quick turnaround time to obtain results. However, RANS methods cannot accurately simulate unsteady separated wake flows, and running direct numerical simulation (DNS) on such complex flows is currently too computationally expensive. Large Eddy Simulation (LES) techniques allow for the computation of the large eddies, which contain most of the Reynolds stress, while modeling the smaller (subgrid) eddies. This results in models which are more computationally expensive than RANS methods, but not as prohibitive as DNS. By complimenting an LES approach with a RANS model, a hybrid LES/RANS method resolves the larger turbulent scales away from surfaces with LES, and switches to a RANS model inside boundary layers. As pointed out by Bertin et al., this type of hybrid approach has shown a lot of promise for predicting turbulent flows, but work is needed to verify that these models work well in hypersonic flows. The very limited amounts of flight and experimental data available presents an additional challenge for researchers. Recently, a joint study by NASA and CUBRC has focused on collecting heat transfer data
Grossman, Bernard
1999-01-01
The technical details are summarized below: Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. . An efficient surface parameterization based
An integral equation approach to smooth 3D Navier-Stokes solution
Costin, O.; Luo, G.; Tanveer, S.
2008-12-01
We summarize a recently developed integral equation (IE) approach to tackling the long-time existence problem for smooth solution v(x, t) to the 3D Navier-Stokes (NS) equation in the context of a periodic box problem with smooth time independent forcing and initial condition v0. Using an inverse-Laplace transform of {\\skew5\\hat v} (k, t) - {\\skew5\\hat v}_0 in 1/t, we arrive at an IE for {\\skew5\\hat U} (k, p) , where p is inverse-Laplace dual to 1/t and k is the Fourier variable dual to x. The advantage of this formulation is that the solution {\\skew5\\hat U} to the IE is known to exist a priori for p \\in \\mathbb{R}^+ and the solution is integrable and exponentially bounded at ∞. Global existence of NS solution in this formulation is reduced to an asymptotics question. If \\parallel\\!{\\skew5\\hat U} (\\cdot, p)\\!\\parallel_{{l^{1} (\\mathbb{Z}^3)}} has subexponential bounds as p→∞, then global existence to NS follows. Moreover, if f=0, then the converse is also true in the following sense: if NS has global solution, then there exists n>=1 for which the inverse-Laplace transform of {\\skew5\\hat v} (k, t) - {\\skew5\\hat v}_0 in 1/tn necessarily decays as q→∞, where q is the inverse-Laplace dual to 1/tn. We also present refined estimates of the exponential growth when the solution {\\skew5\\hat U} is known on a finite interval [0, p0]. We also show that for analytic v[0] and f, with finitely many nonzero Fourier-coefficients, the series for {\\skew5\\hat U} (k, p) in powers of p has a radius of convergence independent of initial condition and forcing; indeed the radius gets bigger for smaller viscosity. We also show that the IE can be solved numerically with controlled errors. Preliminary numerical calculations for Kida (1985 J. Phys. Soc. Japan 54 2132) initial conditions, though far from being optimized, and performed on a modest interval in the accelerated variable q show decay in q.
Modeling tsunami of cosmogenic and landslide origin on the basis of Navier-Stokes equations
Kozelkov, Andrey; Kurkin, Andrey; Pelinovsky, Efim
2016-04-01
An approach to the modeling of the landslide and meteoritic origin tsunami, based on the Navier-Stokes equations for multiphase flows with a free surface, is presented. Description of the system's numerical integration, based on a fully implicit connection of velocity and pressure, is done. The connection of the continuity equation and the equations of conservation of momentum is based on account of the implicit terms of the pressure gradient and mass flow. Basic formulas for discretization of equations and the form of the coefficients, which are summarized in general associated matrix, are performed. Basic steps of the computational procedure are described. The results of proposed method's verification to the problems with experimental data (the problem of the dam collapse, a hydraulic jump and a falling of a box in the water) are presented. Results of the numerical modeling of possible hydrodynamic disturbances in the lake Chebarkul, Russia, caused by the fall of a meteorite in 2013, are presented. The numerical experiments are performed both with and without account of the lake's ice cover. Dimensions of the ice cover disruption are evaluated. Dimensions of the observable ice-hole in the place of the meteorite fall are shown to be in good agreement with the theoretical predictions and the preliminary estimations. In addition, results of the numerical investigation of the influence of angle of the body's entry into the water on the characteristics of the resulting waves in the near field are presented. Dimensions of the perturbation and the regularities of changes in the parameters of the source are studied. It is shown that the greatest change in characteristics of the source occurs most rapidly in the vicinity of the angle of incidence of 20 degrees to the horizontal. The source as a separate phase representing Newtonian fluid with its density and viscosity and the surface is separated from the water and air phase is used to simulate landslide. The results of
Zeng, S.; Wesseling, P.
1993-01-01
The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.
On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation
Wang, Y.
2013-01-01
A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy\\'s law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong solution for this problem, under the assumption that initial density ρ0(x) is bounded away from 0 and other appropriate assumptions (see Theorem 1 and Theorem 2). The semi-Galerkin method is applied to construct the approximate solutions and a prior estimates are made to elaborate upon the compactness of the approximate solutions.
A spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow
Moser, R. D.; Moin, P.; Leonard, A.
1983-01-01
A new spectral method for solving the incompressible Navier-Stokes equations in a plane channel and between concentric cylinders is presented. The method uses spectral expansions which inherently satisfy the boundary conditions and the continuity equation and yield banded matrices which are efficiently solved at each time step. In addition, the number of dependent variables is reduced, resulting in a reduction in computer memory requirements. Several test problems have been computed for the channel flow and for flow between concentric cylinders, including Taylor-Couette flow with axisymmetric Taylor vortices and wavy vortices. In all cases, agreement with available experimental and theoretical results is very good.
Oud, G. T.; van der Heul, D. R.; Vuik, C.; Henkes, R. A. W. M.
2016-11-01
We present a finite difference discretization of the incompressible Navier-Stokes equations in cylindrical coordinates. This currently is, to the authors' knowledge, the only scheme available that is demonstrably capable of conserving mass, momentum and kinetic energy (in the absence of viscosity) on both uniform and non-uniform grids. Simultaneously, we treat the inherent discretization issues that arise due to the presence of the coordinate singularity at the polar axis. We demonstrate the validity of the conservation claims by performing a number of numerical experiments with the proposed scheme, and we show that it is second order accurate in space using the Method of Manufactured Solutions.
Zhai, Xiaoping; Yin, Zhaoyang
2017-02-01
The present paper is dedicated to the global well-posedness for the 3D inhomogeneous incompressible Navier-Stokes equations, in critical Besov spaces without smallness assumption on the variation of the density. We aim at extending the work by Abidi, Gui and Zhang (2012) [2], and (2013) [3] to a lower regularity index about the initial velocity. The key to that improvement is a new a priori estimate for an elliptic equation with nonconstant coefficients in Besov spaces which have the same degree as L2 in R3. Finally, we also generalize our well-posedness result to the inhomogeneous incompressible MHD equations.
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper,we study the one-dimensional motion of viscous gas with a general pres- sure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a jump.We prove the global existence and the uniqueness of weak solutions to the compressible Navier-Stokes equations by using the line method.For this,some new a priori estimates are obtained to take care of the general viscosity coefficientμ(ρ)instead ofρ~θ.
Institute of Scientific and Technical Information of China (English)
Mei-man SUN; Chang-jiang ZHU
2007-01-01
In this paper, we study the one-dimensional motion of viscous gas with a general pressure law and a general density-dependent viscosity coefficient when the initial density connects to the vacuum state with a jump. We prove the global existence and the uniqueness of weak solutions to the compressible Navier-Stokes equations by using the line method. For this, some new a priori estimates are obtained to take care of the general viscosity coefficient μ(ρ) instead of ρθ.
Institute of Scientific and Technical Information of China (English)
罗振东; 朱江; 王会军
2002-01-01
A nonlinear Galerkin/ Petrov- least squares mixed element (NGPLSME) method for the stationary Navier-Stokes equations is presented and analyzed. The scheme is that Petrov-least squares forms of residuals are added to the nonlinear Galerkin mixed element method so that it is stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. The existence, uniqueness and convergence ( at optimal rate ) of the NGPLSME solution is proved in the case of sufficient viscosity ( or small data).
Zheng, Jiashan
2017-09-01
The coupled quasilinear Keller-Segel-Navier-Stokes system is considered under Neumann boundary conditions for $n$ and $c$ and no-slip boundary conditions for $u$ in three-dimensional bounded domains $\\Omega\\subseteq \\mathbb{R}^3$ with smooth boundary, where $m>0,\\kappa\\in \\mathbb{R}$ are given constants, $\\phi\\in W^{1,\\infty}(\\Omega)$. If $ m> 2$, then for all reasonably regular initial data, a corresponding initial-boundary value problem for $(KSNF)$ possesses a globally defined weak solution.
