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1.
Jianye Sun 《国际流体数值方法杂志》2009,59(6):593-609
In this paper, flows of liquid crystalline polymers into two‐dimensional thin cavity moulds are simulated. The flows are modelled by Ericksen–Leslie equations of motion in the high viscosity limit. An elliptic pressure equation is derived under Hele–Shaw approximations, and the non‐isothermal natures of the flow are modelled. The equations are solved using the finite‐difference technique. A new boundary‐mapping technique is developed in this study to solve the difficulty in the finite‐difference treatment of arbitrarily shaped boundaries, which possess no natural coordinate system. This new method avoids the difficult mesh control in the body‐fitted mapping process and makes the mapping process easy to implement. It can also solve the problems caused by the uneven distribution of grid nodes in the traditional body‐fitted mapping technique. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
2.
Thin film flow of an Oldroyd 6‐constant fluid on a vertical moving belt is investigated analytically and numerically. The governing equations for the flow field are derived for a steady one‐dimensional flow. The effect of constant applied magnetic field is included and its influence on the flow field is studied. The nonlinear governing equations are solved analytically and the exact solution is obtained in an elegant way. Numerical solutions are also obtained using higher‐order Chebyshev spectral methods. The influence of various non‐Newtonian parameters, gravitational force and applied magnetic field is investigated. The results showing the effect of gravity, magnetic field and material constants α1 and α2 are presented. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
3.
Robert Jurjevi&#x; 《国际流体数值方法杂志》1999,31(3):601-626
In this paper, a Galerkin weighted residual finite element numerical solution method, with velocity material time derivative discretisation, is applied to solve for a classical fluid mechanics system of partial differential equations modelling two‐dimensional stationary incompressible Newtonian fluid flow. Classical examples of driven cavity laminar flow and laminar flow past a cylinder are presented. Numerical results are compared with data found in the literature. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
4.
Reduced‐resistive magnetohydrodynamics (MHD) models are used in understanding different phenomenon in various domains, for example, astrophysics to model magnetotail or for solar arcades [Finn Bozkaya JM, Guzdar PN. Loss of equilibrium and reconnection in tearing of two dimensional equilibrias. Physics of Fluids B 1993; 5 :2870–2876], modeling plasma confinements in reverse field pinch [Strauss HR. The dynamo effect in fusion plasmas. Physics of Fluids 1985; 28 :2786–2792] and tokamaks [Strauss HR. Reduced MHD in nearly potential magnetic fields. Journal of Plasma Physics 1997; 57 (1):83–87; Freidberg J. Plasma Physics and Fusion Energy. Cambridge University Press: Cambridge, 2008]. In this context, recently, a new generalized reduced‐resistive MHD model, which can make use of an arbitrary density profile was proposed [Després B, Sart R. Reduced resistive MHD in Tokamaks with general density. ESAIM: Mathematical Modelling and Numerical Analysis 2012; 46 (5):1081–1106. EDP Sciences, SMAI, 2012 online 2011]. We in this work show that this proposed theoretical model can be realized numerically as well, and that it is very robust if the equation set is written in a very particular form using the properties of FEM. To illustrate these points, we pick the current hole configuration [Fujita T, Oikawa T, Suzuki T, Ide S, Sakamoto Y, Koide Y, Hatae T, Naito O, Isayama A, Hayashi N, Shirai H. Plasma equilibrium and confinement in a tokamak with nearly zero central current density in JT‐60U. Physical Review Letters 2001; 87 (11):245001; Hawkes NC, Stratton BC, Tala T, Challis CD, Conway G, DeAngelis R, Giroud C, Hobirk J, Joffrin E, Lomas P, Lotte P, Mailloux J, Mazon D, Rachlew E, Reyes‐Cortes S, Solano E, Zastrow K‐D. Observation of zero current density in the core of JET discharges with lower hybrid heating and current drive. Physical Review Letters 2001; 87 (11):115001], which was modeled using reduced‐resistive MHD and remodel it using different combinations of current sources and density profiles. Our model can be implemented with reasonable computational resources at the price of solving a well‐posed global linear system and it is unconditionally stable. These features are also demonstrated as a part of our numerical experiments. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
5.
