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1.
Two methods for coupling the Reynolds‐averaged Navier–Stokes equations with the q–ω turbulence model equations on structured grid systems have been studied; namely a loosely coupled method and a strongly coupled method. The loosely coupled method first solves the Navier–Stokes equations with the turbulent viscosity fixed. In a subsequent step, the turbulence model equations are solved with all flow quantities fixed. On the other hand, the strongly coupled method solves the Reynolds‐averaged Navier–Stokes equations and the turbulence model equations simultaneously. In this paper, numerical stabilities of both methods in conjunction with the approximated factorization‐alternative direction implicit method are analysed. The effect of the turbulent kinetic energy terms in the governing equations on the convergence characteristics is also studied. The performance of the two methods is compared for several two‐ and three‐dimensional problems. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
2.
Evagelia D. Farsirotou Johannes V. Soulis Vassilios D. Dermissis 《International Journal of Computational Fluid Dynamics》2013,27(3):187-200
A fully coupled two-dimensional sub-critical and/or supercritical, free-surface flow numerical model is developed to calculate bed variations in alluvial channels. Vertically averaged free-surface flow equations in conjunction with sediment transport equation are numerically solved using an explicit finite-volume scheme in integral form. The capabilities of the proposed method are first demonstrated by analyzing supercritical flow in an expansion channel. Thereafter, one and two-dimensional applications referring to aggradation and scouring are reported. For each of these test cases, computed results compare satisfactorily with measurements as well as with other numerical solutions. The method is stable, reliable and accurate, although time consuming, handling a variety of sediment transport equations with rapid changes of sediment transport at the boundaries. 相似文献
3.
A theory of general solutions of plane problems is developed for the coupled equations in plane elasticity of two-dimensional
octagonal quasicrystals. In virtue of the operator method, the general solutions of the antiplane and inplane problems are
given constructively with two displacement functions. The introduced displacement functions have to satisfy higher order partial
differential equations, and therefore it is difficult to obtain rigorous analytic solutions directly and is not applicable
in most cases. In this case, a decomposition and superposition procedure is employed to replace the higher order displacement
functions with some lower order displacement functions, and accordingly the general solutions are further simplified in terms
of these functions. In consideration of different cases of characteristic roots, the general solution of the antiplane problem
involves two cases, and the general solution of the inplane problem takes three cases, but all are in simple forms that are
convenient to be applied. Furthermore, it is noted that the general solutions obtained here are complete in x
3-convex domains.
相似文献
4.
《应用数学和力学(英文版)》2017,(11)
This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-modal methods based on the OrrSommerfeld and Squire(OSS) equations that assume simple base flows, this algorithm can be applied to arbitrarily complex base flows. In the proposed algorithm, a reorthogonalization Arnoldi method is used to improve orthogonality of the orthogonal basis of the Krylov subspace generated by solving the linearized forward and adjoint Navier-Stokes(N-S) equations. The linearized adjoint N-S equations with the specific boundary conditions for the channel are derived, and a new convergence criterion is proposed. The algorithm is then applied to a one-dimensional base flow(the plane Poiseuille flow) and a two-dimensional base flow(the plane Poiseuille flow with a low-speed streak)in a channel. For one-dimensional cases, the effects of the spanwise width of the channel and the Reynolds number on the transient growth of perturbations are studied. For two-dimensional cases, the effect of strength of initial low-speed streak is discussed. The presence of the streak in the plane Poiseuille flow leads to a larger and quicker growth of the perturbations than that in the one-dimensional case. For both cases, the results show that an optimal flow field leading to the largest growth of perturbations is characterized by high-and low-speed streaks and the corresponding streamwise vortical structures.The lift-up mechanism that induces the transient growth of perturbations is discussed.The performance of the re-orthogonalization Arnoldi technique in the algorithm for both one-and two-dimensional base flows is demonstrated, and the algorithm is validated by comparing the results with those obtained from the OSS equations method and the crosscheck method. 相似文献
5.
The finite element method is used to find the elastic strain (and thus the stress) for given velocity fields of the Leonov model fluid. With a simple linearization technique and the Galerkin formulation, the quasi-linear coupled first-order hyperbolic differential equations together with a non-linear equality constraint are solved over the entire domain based on a weighted residual scheme. The proposed numerical scheme has yielded efficient and accurate convective integrations for both the planar channel and the diverging radial flows for the Leonov model fluid. Only the strain in the inflow plane is required to be prescribed as the boundary conditions. In application, it can be conveniently incorporated in an existing finite element algorithm to simulate the Leonov viscoelastic fluid flow with more complex geometry in which the velocity field is not known a priori and an iterative procedure is needed. 相似文献
6.