Codding, William H.; Lombard, C. K.; Yang, J. Y.
1988-01-01
The Conservative Supra-Characteristic Method (CSCM) Navier-Stokes solver is applied to ascertain the problems inherent in the design of a nominal Mach 14 nozzle for NASA-Ames' 3.5-ft Hypersonic Wind Tunnel; attention is given to the effects of boundary layer cooling systems on the aerodynamic redesign of the nozzle throat region. Complete nozzle flowfields are calculated with and without slot injection of either hot or cold fluid into the boundary layer just upstream of the throat, as well as with alternatively adiabatic and cold walls. The CSCM method is capable of resolving subtle differences in the flows.
Tsyganov, Eugene
2007-09-01
We investigate the asymptotic behavior of the solutions of the compressible Navier Stokes equations with nonmonotonic pressure when the initial data is large and discontinuous. We provide sufficient conditions on the pressure function for different boundary-value problems that guarantee strong convergence of the volume variable as time approaches infinity and show that, typically, fairly arbitrary discontinuous static phase mixtures can be realized as time-asymptotic limits from smooth initial data. It is required in the analysis that we improve known existence theories, which typically have small data or time-dependent bounds.
Kweon, Jae Ryong
2016-09-01
In this paper, when the initial density has a jump across an interior curve in a bounded domain, we show unique existence, piecewise regularity and jump discontinuity dynamics for the density and the velocity vector governed by the Navier-Stokes equations of compressible viscous barotropic flows. A critical difficulty is in controlling the gradient of the pressure across the jump curve. This is resolved by constructing a vector function associated with the pressure jump value on the convecting curve and extending it to the whole domain.
A numerical method for the vorticity-velocity Navier-Stokes equations in two and three dimensions
Napolitano, M.; Pascazio, G.
A staggered-grid incremental line-Gauss-Seidel method for solving the vorticity-velocity Navier-Stokes equations is described. The governing equations for this method are presented. The applicability of the method is evaluated by solving the classical driven cavity flow problem in two- and three-dimensions. The data derived with the line-Gauss-Seidel method are compared with the results of Ghia et al. (1982). It is noted that the data correlate well and the line-Gauss-Seidel method is effective for driven cavity flow problems.
Yu, Haibo; Zhao, Junning
2017-01-01
In this paper, we study the global existence for classical solutions to the 3D isentropic compressible Navier-Stokes equations in a cuboid domain. Compared to the Cauchy problem studied in Hoff (1995 J. Differ. Equ. 120 215-54), Hoff (2005 J. Math. Fluid Mech. 7 315-38), Huang et al (2012 Commun. Pure Appl. Math. 65 549-85), some new thoughts are applied to obtain upper bounds for density. Precisely, through piecewise estimation and some time-depending a priori estimates, we establish time-uniform upper bounds for density under the assumption that the initial energy is small. The initial vacuum is allowed.
Energy Technology Data Exchange (ETDEWEB)
Wathen, A. [Oxford Univ. (United Kingdom); Golub, G. [Stanford Univ., CA (United States)
1996-12-31
A simple fixed point linearisation of the Navier-Stokes equations leads to the Oseen problem which after appropriate discretisation yields large sparse linear systems with coefficient matrices of the form (A B{sup T} B -C). Here A is non-symmetric but its symmetric part is positive definite, and C is symmetric and positive semi-definite. Such systems arise in other situations. In this talk we will describe and present some analysis for an iteration based on an indefinite and symmetric preconditioner of the form (D B{sup T} B -C).
Institute of Scientific and Technical Information of China (English)
Lan Chieh Huang
2002-01-01
The unsteaiy incompressible Navier-Stokes equations are discretized in space and stud-ied on the fixed mesh as a system of differential algebraic equations. With discrete projec-tion defined, the local errors of Crank Nicholson schemes with three projection methodsare derived in a straightforward manner. Then the approximate factorization of relevantmatrices are used to study the time accuracy with more detail, especially at points adjacentto the boundary. The effects of numerical boundary conditions for the auxiliary velocityand the discrete pressure Poisson equation on the time accuracy are also investigated. Re-sults of numerical experiments with an analytic example confirm the conclusions of ouranalysis.
Two-dimensional numerical simulation of flow around three-stranded rope
Wang, Xinxin; Wan, Rong; Huang, Liuyi; Zhao, Fenfang; Sun, Peng
2016-08-01
Three-stranded rope is widely used in fishing gear and mooring system. Results of numerical simulation are presented for flow around a three-stranded rope in uniform flow. The simulation was carried out to study the hydrodynamic characteristics of pressure and velocity fields of steady incompressible laminar and turbulent wakes behind a three-stranded rope. A three-cylinder configuration and single circular cylinder configuration are used to model the three-stranded rope in the two-dimensional simulation. The governing equations, Navier-Stokes equations, are solved by using two-dimensional finite volume method. The turbulence flow is simulated using Standard κ-ɛ model and Shear-Stress Transport κ-ω (SST) model. The drag of the three-cylinder model and single cylinder model is calculated for different Reynolds numbers by using control volume analysis method. The pressure coefficient is also calculated for the turbulent model and laminar model based on the control surface method. From the comparison of the drag coefficient and the pressure of the single cylinder and three-cylinder models, it is found that the drag coefficients of the three-cylinder model are generally 1.3-1.5 times those of the single circular cylinder for different Reynolds numbers. Comparing the numerical results with water tank test data, the results of the three-cylinder model are closer to the experiment results than the single cylinder model results.
Tsionskiy, A
2012-01-01
Some known results regarding the Euler and Navier-Stokes equations were obtained by different authors. Existence and smoothness of solution for the Navier-Stokes equations in two dimensions have been known for a long time. Leray $\\cite{jL34}$ showed that the Navier-Stokes equations in three space dimensions have a weak solution. Scheffer $\\cite{vS76}, \\cite{vS93}$ and Shnirelman $\\cite{aS97}$ obtained weak solution of the Euler equations with compact support in spacetime. Caffarelli, Kohn and Nirenberg $\\cite{CKN82}$ improved Scheffer's results, and F.-H. Lin $\\cite{fL98}$ simplified the proof of the results of J. Leray. Many problems and conjectures about behavior of weak solutions of the Euler and Navier-Stokes equations are described in the books of Ladyzhenskaya $\\cite{oL69}$, Bertozzi and Majda $\\cite{BM02}$, Temam $\\cite{RT77}$, Constantin $\\cite{pC01}$ or Lemari\\'e-Rieusset $\\cite{pL02}$. Solutions of the Navier-Stokes and Euler equations with initial conditions (Cauchy problem) for 2D and 3D cases wer...
Ergodicity of Truncated Stochastic Navier Stokes with Deterministic Forcing and Dispersion
Majda, Andrew J.; Tong, Xin T.
2016-10-01
Turbulence in idealized geophysical flows is a very rich and important topic. The anisotropic effects of explicit deterministic forcing, dispersive effects from rotation due to the β -plane and F-plane, and topography together with random forcing all combine to produce a remarkable number of realistic phenomena. These effects have been studied through careful numerical experiments in the truncated geophysical models. These important results include transitions between coherent jets and vortices, and direct and inverse turbulence cascades as parameters are varied, and it is a contemporary challenge to explain these diverse statistical predictions. Here we contribute to these issues by proving with full mathematical rigor that for any values of the deterministic forcing, the β - and F-plane effects and topography, with minimal stochastic forcing, there is geometric ergodicity for any finite Galerkin truncation. This means that there is a unique smooth invariant measure which attracts all statistical initial data at an exponential rate. In particular, this rigorous statistical theory guarantees that there are no bifurcations to multiple stable and unstable statistical steady states as geophysical parameters are varied in contrast to claims in the applied literature. The proof utilizes a new statistical Lyapunov function to account for enstrophy exchanges between the statistical mean and the variance fluctuations due to the deterministic forcing. It also requires careful proofs of hypoellipticity with geophysical effects and uses geometric control theory to establish reachability. To illustrate the necessity of these conditions, a two-dimensional example is developed which has the square of the Euclidean norm as the Lyapunov function and is hypoelliptic with nonzero noise forcing, yet fails to be reachable or ergodic.
Gibbon, John D.; Pal, Nairita; Gupta, Anupam; Pandit, Rahul
2016-12-01
We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter ϕ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J. T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984), 10.1007/BF01212349]. By taking an L∞ norm of the energy of the full binary system, designated as E∞, we have shown that ∫0tE∞(τ ) d τ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs) of the 3D CHNS equations for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with 1283 to 5123 collocation points and over the duration of our DNSs confirm that E∞ remains bounded as far as our computations allow.