The objective of this work is to investigate through the numeric simulation, the effects of the weakly viscoelastic flow within a rotating rectangular duct subject to a buoyancy force due to the heating of one of the walls of the duct. A direct velocity–pressure algorithm in primitive variables with a Neumann condition for the pressure is employed. The spatial discretization is made with finite central differences on a staggered grid. The pressure field is directly updated without any iteration. Numerical simulations were done for several Weissemberg numbers (We) and Grashof numbers (Gr) . The numerical results show that for high Weissemberg numbers (We>7.4 × 10?5) and for ducts with aspect ratio 2:1 and 8:1, the secondary flow is restabilized with a stretched double vortex configuration. It is also observed that when the Grashof number is increased (Gr>17 × 10?4) , the buoyancy force neutralizes the effects of the Coriolis force for ducts with aspect ratio 8:1. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
6.
A non‐linear method, PREC, for computation of the movement of a free surface is proposed here. The method is composed of three steps: identifying the free surface by using a non‐linear function from the volume fraction matrix, updating the volume fraction matrix using a volume projection method with error correction, and treatment of the results using overshooting or undershooting. Identification of the free surface includes using a polynomial function with 2, 4, or 8 coefficients for one‐, two‐, or three‐dimensional problems, respectively. The polynomial reconstruction involves non‐negligible numerical error. The second advection step includes a linear projection method in space and time. Advection of the volume fraction matrix is computed from the occupying volume of the mesh at the previous time step. At the new time step, the error at each grid point is assumed to be similar to the error at the previous time step and is used for correction. Overshooting or undershooting develops around the free surface mesh points due to the solution's finite time increment. The third step includes truncating the numerical overshooting or undershooting volumes, i.e. isotropic spreading of the excess fluid volumes. The PREC method is evaluated for a one‐dimensional flow case and several two‐dimensional simple flow cases with circular sections (cases include transition parallel to a coordinate, transition with an intersection angle to a coordinate, and rotation). The results from the present method are compared with analytical solutions and results from a donor‐cell VOF method. As a result of these comparisons, the PREC method is validated. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
7.
This works deals with sensitivity analysis (SA) for the Navier‐Stokes equations. The aim is to provide an estimate of the variance of the velocity field when some of the parameters are uncertain and then to use the variance to compute confidence intervals for the output of the model. First, we introduce the physical model and analyze its stability. The sensitivity equations are derived, and their stability analyzed as well. We propose a finite element‐volume numerical scheme for the state and the sensitivity, which is integrated into the open‐source industrial code TrioCFD. Finally, we present some numerical results: a steady and an unsteady test case for the channel flow problem are investigated. For the steady case, we compare the results to the Monte Carlo method and show how the SA technique succeeds in providing very accurate estimates of the variance. For the unsteady case, a new filtering procedure is proposed to deal with a sensitivity that grows in time. The filtered sensitivity is then used to compute the variance of the output and to provide confidence intervals. 相似文献
8.
A new numerical procedure for solving the two‐dimensional, steady, incompressible, viscous flow equations on a staggered Cartesian grid is presented in this paper. The proposed methodology is finite difference based, but essentially takes advantage of the best features of two well‐established numerical formulations, the finite difference and finite volume methods. Some weaknesses of the finite difference approach are removed by exploiting the strengths of the finite volume method. In particular, the issue of velocity–pressure coupling is dealt with in the proposed finite difference formulation by developing a pressure correction equation using the SIMPLE approach commonly used in finite volume formulations. However, since this is purely a finite difference formulation, numerical approximation of fluxes is not required. Results presented in this paper are based on first‐ and second‐order upwind schemes for the convective terms. This new formulation is validated against experimental and other numerical data for well‐known benchmark problems, namely developing laminar flow in a straight duct, flow over a backward‐facing step, and lid‐driven cavity flow. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
9.
A numerical algorithm to study the boundary‐value problem in which the governing equations are the steady Euler equations and the vorticity is given on the inflow parts of the domain boundary is developed. The Euler equations are implemented in terms of the stream function and vorticity. An irregular physical domain is transformed into a rectangle in the computational domain and the Euler equations are rewritten with respect to a curvilinear co‐ordinate system. The convergence of the finite‐difference equations to the exact solution is shown experimentally for the test problems by comparing the computational results with the exact solutions on the sequence of grids. To find the pressure from the known vorticity and stream function, the Euler equations are utilized in the Gromeka–Lamb form. The numerical algorithm is illustrated with several examples of steady flow through a two‐dimensional channel with curved walls. The analysis of calculations shows strong dependence of the pressure field on the vorticity given at the inflow parts of the boundary. Plots of the flow structure and isobars, for different geometries of channel and for different values of vorticity on entrance, are also presented. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
10.