C. David Pruett 《国际流体数值方法杂志》1993,16(2):133-152
We consider a problem which arises in the numerical solution of the compressible two-dimensional or axisymmetric boundary-layer equations. Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x, y) plane to a computational (ξ, η) plane in which the evolution of the flow is ‘slow’ in the time-like ξ direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently non-linear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which satisfies the continuity equation nearly to machine precision. As demonstration of the utility of the method, the boundary layers of three prototypical high-speed flows are investigated and compared: the flat plate, the hollow cylinder, and the cone. An important implication for classical linear stability theory is also briefly discussed. 相似文献
7.
This paper deals with the numerical simulation of fluid dynamics using the boundary–domain integral technique (BEM). The steady 2D diffusion–convection equations are discussed and applied to solve the plane Navier-Stokes equations. A vorticity–velocity formulation has been used. The numerical scheme was tested on the well-known ‘driven cavity’ problem. Results for Re = 1000 and 10,000 are compared with benchmark solutions. There are also results for Re = 15,000 but they have only qualitative value. The purpose was to show the stability and robustness of the method even when the grid is relatively coarse. 相似文献
8.
W. G. Habashi M. Robichaud V.-N. Nguyen W. S. Ghaly M. Fortin J. W. H. Liu 《国际流体数值方法杂志》1994,18(11):1083-1105
Solution methods are presented for the large systems of linear equations resulting from the implicit, coupled solution of the Navier-Stokes equations in three dimensions. Two classes of methods for such solution have been studied: direct and iterative methods. For direct methods, sparse matrix algorithms have been investigated and a Gauss elimination, optimized for vector-parallel processing, has been developed. Sparse matrix results indicate that reordering algorithms deteriorate for rectangular, i.e. M × M × N, grids in three dimensions as N gets larger than M. A new local nested dissection reordering scheme that does not suffer from these difficulties, at least in two dimensions, is presented. The vector-parallel Gauss elimination is very efficient for processing on today's supercomputers, achieving execution rates exceeding 2.3 Gflops the Cray YMP-8 and 9.2 Gflops on the NEC on SX3. For iterative methods, two approaches are developed. First, conjugate-gradient-like methods are studied and good results are achieved with a preconditioned conjugate gradient squared algorithm. Convergence of such a method being sensitive to the preconditioning, a hybrid viscosity method is adopted whereby the preconditioner has an artificial viscosity that is gradually lowered, but frozen at a level higher than the dissipation introduced in the physical equations. The second approach is a domain decomposition one in which overlapping domain and side-by-side methods are tested. For the latter, a Lagrange multiplier technique achieves reasonable rates of convergence. 相似文献
9.
Hairpin-like vortical structures that form in the wall region of turbulent channel flow are investigated. The analysis is
performed by following a procedure in which the Navier-Stokes equations are first integrated by means of a computational code
based on a mixed spectral-finite difference technique in the case of the flow in a plane channel. A DNS turbulent-flow database,
representing the turbulent statistically steady state of the velocity field through 10 viscous time units, is computed and
the vortex-detection method of the imaginary part of the complex eigenvalue pair of the velocity-gradient tensor is applied to the velocity field. As a result, hairpin-like vortical structures are educed. Flow visualizations are provided
of the processes of evolution that characterize hairpin vortices in the wall region of turbulent channel flow. The relationship
is investigated between vortex dynamics and 2nd- and 4th- quadrant events, showing that ejections and sweeps play a fundamental
role in the way the morphological evolution of a hairpin vortex develops with time. 相似文献
10.
The diffraction pattern due to a plane H-polarized electromagnetic wave is investigated, when this wave is incident upon an infinitely long slit of finite width in
an opaque screen of non-vanishing thickness. The screen is located between the plane boundaries of two media with different
electromagnetic properties. A Green's function formulation of the problem is employed, leading to a system of four coupled
integral equations in which the field distributions in the slit occur as unknowns. Numerical results are presented for the
field just below the screen as well as for the far field pattern. 相似文献
11.