Application of the Poor Man's Navier-Stokes Equations to Real-Time Control of Fluid Flow
Directory of Open Access Journals (Sweden)
James B. Polly
2012-01-01
Full Text Available Control of fluid flow is an important, underutilized process possessing potential benefits ranging from avoidance of separation and stall on aircraft wings to reduction of friction in oil and gas pipelines to mitigation of noise from wind turbines. But the Navier-Stokes (N.-S. equations, whose solutions describe such flows, consist of a system of time-dependent, multidimensional, nonlinear partial differential equations (PDEs which cannot be solved in real time using current computing hardware. The poor man's Navier-Stokes (PMNS equations comprise a discrete dynamical system that is algebraic—hence, easily (and rapidly solved—and yet which retains many (possibly all of the temporal behaviors of the PDE N.-S. system at specific spatial locations. Herein, we outline derivation of these equations and discuss their basic properties. We consider application of these equations to the control problem by adding a control force. We examine the range of behaviors that can be achieved by changing this control force and, in particular, consider controllability of this (nonlinear system via numerical experiments. Moreover, we observe that the derivation leading to the PMNS equations is very general and may be applied to a wide variety of problems governed by PDEs and (possibly time-delay ordinary differential equations such as, for example, models of machining processes.
Computation of Steady Incompressible Flows in Unbounded Domains
Gustafsson, Jonathan
2014-01-01
In this study we revisit the problem of computing steady Navier-Stokes flows in two-dimensional unbounded domains. Precise quantitative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical fluid dynamics. Following a review of key mathematical properties of such solutions related to the slow decay of the velocity field at large distances from the obstacle, we develop and carefully validate a spectrally-accurate computational approach which ensures the correct behavior of the solution at infinity. In the proposed method the numerical solution is defined on the entire unbounded domain without the need to truncate this domain to a finite box with some artificial boundary conditions prescribed at its boundaries. Since our approach relies on the streamfunction-vorticity formulation, the main complication is the presence of a discontinuity in the streamfunction field at infinity which is related to the slow decay of this field. We demonstrate how this difficulty ca...
Energy Technology Data Exchange (ETDEWEB)
Martineau, Richard C., E-mail: Richard.Martineau@inl.go [Fuels Modeling and Simulation, Nuclear Fuels and Materials Division, Idaho National Laboratory, P.O. Box 1625, Idaho Falls, ID 83415-3860 (United States); Berry, Ray A.; Esteve, Aurelia; Hamman, Kurt D.; Knoll, Dana A.; Park, HyeongKae; Taitano, William [Fuels Modeling and Simulation, Nuclear Fuels and Materials Division, Idaho National Laboratory, P.O. Box 1625, Idaho Falls, ID 83415-3860 (United States)
2010-06-15
This paper illustrates a comparative study to analyze the physical differences between numerical simulations obtained with both the conservation and incompressible forms of the Navier-Stokes equations for natural convection flows in simple geometries. The purpose of this study is to quantify how the incompressible flow assumption (which is based upon constant density advection, divergence-free flow, and the Boussinesq gravitational body force approximation) differs from the conservation form (which only assumes that the fluid is a continuum) when solving flows driven by gravity acting upon density variations resulting from local temperature gradients. Driving this study is the common use of the incompressible flow assumption in fluid flow simulations for nuclear power applications in natural convection flows subjected to a high heat flux (large temperature differences). A series of simulations were conducted on two-dimensional, differentially heated rectangular geometries and modeled with both hydrodynamic formulations. From these simulations, the selected characterization parameters of maximum Nusselt number, average Nusselt number, and normalized pressure reduction were calculated. Comparisons of these parameters were made with available benchmark solutions for air with the ideal gas assumption at both low and high heat fluxes. Additionally, we generated specific force quantities and velocity and temperature distributions to provide a basis for further analysis. The simulations and analysis were then extended to include helium at the Very High Temperature gas-cooled Reactor (VHTR) normal operating conditions. Our results show that the consequences of incorporating the incompressible flow assumption in high heat flux situations may lead to unrepresentative results. The results question the use of the incompressible flow assumption for simulating fluid flow in an operating nuclear reactor, where large temperature variations are present.
Energy Technology Data Exchange (ETDEWEB)
Richard C. Martineau; Ray A. Berry; Aurélia Esteve; Kurt D. Hamman; Dana A. Knoll; Ryosuke Park; William Taitano
2009-01-01
This report illustrates a comparative study to analyze the physical differences between numerical simulations obtained with both the conservation and incompressible forms of the Navier-Stokes equations for natural convection flows in simple geometries. The purpose of this study is to quantify how the incompressible flow assumption (which is based upon constant density advection, divergence-free flow, and the Boussinesq gravitational body force approximation) differs from the conservation form (which only assumes that the fluid is a continuum) when solving flows driven by gravity acting upon density variations resulting from local temperature gradients. Driving this study is the common use of the incompressible flow assumption in fluid flow simulations for nuclear power applications in natural convection flows subjected to a high heat flux (large temperature differences). A series of simulations were conducted on two-dimensional, differentially-heated rectangular geometries and modeled with both hydrodynamic formulations. From these simulations, the selected characterization parameters of maximum Nusselt number, average Nusselt number, and normalized pressure reduction were calculated. Comparisons of these parameters were made with available benchmark solutions for air with the ideal gas assumption at both low and high heat fluxes. Additionally, we generated body force, velocity, and divergence of velocity distributions to provide a basis for further analysis. The simulations and analysis were then extended to include helium at the Very High Temperature gas-cooled Reactor (VHTR) normal operating conditions. Our results show that the consequences of incorporating the incompressible flow assumption in high heat flux situations may lead to unrepresentative results. The results question the use of the incompressible flow assumption for simulating fluid flow in an operating nuclear reactor, where large temperature variations are present. The results show that the use of
Muriel, Amador
2017-01-01
There have been several papers published which show exact solutions of the Navier-Stokes equation. None of the solutions admit any possibility of turbulence. It is strongly suggested that the Navier-Stokes equation is not the correct problem definition for turbulence. Yet, by contrast, in a simple example, it s shown that turbulence can result quite directly by using two or more species of fluids. The species are in fact identical atoms with different quantum states, provoking the strong suggestion that a plausible explanation for the origin of turbulence is quantum mechanical. This suggestion is heavily supported by actual modern pipe flow experiments [Muriel, Quantum Theory of Turbulence, Harvard Book Store (2011),which may be downloaded from (Muriel, ResearchGate)] The most general exact solutions of the Navier-Stokes equation will be displayed. In addition, experiments supporting a quantum interpretation will be reviewed.
Large Deviations for 2-D Stochastic Navier-Stokes Equations with Jumps%二维带跳Navier-Stokes方程解的大偏差原理
Institute of Scientific and Technical Information of China (English)
赵辉艳
2012-01-01
在带泊松跳二维随机Navier-Stokes方程解的解的存在唯一性的基础上,利用弱收敛的方法证明了带泊松跳二维随机Navier-Stokes方程解的Freidlin-Wentzell型的大偏差原理.%In this paper,under the existence and uniqueness of the solution of stochastic 2-D Navier-Stokes equation,we prove Freidlin-Wentzell＇s large deviation principle for 2-D Stochastic Navier-Stokes Equation driven by multiplicative noise with Poisson jumps by using weak convergence approach.
Institute of Scientific and Technical Information of China (English)
ZHAO Li-Yun; GUO Bo-Ling; HUANG Hai-Yang
2011-01-01
@@ The explicit solutions to both the Oldroyd-B model with an infinite Weissenberg number and the coupled Navier- Stokes/phase-field system are constructed by the method of separation of variables.It is found that the solutions blow up in finite time.%The explicit solutions to both the Oldroyd-B model with an infinite Weissenberg number and the coupled Navier- Stokes/phase-Beld system are constructed by the method of separation of variables. It is found that the solutions blow up in finite time.
Sharma, Ati S; Moarref, Rashad; McKeon, Beverley J; Park, Jae Sung; Graham, Michael D; Willis, Ashley P
2016-02-01
We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010)]. This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence.
On t-local solvability of inverse scattering problems in two-dimensional layered media
Baev, A. V.
2015-06-01
The solvability of two-dimensional inverse scattering problems for the Klein-Gordon equation and the Dirac system in a time-local formulation is analyzed in the framework of the Galerkin method. A necessary and sufficient condition for the unique solvability of these problems is obtained in the form of an energy conservation law. It is shown that the inverse problems are solvable only in the class of potentials for which the stationary Navier-Stokes equation is solvable.
Degani, D.