Jacob Nagler 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2019,99(11)
The radial planar wedge pattern flow with friction and normalized non‐uniform viscosity function will be discussed here. Solving this problem will be done using the flow theory equations for Newtonian and Non‐Newtonian cases with non‐uniform viscosity assumption. General differential equation that connects between the normalized velocity profile and the normalized viscosity has been derived analytically from the flow equations. It was found that for specific wedge semi angle, the radial assumption is no longer valid for the flow velocity. Moreover, it was found that for inlet/outlet conditions the normalized mean hydrostatic pressure for Newtonian fluid is dependent on the geometry, the normalized velocity and the viscosity functions. In addition, it was found that inertia phenomenon can be neglected for small wedge semi angle. A comparison between the axial and the hydrostatic pressure distributions for inlet/outlet conditions was performed for Newtonian and non‐Newtonian flows. Finally, it was found that the axial pressure distribution profile was converged to the hydrostatic profile for critical wedge semi angle. 相似文献
11.
The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis. In either of these scenarios, it can be important to assess uncertainties in the assimilated state. Ideally, it is desirable to have complete information concerning the Bayesian posterior distribution for unknown state given data. We show that complete computational probing of this posterior distribution is now within the reach in the offline situation. We introduce a Markov chain–Monte Carlo (MCMC) method which enables us to directly sample from the Bayesian posterior distribution on the unknown functions of interest given observations. Since we are aware that these methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk‐type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however, more sophisticated MCMC methods are available which exploit derivative information. For simplicity of exposition, we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number flow in a two‐dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
12.
IntroductionManyproblemsencounteredinengineeringpracticeandotherdisciplinescanbesummarizedintoPDEssuchasosmosis,diffusion,heatconduction,wavepropagation,etc.ItisthenofvitalsignificancehowtosolvePDEsbothrapidlyandefficiently,ThenumericalsolutionsofPDEsarecustomarilyobtainedbythefiniteelementmethod(FEM),thefinitedifferencemethod(FDM)!and.the,,[l'2).Thesemethods,however,showtheirdemeritsforlargercomputationaldomains.AsforFEM,thevastnumberofunknownscausedbyspacecoordinatediscretizationlead… 相似文献
13.
This paper examines the performance of optimal linear quadratic state and output feedback controllers in stabilizing two‐dimensional perturbations in a plane Poiseuille flow. The synthesis of the controllers is based on a linearized model of the flow using a new set of interpolating polynomials in the wall‐normal direction, which automatically satisfy the homogeneous Dirichlet and Neumann boundary conditions at the walls and eliminate spurious eigenvalues. The controllers are implemented into a non‐linear Navier–Stokes solver, which is modified to compute the evolution of the flow perturbations. Two cases are examined, one with small initial disturbances that do not violate the linearity assumptions and the other with much larger disturbances that trigger the non‐linear convection terms. For the smallest disturbances, the solver accurately reproduced the results of the linear simulations of open‐ and closed‐loop systems. The simulations for the larger disturbances without control showed a rapid initial growth but the flow soon reached a saturated state in agreement with previous findings in the literature. The large initial growth is a consequence of the non‐normal nature of the system dynamics. The state feedback and output feedback controllers were able to reduce significantly the perturbation energy. For the larger disturbances, the energy calculated from the state variables is well below the energy evaluated by direct integration of the velocity field. This is probably due to the non‐linear terms transferring energy to harmonics of the considered wavenumber, which are not sensed by the linear controller. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
14.
Frank Muldoon 《国际流体数值方法杂志》2013,72(1):90-118
The problem of controlling the hydrothermal waves in a thermocapillary flow is addressed using a gradient‐based control strategy. The state equations are the two‐dimensional unsteady incompressible Navier–Stokes and energy equations under the Boussinesq approximation. The modeled problem is the ‘open boat’ process of crystal growth, the flow which is driven by Marangoni and buoyancy effects. The control is a spatially and temporally varying heat flux boundary condition at the free surface. The control that minimizes the hydrothermal waves is found using a conjugate gradient method, where the gradient of the objective function with respect to the control variables is obtained from solving a set of adjoint equations. The effectiveness of choices of the parameters governing the control algorithm is examined. Almost complete suppression of the hydrothermal waves is obtained for certain choices of the parameters governing the control algorithm. The numerical issues involved with finding the control using the optimizer are discussed, and the features of the resulting control are analyzed with the goal of understanding how it affects the flow.Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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16.