M. M. Grigor'Ev 《国际流体数值方法杂志》1993,16(7):549-579
A new boundary element method is described for calculation of the steady incompressible laminar flows. The method is based on the well-known SIMPLE algorithm. The new boundary element method allows one to find the fields of the pressure and velocity corrections without inner iterations, thus reducing the computational time drastically. This makes it different from the method developed by Patankar and Spalding.32 However, the new method demands a much larger computer strorage. The boundary integral equations are discretized with the help of constant boundary elements and constant cells. The values of the integrals along the boundary elements and the cells for the two-dimensional domain are found analytically. To preserve the stability in the iteration process, under-relaxation for the convection terms is used. This paper gives the results of calculations of the flows between two plane parallel plates at Re = 20 and Re = 200, the flows in a square cavity with a moving upper lid at Re = 1 and Re = 100 and the flow in a plane channel with sudden symmetric expansion at Re =46·6. 相似文献
12.
Andrew P. Bassom Peter A. Clarkson C. K. Law J. Bryce McLeod 《Archive for Rational Mechanics and Analysis》1998,143(3):241-271
In this work we propose a new method for investigating connection problems for the class of nonlinear second‐order differential
equations known as the Painlevé equations. Such problems can be characterized by the question as to how the asymptotic behaviours
of solutions are related as the independent variable is allowed to pass towards infinity along different directions in the
complex plane. Connection problems have been previously tackled by a variety of methods. Frequently these are based on the
ideas of isomonodromic deformation and the matching of WKB solutions. However, the implementation of these methods often tends
to be heuristic in nature and so the task of rigorising the process is complicated. The method we propose here develops uniform
approximations to solutions. This removes the need to match solutions, is rigorous, and can lead to the solution of connection
problems with minimal computational effort. Our method relies on finding uniform approximations of differ
ential equations of the generic form as the complex‐valued parameter . The details of the treatment rely heavily on the locations of the zeros of the function F in this limit. If they are isolated, then a uniform approximation to solutions can be derived in terms of Airy functions
of suitable argument. On the other hand, if two of the zeros of F coalesce as , then an approximation can be derived in terms of parabolic cylinder functions. In this paper we discuss both cases, but
illustrate our technique in action by applying the parabolic cylinder case to the “classical” connection problem associated
with the second Painlevé transcendent. Future papers will show how the technique can be applied with very little change to
the other Painlevé equations, and to the wider problem of the asymptotic behavio
ur of the general solution to any of these equations.
(Accepted May 15, 1997) 相似文献
13.
This paper studies nonlinear waves in a prestretched cylinder composed of a Blatz-Ko material. Starting from the three-dimensional field equations, two coupled PDEs for modeling weakly nonlinear long waves are derived by using the method of coupled series and asymptotic expansions. Comparing with some other existing models in literature, an important feature of these equations is that they are consistent with traction-free surface conditions asymptotically. Also, the material nonlinearity is kept to the third order. As these two PDEs are quite complicated, the attention is focused on traveling waves, for which a first-order system of ODEs are obtained. We use the technique of dynamical systems to carry out the analysis. It turns out that the system is three parameters (the prestretch, the propagating speed and an integration constant) dependent and there are totally seven types of phase planes which contain trajectories representing bounded traveling waves. The parametric conditions for each phase plane are established. A variety of solitary and periodic waves are found. An important finding is that kink waves can propagate in a Blatz-Ko cylinder. We also find that one type of periodic waves has an interesting feature in the profile slope. Analytical expressions for all bounded traveling waves are obtained. 相似文献
14.
Baljeet Singh 《Archive of Applied Mechanics (Ingenieur Archiv)》2006,75(8-9):513-520
The propagation of plane waves in a fibre-reinforced, anisotropic, generalized thermoelastic media is discussed. The governing
equations in x–y plane are solved to obtain a cubic equation in phase velocity. Three coupled waves, namely quasi-P, quasi-SV and quasi-thermal
waves are shown to exist. The propagation of Rayleigh waves in stress free thermally insulated and transversely isotropic
fibre-reinforced thermoelastic solid half-space is also investigated. The frequency equation is obtained for these waves.
The velocities of the plane waves are shown graphically with the angle of propagation. The numerical results are also compared
to those without thermal disturbances and anisotropy parameters. 相似文献
15.