1984-01-01
A numerical algorithm that is second-order accurate in time has been developed for the conjugated problem of a separated, compressible flow field and a conductive solid body. The full two-dimensional time-dependent Navier-Stokes equations are coupled with the time-dependent energy equation for the solid body and are solved simultaneously. using implicit algorithms. The energy equation for the solid body may include arbitrarily distributed heat sources. The algorithm has been exmined for the case of two-dimensional supersonic compression-corner interaction, with a heat source embedded in the wall in the vicinity of the separation bubble and the attached boundary layer. The effect of the heat source on the flow field is studied for steady and transient cases.
Smoothed Particle Hydrodynamics Method for Two-dimensional Stefan Problem
Tarwidi, Dede
2016-01-01
Smoothed particle hydrodynamics (SPH) is developed for modelling of melting and solidification. Enthalpy method is used to solve heat conduction equations which involved moving interface between phases. At first, we study the melting of floating ice in the water for two-dimensional system. The ice objects are assumed as solid particles floating in fluid particles. The fluid and solid motion are governed by Navier-Stokes equation and basic rigid dynamics equation, respectively. We also propose a strategy to separate solid particles due to melting and solidification. Numerical results are obtained and plotted for several initial conditions.
Energy Technology Data Exchange (ETDEWEB)
Souza, Altivo Monteiro de
2008-12-15
The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS{sub S}OLVER{sub M}PI{sub 2}D{sub A} program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)
Energy Technology Data Exchange (ETDEWEB)
Sabundjian, Gaiane [Instituto de Pesquisas Energeticas e Nucleares (IPEN), Sao Paulo, SP (Brazil). E-mail: gdjian@net.ipen.br; Cabral, Eduardo Lobo Lustosa [Sao Paulo Univ., SP (Brazil). Escola Politecnica. E-mail: elcabral@usp.br
2000-07-01
This work applied of the expansion of the variables in hierarchical functions for the solution of the Navier-Stokes equations for incompressible fluids in two dimensions in laminar flow. This work is based on the finite element method. The used expansion functions are based on Legendre polynomials, adjusted in the rectangular elements in a such a way that corner, side and area functions are defined. The order of the expansion functions associated with the sides and with the area of the elements can be adjusted to the necessary or desire degree. This method is denominated by Hierarchical Expansion Method. In order to validate the proposed numeric method three well-known problems of the literature are analyze. The results show the method capacity in supplying precise results. (author)
Pan, Liang; Xu, Kun; Li, Qibing; Li, Jiequan
2016-12-01
For computational fluid dynamics (CFD), the generalized Riemann problem (GRP) solver and the second-order gas-kinetic scheme (GKS) provide a time-accurate flux function starting from a discontinuous piecewise linear flow distributions around a cell interface. With the adoption of time derivative of the flux function, a two-stage Lax-Wendroff-type (L-W for short) time stepping method has been recently proposed in the design of a fourth-order time accurate method for inviscid flow [21]. In this paper, based on the same time-stepping method and the second-order GKS flux function [42], a fourth-order gas-kinetic scheme is constructed for the Euler and Navier-Stokes (NS) equations. In comparison with the formal one-stage time-stepping third-order gas-kinetic solver [24], the current fourth-order method not only reduces the complexity of the flux function, but also improves the accuracy of the scheme. In terms of the computational cost, a two-dimensional third-order GKS flux function takes about six times of the computational time of a second-order GKS flux function. However, a fifth-order WENO reconstruction may take more than ten times of the computational cost of a second-order GKS flux function. Therefore, it is fully legitimate to develop a two-stage fourth order time accurate method (two reconstruction) instead of standard four stage fourth-order Runge-Kutta method (four reconstruction). Most importantly, the robustness of the fourth-order GKS is as good as the second-order one. In the current computational fluid dynamics (CFD) research, it is still a difficult problem to extend the higher-order Euler solver to the NS one due to the change of governing equations from hyperbolic to parabolic type and the initial interface discontinuity. This problem remains distinctively for the hypersonic viscous and heat conducting flow. The GKS is based on the kinetic equation with the hyperbolic transport and the relaxation source term. The time-dependent GKS flux function
Pietarila Graham, Jonathan; Holm, Darryl D; Mininni, Pablo D; Pouquet, Annick
2007-11-01
We compute solutions of the Lagrangian-averaged Navier-Stokes alpha - (LANS alpha ) model for significantly higher Reynolds numbers (up to Re approximately 8300 ) than have previously been accomplished. This allows sufficient separation of scales to observe a Navier-Stokes inertial range followed by a second inertial range specific to the LANS alpha model. Both fully helical and nonhelical flows are examined, up to Reynolds numbers of approximately 1300. Analysis of the third-order structure function scaling supports the predicted l3 scaling; it corresponds to a k-1 scaling of the energy spectrum for scales smaller than alpha. The energy spectrum itself shows a different scaling, which goes as k1. This latter spectrum is consistent with the absence of stretching in the subfilter scales due to the Taylor frozen-in hypothesis employed as a closure in the derivation of the LANS alpha model. These two scalings are conjectured to coexist in different spatial portions of the flow. The l3 [E(k) approximately k-1] scaling is subdominant to k1 in the energy spectrum, but the l3 scaling is responsible for the direct energy cascade, as no cascade can result from motions with no internal degrees of freedom. We demonstrate verification of the prediction for the size of the LANS alpha attractor resulting from this scaling. From this, we give a methodology either for arriving at grid-independent solutions for the LANS alpha model, or for obtaining a formulation of the large eddy simulation optimal in the context of the alpha models. The fully converged grid-independent LANS alpha model may not be the best approximation to a direct numerical simulation of the Navier-Stokes equations, since the minimum error is a balance between truncation errors and the approximation error due to using the LANS alpha instead of the primitive equations. Furthermore, the small-scale behavior of the LANS alpha model contributes to a reduction of flux at constant energy, leading to a shallower energy
Erpelding, Marion; Sinha, Santanu; Tallakstad, Ken Tore; Hansen, Alex; Flekkøy, Eirik Grude; Måløy, Knut Jørgen
2013-11-01
It is well known that the transient behavior during drainage or imbibition in multiphase flow in porous media strongly depends on the history and initial condition of the system. However, when the steady-state regime is reached and both drainage and imbibition take place at the pore level, the influence of the evolution history and initial preparation is an open question. Here, we present an extensive experimental and numerical work investigating the history dependence of simultaneous steady-state two-phase flow through porous media. Our experimental system consists of a Hele-Shaw cell filled with glass beads which we model numerically by a network of disordered pores transporting two immiscible fluids. From measurements of global pressure evolution, histograms of saturation, and cluster-size distributions, we find that when both phases are flowing through the porous medium, the steady state does not depend on the initial preparation of the system or on the way it has been reached.
Yin, W.-L.
1984-04-01
It is shown that, in the case of non-zero charge density, the class of steady, plane, incompressible, aligned-fluid magnetofluiddynamic flows contains no rotational motions. Therefore, this class of flows is exhausted by the irrotational solutions of Kingston and Power.
Institute of Scientific and Technical Information of China (English)
Ping ZHANG
2008-01-01
Motivated by the results of J.Y.Chemin in "J.Anal.Math.,77,1999,27-50" and G.Furioli et al in "Revista Mat.Iberoamer.,16,2002,605-667",the author considers further regularities of the mild solutions to Navier-Stokes equation with initial data u0∈Ld(Rd).In particular,it is proved that if u∈C([0,T*); Ld(Rd)) is a mild solution of (NSv),then u(t,x) -evt△u0∈(L)∞ ((0,T); (B)1/d/2,∞)∩(L)1((0,T);(B)3/d/2,∞) for any T＜T*.
Maccormack, R. W.; Baldwin, B. S.
1975-01-01
A numerical method for solving the compressible form of the unsteady Navier-Stokes equations is described. This method was originally presented in 1970 and has since been modified during the development of computer programs at Ames for implementing models that account for the effects of turbulence in shock-induced separated flows. Although this paper does not describe the turbulence models themselves, a complete description of the basic numerical method is given with emphasis on the choice of a computational mesh for high Reynolds number flows, finite-difference approximations for mixed partial derivatives, extension of the Courant-Friedrichs-Lewy stability condition for viscous flows, mesh boundary conditions, and numerical smoothing for strong shock-wave calculations.
Salama, Amgad
2015-06-01
In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique.
On the validity of the Navier-Stokes equations for nanoscale liquid flows: The role of channel size
Directory of Open Access Journals (Sweden)
Chong Liu
2011-09-01
Full Text Available In this work, we investigate the validity of the Navier-Stokes (NS equations for nanoscale liquid flows through molecular dynamics simulations. We focus on the role of channel size by considering the fluid-wall interaction. Liquid flows between two planar parallel walls driven by an external force with channel size ranging from 2 to 80 nm are studied. The volumetric flux is computed and the dependence of the volumetric flux on the channel size is explained both qualitatively and quantitatively. It is found that the flow is sensitive to the fluid-wall binding energy and the classical fluid mechanics falls apart in small nanochannels. However, the wall effects become insignificant and the NS equations are valid when the channel size is larger than about 150 molecular diameters (∼ 50 nm.