Ricardo Carvalho de Almeida Giovana Araújo Siqueira Costa Luiz Claudio Monteiro da Fonseca José Luis Drummond Alves 《国际流体数值方法杂志》2009,61(9):995-1028
This study proposes a new two‐step three‐time level semi‐Lagrangian scheme for calculation of particle trajectories. The scheme is intended to yield accurate determination of the particle departure position, particularly in the presence of significant flow curvature. Experiments were performed both for linear and non‐linear idealized advection problems, with different flow curvatures. Results for simulations with the proposed scheme, and with three other semi‐Lagrangian schemes, and with an Eulerian method are presented. In the linear advection problem the two‐step three‐time level scheme produced smaller root mean square errors and more accurate replication of the angular displacement of a Gaussian hill than the other schemes. In the non‐linear advection experiments the proposed scheme produced, in general, equal or better conservation of domain‐averaged quantities than the other semi‐Lagrangian schemes, especially at large Courant numbers. In idealized frontogenesis simulations the scheme performed equally or better than the other schemes in the representation of sharp gradients in a scalar field. The two‐step three‐time level scheme has some computational overhead as compared with the other three semi‐Lagrangian schemes. Nevertheless, the additional computational effort was shown to be worthwhile, due to the accuracy obtained by the scheme in the experiments with large time steps. The most remarkable feature of the scheme is its robustness, since it performs well both for small and large Courant numbers, in the presence of weak as well strong flow curvatures. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
17.
J. Thuburn 《国际流体数值方法杂志》2011,66(1):123-133
Different discretizations of the gradient and curl operators are considered for a staggered grid in a height‐based terrain‐following coordinate system. A combination of discrete operators is identified that guarantees the mimetic property that the curl of the gradient of any scalar vanishes identically. The result is illustrated with some numerical examples. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
18.
Governing equations for a two‐phase 3D helical pipe flow of a non‐Newtonian fluid with large particles are derived in an orthogonal helical coordinate system. The Lagrangian approach is utilized to model solid particle trajectories. The interaction between solid particles and the fluid that carries them is accounted for by a source term in the momentum equation for the fluid. The force‐coupling method (FCM), developed by M.R. Maxey and his group, is adopted; in this method the momentum source term is no longer a Dirac delta function but is spread on a numerical mesh by using a finite‐sized envelop with a spherical Gaussian distribution. The influence of inter‐particle and particle–wall collisions is also taken into account. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
19.
Hybrid three‐dimensional algorithms for the numerical integration of the incompressible Navier–Stokes equations are analyzed with respect to hydrodynamic stability in both linear and nonlinear fields. The computational schemes are mixed—spectral and finite differences—and are applied to the case of the channel flow driven by constant pressure gradient; time marching is handled with the fractional step method. Different formulations—fully explicit convective term, partially and fully implicit viscous term combined with uniform, stretched, staggered and non‐staggered meshes, x‐velocity splitted and non‐splitted in average and perturbation component – are analyzed by monitoring the evolution in time of both small and finite amplitude perturbations of the mean flow. The results in the linear field are compared with correspondent solutions of the Orr–Sommerfeld equation; in the nonlinear field, the comparison is made with results obtained by other authors. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
20.
In the present work a finite‐difference technique is developed for the implementation of a new method proposed by Aristov and Pukhnachev (Doklady Phys. 2004; 49 (2):112–115) for modeling of the axisymmetric viscous incompressible fluid flows. A new function is introduced that is related to the pressure and a system similar to the vorticity/stream function formulation is derived for the cross‐flow. This system is coupled to an equation for the azimuthal velocity component. The scheme and the algorithm treat the equations for the cross‐flow as an inextricably coupled system, which allows one to satisfy two conditions for the stream function with no condition on the auxiliary function. The issue of singularity of the matrix is tackled by adding a small parameter in the boundary conditions. The scheme is thoroughly validated on grids with different resolutions. The new numerical tool is applied to the Taylor flow between concentric rotating cylinders when the upper and lower lids are allowed to rotate independently from the inner cylinder, while the outer cylinder is held at rest. The phenomenology of this flow is adequately represented by the numerical model, including the hysteresis that takes place near certain specific values of the Reynolds number. Thus, the present results can be construed to demonstrate the viability of the new model. The success can be attributed to the adequate physical nature of the auxiliary function. The proposed technique can be used in the future for in‐depth investigations of the bifurcation phenomena in rotating flows. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献