A control-volume based finite element method of equal-order type for three-dimensional incompressible turbulent fluid flow, heat transfer, and related phenomena is presented. The discretization equations are based mainly on the physics of the phenomena under consideration, more than on mathematical arguments. Special emphasis is devoted to the discretization of the convective terms and the continuity equation, and to the treatment of the boundary conditions imposed by the use of a high Reynolds k-?, type turbulence model. The pressure-velocity coupling in the fluid flow calculation is made from a derivative of the original SIMPLER method, without pressure correction. The discretized equations are solved in a sequential, rather than a coupled, form with significant advantage in the required computer time and storage. The method is an extension of a former version proposed by us for two-dimensional, laminar problems, and is here successfully applied to the following situations: three-dimensional deflected turbulent jet, and flows in 90° and 45° junctions of ducts with rectangular cross sections. The calculated results are in very good agreement with the experimental and numerical (obtained with the well established finite difference method) data available in the literature. 相似文献
16.
Alvaro Valencia 《Heat and Mass Transfer》1998,33(5-6):465-470
A numerical investigation was conducted into channel flows with a tandem of transverse vortex generators in the form of rectangular
cylinders. The oscillatory behavior of the flow is studied. Data for heat transfer and flow losses are presented for 100≤Re≤400
and cylinder separation distances 1≤S/H≤4. The results are obtained by numerical solution of the full Navier-Stokes equations and the energy equation. Self-sustained
flow oscillations are found for Re>100. Alternate and dynamic shedding of large vortex structures from the cylinders is observed
by visualization of the numerically determined flow field. A heat transfer enhancement up to a factor 1.78 compared to plane
channel flow is observed.
Received on 16 July 1997 相似文献
17.
A new numerical method for Nwogu's (ASCE Journal of Waterway, Port, Coastal and Ocean Engineering 1993; 119 :618)two‐dimensional extended Boussinesq equations is presented using a linear triangular finite element spatial discretization coupled with a sophisticated adaptive time integration package. The authors have previously presented a finite element method for the one‐dimensional form of these equations (M. Walkley and M. Berzins (International Journal for Numerical Methods in Fluids 1999; 29 (2):143)) and this paper describes the extension of these ideas to the two‐dimensional equations and the application of the method to complex geometries using unstructured triangular grids. Computational results are presented for two standard test problems and a realistic harbour model. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
18.
A p-version least squares finite element formulation for non-linear problems is applied to the problem of steady, two-dimensional, incompressible fluid flow. The Navier-Stokes equations are cast as a set of first-order equations involving viscous stresses as auxiliary variables. Both the primary and auxiliary variables are interpolated using equal-order C0 continuity, p-version hierarchical approximation functions. The least squares functional (or error functional) is constructed using the system of coupled first-order non-linear partial differential equations without linearization, approximations or assumptions. The minimization of this least squares error functional results in finding a solution vector {δ} for which the partial derivative of the error functional (integrated sum of squares of the errors resulting from individual equations for the entire discretization) with respect to the nodal degrees of freedom {δ} becomes zero. This is accomplished by using Newton's method with a line search. Numerical examples are presented to demonstrate the convergence characteristics and accuracy of the method. 相似文献
19.
Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method 总被引:2,自引:0,他引:2
In this study, the effects of magnetic field and nanoparticle on the Jeffery-Hamel flow are studied using a powerful analytical method called the Adomian decomposition method (ADM). The traditional Navier-Stokes equation of fluid mechanics and Maxwell’s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different α, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated. 相似文献
20.
The Navier-Stokes equations for a steady, viscous rotating fluid, rotating about the z-axis with angular velocity ω are linearized using the Stokes approximation. The linearized Navier-Stokes equations governing the axisymmetric flow can be written as three coupled partial differential equations for the stream function, vorticity and rotational velocity components. One parameter, Reω = 2ωa2/v, enters the resulting equations. For Reω « 1, the coupled equations are solved by the Peaceman-Rachford A.D.I. (Alternating Direction Implicit) method and the resulting algebraic equations are solved by the ‘method of sweeps’. Stream lines for ψ = 0·05, 0·2, 0·5 and magnitude of the vorticity vector z = 0·2 are plotted for Reω = 0·1, 0·3, 0·5. Correction to the Stokes drag due to the rotation of fluid is calculated. 相似文献