Directory of Open Access Journals (Sweden)
Zhengrong Zhang
2012-01-01
Full Text Available Numerical manifold method was applied to directly solve Navier-Stokes (N-S equations for incompressible viscous flow in this paper, and numerical manifold schemes for N-S equations coupled velocity and pressure were derived based on Galerkin weighted residuals method as well. Mixed cover with linear polynomial function for velocity and constant function for pressure was employed in finite element cover system. As an application, mixed cover 4-node rectangular manifold element has been used to simulate the incompressible viscous flow around a square cylinder in a channel. Numerical tests illustrate that NMM is an effective and high-order accurate numerical method for incompressible viscous flow N-S equations.
Eklund, Dean R.; Northam, G. B.; Mcdaniel, J. C.; Smith, Cliff
1992-01-01
A CFD (Computational Fluid Dynamics) competition was held at the Third Scramjet Combustor Modeling Workshop to assess the current state-of-the-art in CFD codes for the analysis of scramjet combustors. Solutions from six three-dimensional Navier-Stokes codes were compared for the case of staged injection of air behind a step into a Mach 2 flow. This case was investigated experimentally at the University of Virginia and extensive in-stream data was obtained. Code-to-code comparisons have been made with regard to both accuracy and efficiency. The turbulence models employed in the solutions are believed to be a major source of discrepancy between the six solutions.
Sharma, Ati S.; Mezić, Igor; McKeon, Beverley J.
2016-07-01
The relationship between Koopman mode decomposition, resolvent mode decomposition, and exact invariant solutions of the Navier-Stokes equations is clarified. The correspondence rests upon the invariance of the system operators under symmetry operations such as spatial translation. The usual interpretation of the Koopman operator is generalized to permit combinations of such operations, in addition to translation in time. This invariance is related to the spectrum of a spatiotemporal Koopman operator, which has a traveling-wave interpretation. The relationship leads to a generalization of dynamic mode decomposition, in which symmetry operations are applied to restrict the dynamic modes to span a subspace subject to those symmetries. The resolvent is interpreted as the mapping between the Koopman modes of the Reynolds stress divergence and the velocity field. It is shown that the singular vectors of the resolvent (the resolvent modes) are the optimal basis in which to express the velocity field Koopman modes where the latter are not a priori known.
Institute of Scientific and Technical Information of China (English)
Lan-chieh Huang
2000-01-01
In this paper, the Crank-Nicholson + component-consistent pressure correction method for the numerical solution of the unsteady incompressible Navier-Stokes equation of [1] on the rectangular half-staggered mesh has been extended to the curvilinear half-staggered mesh. The discrete projection, both for the projection step in the solution procedure and for the related differential-algebraic equations, has been carefully studied and verified. It is proved that the proposed method is also unconditionally (in△t) nonlinearly stable on the curvilinear mesh, provided the mesh is not too skewed. It is seen that for problems with an outflow bound- ary, the half-staggered mesh is especially advantageous. Results of preliminary numerical experiments support these claims.
Bresch, Didier
2015-01-01
We prove global existence of appropriate weak solutions for the compressible Navier--Stokes equations for more general stress tensor than those covered by P.-L. Lions and E. Feireisl's theory. More precisely we focus on more general pressure laws which are not thermodynamically stable; we are also able to handle some anisotropy in the viscous stress tensor. To give answers to these two longstanding problems, we revisit the classical compactness theory on the density by obtaining precise quantitative regularity estimates: This requires a more precise analysis of the structure of the equations combined to a novel approach to the compactness of the continuity equation. These two cases open the theory to important physical applications, for instance to describe solar events (virial pressure law), geophysical flows (eddy viscosity) or biological situations (anisotropy).
Sharma, Ati; McKeon, Beverley
2016-01-01
The relationship between Koopman mode decomposition, resolvent mode decomposition and exact invariant solutions of the Navier-Stokes equations is clarified. The correspondence rests upon the invariance of the system operators under symmetry operations such as spatial translation. The usual interpretation of the Koopman operator is generalised to permit combinations of such operations, in addition to translation in time. This invariance is related to the spectrum of a spatio-temporal Koopman operator, which has a travelling wave interpretation. The relationship leads to a generalisation of dynamic mode decomposition, in which symmetry operations are applied to restrict the dynamic modes to span a subspace subject to those symmetries. For example, dynamic modes found using spatial and temporal translation will identify structures convecting with corresponding wavespeeds.
Sahai, A.; Mansour, N. N.; Lopez, B.; Panesi, M.
2017-05-01
This work addresses the modeling of high pressure electric discharge in an arc-heated wind tunnel. The combined numerical solution of Poisson’s equation, radiative transfer equations, and the set of Favre-averaged thermochemical nonequilibrium Navier-Stokes equations allows for the determination of the electric, radiation, and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles with the Chapman-Enskog method. A multi-temperature formulation is used to account for thermal non-equilibrium. Finally, the turbulence closure of the flow equations is obtained by means of the Spalart-Allmaras model, which requires the solution of an additional scalar transport equation. A Streamline upwind Petrov-Galerkin stabilized finite element formulation is employed to solve the Navier-Stokes equation. The electric field equation is solved using the standard Galerkin formulation. A stable formulation for the radiative transfer equations is obtained using the least-squares finite element method. The developed simulation framework has been applied to investigate turbulent plasma flows in the 20 MW Aerodynamic Heating Facility at NASA Ames Research Center. The current model is able to predict the process of energy addition and re-distribution due to Joule heating and thermal radiation, resulting in a hot central core surrounded by colder flow. The use of an unsteady three-dimensional treatment also allows the asymmetry due to a dynamic electric arc attachment point in the cathode chamber to be captured accurately. The current work paves the way for detailed estimation of operating characteristics for arc-heated wind tunnels which are critical in testing thermal protection systems.
Haspot, Boris
2016-06-01
We consider the compressible Navier-Stokes equations for viscous and barotropic fluids with density dependent viscosity. The aim is to investigate mathematical properties of solutions of the Navier-Stokes equations using solutions of the pressureless Navier-Stokes equations, that we call quasi solutions. This regime corresponds to the limit of highly compressible flows. In this paper we are interested in proving the announced result in Haspot (Proceedings of the 14th international conference on hyperbolic problems held in Padova, pp 667-674, 2014) concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that it exists classical quasi-solutions in the sense that they are {C^{∞}} on {(0,T)× {R}N} for any {T > 0}. Finally we show the convergence of the global weak solution of compressible Navier-Stokes equations to the quasi solutions in the case of a vanishing pressure limit process. In particular for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to {μ(ρ)=ρ^{α}} with {α > 1}. Furthermore the density is not far from converging asymptotically in time to the Barrenblatt solution of mass the initial density {ρ0}.
Galaktionov, V A
2011-01-01
It is shown that Wiener's regularity of the vertex of a backward paraboloid for 3D Navier-Stokes equations with zero Dirichlet conditions on the paraboloid boundary is given by Petrovskii's criterion for the heat equation (1934), i.e., the nonlinear convection term does not affect the regularity result.
Wai, J. C.; Blom, G.; Yoshihara, H.; Chaussee, D.
1986-01-01
The NASA/Ames parabolized Navier/Stokes computer code was used to calculate the turbulent flow over the wing/fuselage for a generic fighter at M = 2.2. 18 deg angle-of-attack, and 0 and 5 deg yaw. Good test/theory agreement was achieved in the zero yaw case. No test data were available for the yaw case.
User's manual for EVITS: a steady state fluids code for complex two-dimensional geometries
Energy Technology Data Exchange (ETDEWEB)
Domanus, H.M.
1976-07-01
A 2-D computer code, EVITS, has been developed for estimating steady state, incompressible, isothermal flow fields in complex geometries. A vorticity-stream function formulation is used along with a model to resolve viscous effects at solid boundaries. Sufficient geometry and boundary type options are included within the code so that a large number of flow situations can be specified without modifying the program. All instructions to the code are via an input dataset. Detailed instructions for preparing the user oriented input, along with examples, are included in this users' manual.
Zhou, Xiangzhi; Tsaftaris, Sotirios A; Liu, Ying; Tang, Richard; Klein, Rachel; Zuehlsdorff, Sven; Li, Debiao; Dharmakumar, Rohan
2010-04-01
To minimize image artifacts in long TR cardiac phase-resolved steady state free precession (SSFP) based blood-oxygen-level-dependent (BOLD) imaging. Nine healthy dogs (four male, five female, 20-25 kg) were studied in a clinical 1.5 Tesla MRI scanner to investigate the effect of temporal resolution, readout bandwidth, and motion compensation on long repetition time (TR) SSFP images. Breath-held 2D SSFP cine sequences with various temporal resolutions (10-204 ms), bandwidths (239-930 Hz/pixel), with and without first-order motion compensation were prescribed in the basal, mid-ventricular, and apical along the short axis. Preliminary myocardial BOLD studies in dogs with controllable coronary stenosis were performed to assess the benefits of artifact-reduction strategies. Shortening the readout time by means of increasing readout bandwidth had no observable reduction in image artifacts. However, increasing the temporal resolution in the presence of first-order motion compensation led to significant reduction in image artifacts. Preliminary studies demonstrated that BOLD signal changes can be reliably detected throughout the cardiac cycle. Artifact-reduction methods used in this study provide significant improvement in image quality compared with conventional long TR SSFP BOLD MRI. It is envisioned that the methods proposed here may enable reliable detection of myocardial oxygenation changes throughout the cardiac cycle with long TR SSFP-based myocardial BOLD MRI. (c) 2010 Wiley-Liss, Inc.
Wong, Teresa; Solomatov, Viatcheslav S.
2015-12-01
The strongly temperature-dependent viscosity of rocks leads to the formation of nearly rigid lithospheric plates. Previous studies showed that a very low yield stress might be necessary to weaken and mobilize the plates, for example, due to water. However, the magnitude of the yield stress remains poorly understood. While the convective stresses below the lithosphere are relatively small, sublithospheric convection can induce large stresses in the lithosphere indirectly, through thermal thinning of the lithosphere. The magnitude of the thermal thinning, the stresses associated with it, and the critical yield stress to initiate subduction depend on several factors including the viscosity law, the Rayleigh number, and the aspect ratio of the convective cells. We conduct a systematic numerical analysis of lithospheric stresses and other convective parameters for single steady-state convection cells. Such cells can be considered as part of a multi-cell, time-dependent convective system. This allows us a better control of convective solutions and a relatively simple scaling analysis. We find that subduction initiation depends much stronger on the aspect ratio than in previous studies and speculate that plate tectonics initiation may not necessarily require significant weakening and can, at least in principle, start if a sufficiently long cell develops during planetary evolution.
Energy Technology Data Exchange (ETDEWEB)
Ray, Samriddhi Sankar; Pandit, Rahul [Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore (India); Mitra, Dhrubaditya [Departement Cassiopee, Observatoire de la Cote d' Azur, BP4229, 06304 Nice Cedex 4 (France)], E-mail: ssray@physics.iisc.ernet.in, E-mail: dhruba.mitra@gmail.com, E-mail: rahul@physics.iisc.ernet.in
2008-03-15
We systematize the study of dynamic multiscaling of time-dependent structure functions in different models of passive-scalar and fluid turbulence. We show that, by suitably normalizing these structure functions, we can eliminate their dependence on the origin of time at which we start our measurements and that these normalized structure functions yield the same linear bridge relations that relate the dynamic-multiscaling and equal-time exponents for statistically steady turbulence. We show analytically, for both the Kraichnan model of passive-scalar turbulence and its shell model analogue, and numerically, for the Gledzer-Ohkitani-Yamada (GOY) shell model of fluid turbulence and a shell model for passive-scalar turbulence, that these exponents and bridge relations are the same for statistically steady and decaying turbulence. Thus, we provide strong evidence for dynamic universality, i.e. dynamic-multiscaling exponents do not depend on whether the turbulence decays or is statistically steady.
Spectrum and energy transfer in steady Burgers turbulence
Girimaji, Sharath S.; Zhou, YE
1995-01-01
The spectrum, energy transfer, and spectral interactions in steady Burgers turbulence are studied using numerically generated data. The velocity field is initially random and the turbulence is maintained steady by forcing the amplitude of a band of low wavenumbers to be invariant in time, while permitting the phase to change as dictated by the equation. The spectrum, as expected, is very different from that of Navier-Stokes turbulence. It is demonstrated that the far range of the spectrum scales as predicted by Burgers. Despite the difference in their spectra, in matters of the spectral energy transfer and triadic interactions Burgers turbulence is similar to Navier-Stokes turbulence.
Large-Eddy / Reynolds-Averaged Navier-Stokes Simulations of a Dual-Mode Scramjet Combustor
Fulton, Jesse A.; Edwards, Jack R.; Hassan, Hassan A.; Rockwell, Robert; Goyne, Christopher; McDaniel, James; Smith, Chad; Cutler, Andrew; Johansen, Craig; Danehy, Paul M.; Kouchi, Toshinori
2012-01-01
Numerical simulations of reacting and non-reacting flows within a scramjet combustor configuration experimentally mapped at the University of Virginia s Scramjet Combustion Facility (operating with Configuration A ) are described in this paper. Reynolds-Averaged Navier-Stokes (RANS) and hybrid Large Eddy Simulation / Reynolds-Averaged Navier-Stokes (LES / RANS) methods are utilized, with the intent of comparing essentially blind predictions with results from non-intrusive flow-field measurement methods including coherent anti-Stokes Raman spectroscopy (CARS), hydroxyl radical planar laser-induced fluorescence (OH-PLIF), stereoscopic particle image velocimetry (SPIV), wavelength modulation spectroscopy (WMS), and focusing Schlieren. NC State's REACTMB solver was used both for RANS and LES / RANS, along with a 9-species, 19- reaction H2-air kinetics mechanism by Jachimowski. Inviscid fluxes were evaluated using Edwards LDFSS flux-splitting scheme, and the Menter BSL turbulence model was utilized in both full-domain RANS simulations and as the unsteady RANS portion of the LES / RANS closure. Simulations were executed and compared with experiment at two equivalence ratios, PHI = 0.17 and PHI = 0.34. Results show that the PHI = 0.17 flame is hotter near the injector while the PHI = 0.34 flame is displaced further downstream in the combustor, though it is still anchored to the injector. Reactant mixing was predicted to be much better at the lower equivalence ratio. The LES / RANS model appears to predict lower overall heat release compared to RANS (at least for PHI = 0.17), and its capability to capture the direct effects of larger turbulent eddies leads to much better predictions of reactant mixing and combustion in the flame stabilization region downstream of the fuel injector. Numerical results from the LES/RANS model also show very good agreement with OH-PLIF and SPIV measurements. An un-damped long-wave oscillation of the pre-combustion shock train, which caused
Whitehead, Jared P
2011-01-01
Rigorous upper limits on the vertical heat transport in two dimensional Rayleigh-Benard convection between stress-free isothermal boundaries are derived from the Boussinesq approximation of the Navier-Stokes equations. The Nusselt number Nu is bounded in terms of the Rayleigh number Ra according to $Nu \\leq 0.2295 Ra^{5/12}$ uniformly in the Prandtl number Pr. This Nusselt number scaling challenges some theoretical arguments regarding the asymptotic high Rayleigh number heat transport by turbulent convection.
2009-08-01
10 4.1 Plane Poiseuille and Couette Flow ... Couette Flow First we consider steady-state flow between two parallel plates of infinite extent, where the flow is driven by the movement of the top...al., 2006). The flow domain is again Ω = [0,1] × [0,1]. The analytical ERDC/CHL TR-09-12 12 Table 2. Grid refinement study for 3D Poiseuille problem. h
Navier-Stokes方程SPH的公式解法%SPH formula solution of the Navier-Stokes equation
Institute of Scientific and Technical Information of China (English)
丁亮
2013-01-01
Navier-Stokes equation ( abbreviation N-S equation) is the basic equation which describes fluid motion and now it has already had a variety of different numerical methods. This paper presents a meshless method to solve N-S equation: smoothed particle fluid dynamics ( SPH, Smoothed Particle Hydrodynamics) method. This method discretizes N-S equation of motion into SPH equation by using SPH approximation ( kernel approximation and particle approximation) and it is more beneficial to solve the N-S equation.%Navier-Stokes方程(简称N-S方程)是描述流体运动的基本方程,现已有多种不同的数值求解方法.文中提出一种求解N-S方程的无网格方法:光滑粒子流体动力学(SPH,Smoothed Particle Hydrodynamic)方法,该方法是应用SPH近似法(核近似和粒子近似)将N-S运动方程离散化为SPH方程的形式,有利于求解N-S方程.
A data-driven adaptive Reynolds-averaged Navier-Stokes k-ω model for turbulent flow
Li, Zhiyong; Zhang, Huaibao; Bailey, Sean C. C.; Hoagg, Jesse B.; Martin, Alexandre
2017-09-01
This paper presents a new data-driven adaptive computational model for simulating turbulent flow, where partial-but-incomplete measurement data is available. The model automatically adjusts the closure coefficients of the Reynolds-averaged Navier-Stokes (RANS) k- ω turbulence equations to improve agreement between the simulated flow and the measurements. This data-driven adaptive RANS k- ω (D-DARK) model is validated with 3 canonical flow geometries: pipe flow, backward-facing step, and flow around an airfoil. For all test cases, the D-DARK model improves agreement with experimental data in comparison to the results from a non-adaptive RANS k- ω model that uses standard values of the closure coefficients. For the pipe flow, adaptation is driven by mean stream-wise velocity data from 42 measurement locations along the pipe radius, and the D-DARK model reduces the average error from 5.2% to 1.1%. For the 2-dimensional backward-facing step, adaptation is driven by mean stream-wise velocity data from 100 measurement locations at 4 cross-sections of the flow. In this case, D-DARK reduces the average error from 40% to 12%. For the NACA 0012 airfoil, adaptation is driven by surface-pressure data at 25 measurement locations. The D-DARK model reduces the average error in surface-pressure coefficients from 45% to 12%.
Luo, Xianwu; Huang, Renfang; Ji, Bin
2016-01-01
For accurate simulations of wall-bounded turbulent cavitating flows, the present paper proposed a partially averaged Navier-Stokes (PANS) method derived from the k-ω turbulence model. Transient cavitating vortical flows around a NACA66 hydrofoil were simulated by using the k-ω PANS model with various filter parameters (fk = 0.2, 0.5 and 1, while fω = 1/fk) and a mass transfer cavitation model based on the Rayleigh-Plesset equation. Compared with the available experimental data, the k-ω PANS model with fk = 0.2 can accurately reproduce the cavitation evolution with more complicated structures due to the reduction in the predicted eddy viscosity. Further analyses, using the vorticity transport equation, indicate that the transition of cavitation structure from two dimension to three dimension is associated with strong vortex-cavitation interaction, where vortex stretching and dilation may play a major role. Therefore, the k-ω PANS model with the filter parameter of fk = 0.2 is an effective method to numerically predict the transient cavitating vortical flows around hydrofoils. The results obtained in this paper are helpful to provide a physical insight into the mechanisms of cavitation shedding dynamics.
Nelson, Daniel A.; Jacobs, Gustaaf B.; Kopriva, David A.
2016-08-01
The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier-Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.
Crifo, J. F.; Lukianov, G. A.; Rodionov, A. V.; Khanlarov, G. O.; Zakharov, V. V.
2002-03-01
The structure of the near-nucleus H 2O atmosphere formed by sublimation under solar heating of a hypothetical large dusty ice sphere is computed (1) by the direct simulation Monte-Carlo method (DSMC) and (2) by solving Navier-Stokes equations (NSE) combined with a locally plane-parallel solution of the collisional Boltzmann equation for the nonequilibrium near-surface Knudsen layer. For Hale-Bopp-like comets, perfect agreement is obtained between the two methods on the day and night sides. This excellent agreement is maintained on the near-nucleus dayside for less productive comets, even down to production rates as low as those expected for Comet P/Wirtanen near 3 AU. It provides a direct validation of the gasdynamic simulations performed in support of the ESA Rosetta mission lander descent optimization studies (Crifo et al. 2001) and also confirms the similarity between the dayside coma and underexpanded axially symmetric free jets pointed out in Crifo (1986). On the nightside, moderate to high discrepancies appear between the two solutions as the production rate decreases, revealing the limits of the NSE method. The limits of the present study are delineated, and directions for future investigations are indicated.
Svärd, Magnus; Nordström, Jan
2008-05-01
A stable wall boundary procedure is derived for the discretized compressible Navier-Stokes equations. The procedure leads to an energy estimate for the linearized equations. We discretize the equations using high-order accurate finite difference summation-by-parts (SBP) operators. The boundary conditions are imposed weakly with penalty terms. We prove linear stability for the scheme including the wall boundary conditions. The penalty imposition of the boundary conditions is tested for the flow around a circular cylinder at Ma=0.1 and Re=100. We demonstrate the robustness of the SBP-SAT technique by imposing incompatible initial data and show the behavior of the boundary condition implementation. Using the errors at the wall we show that higher convergence rates are obtained for the high-order schemes. We compute the vortex shedding from a circular cylinder and obtain good agreement with previously published (computational and experimental) results for lift, drag and the Strouhal number. We use our results to compare the computational time for a given for a accuracy and show the superior efficiency of the 5th-order scheme.
Institute of Scientific and Technical Information of China (English)
Gui-Qiang Chen; Dan Osborne; Zhongmin Qian
2009-01-01
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in RN with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-fiat boundary. We observe that, under the nonhomogeneons boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition (without the incompressibility condition), which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in RN(n≥3) with nonhomogeneous vorticity boundary condition converge in L2 to the corresponding Euler equations satisfying the kinematic condition.
Deng, Liang; Bai, Hanli; Wang, Fang; Xu, Qingxin
2016-06-01
CPU/GPU computing allows scientists to tremendously accelerate their numerical codes. In this paper, we port and optimize a double precision alternating direction implicit (ADI) solver for three-dimensional compressible Navier-Stokes equations from our in-house Computational Fluid Dynamics (CFD) software on heterogeneous platform. First, we implement a full GPU version of the ADI solver to remove a lot of redundant data transfers between CPU and GPU, and then design two fine-grain schemes, namely “one-thread-one-point” and “one-thread-one-line”, to maximize the performance. Second, we present a dual-level parallelization scheme using the CPU/GPU collaborative model to exploit the computational resources of both multi-core CPUs and many-core GPUs within the heterogeneous platform. Finally, considering the fact that memory on a single node becomes inadequate when the simulation size grows, we present a tri-level hybrid programming pattern MPI-OpenMP-CUDA that merges fine-grain parallelism using OpenMP and CUDA threads with coarse-grain parallelism using MPI for inter-node communication. We also propose a strategy to overlap the computation with communication using the advanced features of CUDA and MPI programming. We obtain speedups of 6.0 for the ADI solver on one Tesla M2050 GPU in contrast to two Xeon X5670 CPUs. Scalability tests show that our implementation can offer significant performance improvement on heterogeneous platform.
Ni, Ming-Jiu
2009-10-01
Two consistent projection methods of second-order temporal and spatial accuracy have been developed on a rectangular collocated mesh for variable density Navier-Stokes equations with a continuous surface force. Instead of the original projection methods (denoted as algorithms I and II in this paper), in which the updated cell center velocity from the intermediate velocity and the pressure gradient is not guaranteed solenoidal, the consistent projection methods (denoted as algorithms III and IV) obtain the cell center velocity based on an interpolation from a conservative fluxes with velocity unit on surrounding cell faces. Dependent on treatment of the continuous surface force, the pressure gradient in algorithm III or the sum of the pressure gradient and the surface force in algorithm IV at a cell center is then conducted from the difference between the updated velocity and the intermediate velocity in a consistent projection method. A non-viscous 3D static drop with serials of density ratios is numerically simulated. Using the consistent projection methods, the spurious currents can be greatly reduced and the pressure jump across the interface can be accurately captured without oscillations. The developed consistent projection method are also applied for simulation of interface evolution of an initial ellipse driven by the surface tension and of an initial sphere bubble driven by the buoyancy with good accuracy and good resolution.
Lerat, A.
2016-10-01
Residual-Based Compact (RBC) schemes approximate the 3-D compressible Euler equations with a 5th- or 7th-order accuracy on a 5 × 5 × 5-point stencil and capture shocks pretty well without correction. For unsteady flows however, they require a costly algebra to extract the time-derivative occurring at several places in the scheme. A new high-order time formulation has been recently proposed [13] for simplifying the RBC schemes and increasing their temporal accuracy. The present paper goes much further in this direction and deeply reconsiders the method. An avatar of the RBC schemes is presented that greatly reduces the computing time and the memory requirements while keeping the same type of successful numerical dissipation. Two and three-dimensional linear stability are analyzed and the method is extended to the 3-D compressible Navier-Stokes equations. The new compact scheme is validated for several unsteady problems in two and three dimension. In particular, an accurate DNS at moderate cost is presented for the evolution of the Taylor-Green Vortex at Reynolds 1600 and Prandtl 0.71. The effects of the mesh size and of the accuracy order in the approximation of Euler and viscous terms are discussed.
Finite element solution of 3-D turbulent Navier-Stokes equations for propeller-driven slender bodies
Thomas, Russell Hicks
1987-12-01
Three-dimensional turbulent flow over the aft end of a slender propeller driven body with the wake from a slender, planar appendage was calculated for 4 configurations. The finite element method in the form of the weak Galerkin formulation with the penalty method was used to solve the Reynolds averaged Navier-Stokes equations. The actual code was FIDAP, modified with a propeller body force and turbulence model, used for the solution. The turbulence model included an Inner Layer Integrated TKE model, and Outer Layer mixing length model, and a Planar Wake model. No separate boundary layer method was used for the body, rather modifications to the Integrated TKE model were made to account for the primary effects of the surface boundary layer on the flow. The flow was calculated at two levels of thrust and corresponding swirl, selfpropelled and 100 percent overthrust, as well as with selfpropelled thrust but no torque simulating an ideal rotor stator combination. Also, the selfpropelled case was calculated with a simplified turbulence model using only the Inner Layer and Planar Wake model. The results compared favorably with experiments.
Energy Technology Data Exchange (ETDEWEB)
Wang, Z J
2012-12-06
The overriding objective for this project is to develop an efficient and accurate method for capturing strong discontinuities and fine smooth flow structures of disparate length scales with unstructured grids, and demonstrate its potentials for problems relevant to DOE. More specifically, we plan to achieve the following objectives: 1. Extend the SV method to three dimensions, and develop a fourth-order accurate SV scheme for tetrahedral grids. Optimize the SV partition by minimizing a form of the Lebesgue constant. Verify the order of accuracy using the scalar conservation laws with an analytical solution; 2. Extend the SV method to Navier-Stokes equations for the simulation of viscous flow problems. Two promising approaches to compute the viscous fluxes will be tested and analyzed; 3. Parallelize the 3D viscous SV flow solver using domain decomposition and message passing. Optimize the cache performance of the flow solver by designing data structures minimizing data access times; 4. Demonstrate the SV method with a wide range of flow problems including both discontinuities and complex smooth structures. The objectives remain the same as those outlines in the original proposal. We anticipate no technical obstacles in meeting these objectives.
On the use of a three-dimensional Navier-Stokes solver for rocket engine pump impeller design
Chen, Wei-Chung; Prueger, George H.; Chan, Daniel C.; Eastland, Anthony H.
1992-07-01
A 3D Reynolds-averaged Navier-Stokes Solver and a Fast Grid Generator (FGG), developed specially for centrifugal impeller design, were incorporated into the pump impeller design process. The impeller performance from the CFD analysis was compared to one-dimensional prediction. Both analyses showed good agreement of the impeller hydraulic efficiency, 94.5 percent, but with an 8 percent discrepancy of Euler head prediction. The impeller blade angle, discharge hub to shroud width, axial length and blade stacking were systematically changed to achieve an optimum impeller design. Impeller overall efficiency, loss distribution, hub-to-tip flow angle distortion and blade-to-blade flow angle change are among those criteria used to evaluate impeller performance. Two grid sizes, one with 10 K grid points and one with 80 K grid points were used to evaluate grid dependency issues. The effects of grid resolution on the accuracy and turnaround time are discussed. In conclusion, it is demonstrated that CFD can be effectively used for design and optimization of rocket engine pump components.
Energy Technology Data Exchange (ETDEWEB)
Shadid, John Nicolas; van Bloemen Waanders, Bart Gustaaf; Hammond, Glenn E.; Collis, Samuel Scott; Murray, Regan Elizabeth (Environmental Protection Agency)
2005-03-01
We investigate the accuracy of chemical transport in network models for small geometric configurations. Network model have successfully simulated the general operations of large water distribution systems. However, some of the simplifying assumptions associated with the implementation may cause inaccuracies if chemicals need to be carefully characterized at a high level of detail. In particular, we are interested in precise transport behavior so that inversion and control problems can be applied to water distribution networks. As an initial phase, Navier Stokes combined with a convection-diffusion formulation was used to characterize the mixing behavior at a pipe intersection in two dimensions. Our numerical models predict only on the order of 12-14 % of the chemical to be mixed with the other inlet pipe. Laboratory results show similar behavior and suggest that even if our numerical model is able to resolve turbulence, it may not improve the mixing behavior. This conclusion may not be appropriate however for other sets of operating conditions, and therefore we have started to develop a 3D implementation. Preliminary results for duct geometry are presented.
Near Zone Navier-Stokes Analysis of Heavy Quark Jet Quenching in an $\\mathcal{N}$ =4 SYM Plasma
Noronha, Jorge; Gyulassy, Miklos
2007-01-01
The near zone energy-momentum tensor of a supersonic heavy quark jet moving through a strongly-coupled $\\mathcal{N}=4$ SYM plasma is analyzed in terms of nonlinear Navier-Stokes hydrodynamics. We show that local isotropic equilibrium in the Landau frame holds to within 20% accuracy down to a length scale $\\sim 1/\\pi T$, much smaller than found previously from far zone analysis. For distances less than this scale, the AdS solution rapidly becomes non-isotropic and local equilibrium breaks down. The component of the dissipative stress also remain small compared to the advective (non-viscous) fluid stress down to distances $\\sim 1/\\pi T$ from the heavy quark jet. Our result, which is compatible with the thermalization timescales extracted from elliptic flow measurements, suggests that if AdS/CFT provides a good description of the RHIC system, the bulk of the quenched jet energy has more than enough time to locally thermalize and become encoded in the collective flow. The resulting flow pattern close to the quark...
Hintermüller, M.; Hinze, M.; Kahle, C.
2013-02-01
An adaptive a posteriori error estimator based finite element method for the numerical solution of a coupled Cahn-Hilliard/Navier-Stokes system with a double-obstacle homogenous free (interfacial) energy density is proposed. A semi-implicit Euler scheme for the time-integration is applied which results in a system coupling a quasi-Stokes or Oseen-type problem for the fluid flow to a variational inequality for the concentration and the chemical potential according to the Cahn-Hilliard model [16]. A Moreau-Yosida regularization is employed which relaxes the constraints contained in the variational inequality and, thus, enables semi-smooth Newton solvers with locally superlinear convergence in function space. Moreover, upon discretization this yields a mesh independent method for a fixed relaxation parameter. For the finite dimensional approximation of the concentration and the chemical potential piecewise linear and globally continuous finite elements are used, and for the numerical approximation of the fluid velocity Taylor-Hood finite elements are employed. The paper ends by a report on numerical examples showing the efficiency of the new method.
Xin, Bo; Sun, Dakun; Jing, Xiaodong; Sun, Xiaofeng
2016-07-01
Lined ducts are extensively applied to suppress noise emission from aero-engines and other turbomachines. The complex noise/flow interaction in a lined duct possibly leads to acoustic instability in certain conditions. To investigate the instability, the full linearized Navier-Stokes equations with eddy viscosity considered are solved in frequency domain using a Galerkin finite element method to compute the sound transmission in shear flow in the lined duct as well as the flow perturbation over the impedance wall. A good agreement between the numerical predictions and the published experimental results is obtained for the sound transmission, showing that a transmission peak occurs around the resonant frequency of the acoustic liner in the presence of shear flow. The eddy viscosity is an important influential factor that plays the roles of both providing destabilizing and making coupling between the acoustic and flow motions over the acoustic liner. Moreover, it is shown from the numerical investigation that the occurrence of the sound amplification and the magnitude of transmission coefficient are closely related to the realistic velocity profile, and we find it essential that the actual variation of the velocity profile in the axial direction over the liner surface be included in the computation. The simulation results of the periodic flow patterns possess the proper features of the convective instability over the liner, as observed in Marx et al.'s experiment. A quantitative comparison between numerical and experimental results of amplitude and phase of the instability is performed. The corresponding eigenvalues achieve great agreement.
Institute of Scientific and Technical Information of China (English)
Hua Huang; Mao Sun
2012-01-01
The forward flight of a model butterfly was studied by simulation using the equations of motion coupled with the Navier-Stokes equations.The model butterfly moved under the action of aerodynamic and gravitational forces,where the aerodynamic forces were generated by flapping wings which moved with the body,allowing the body oscillations of the model butterfly to be simulated.The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the upstroke.In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward,giving the weight-supporting vertical force and a small negative horizontal force,whilst in the upstroke,the body angle is large and the relatively small aerodynamic force points forward and slightly downward,giving a positive horizontal force which overcomes the body drag and the negative horizontal force generated in the downstroke.(2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects.(3) The body-massspecific power of the model butterfly is 33.3 W/kg,not very different from that of many other insects,e.g.,fruitflies and dragonflies.
Navier-Stokes flow around a rotating obstacle mathematical analysis of its asymptotic behavior
Necasova, Sarka
2016-01-01
The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of problems arising from the motion of viscous incompressible fluids around rotating obstacles. It offers a new approach to this type of problems. We derive the fundamental solution of the steady case and we give pointwise estimates of velocity and its gradient (first and second one). Each chapter is preceded by a thorough discussion of the investigated problems, along with their motivation and the strategy used to solve them. The book will be useful to researchers and graduate students in mathematics, in particular mathematical fluid mechanics and differential equations.