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A numerical method for solving three‐dimensional free surface flows is presented. The technique is an extension of the GENSMAC code for calculating free surface flows in two dimensions. As in GENSMAC, the full Navier–Stokes equations are solved by a finite difference method; the fluid surface is represented by a piecewise linear surface composed of quadrilaterals and triangles containing marker particles on their vertices; the stress conditions on the free surface are accurately imposed; the conjugate gradient method is employed for solving the discrete Poisson equation arising from a velocity update; and an automatic time step routine is used for calculating the time step at every cycle. A program implementing these features has been interfaced with a solid modelling routine defining the flow domain. A user‐friendly input data file is employed to allow almost any arbitrary three‐dimensional shape to be described. The visualization of the results is performed using computer graphic structures such as phong shade, flat and parallel surfaces. Results demonstrating the applicability of this new technique for solving complex free surface flows, such as cavity filling and jet buckling, are presented. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

3.
An incompressible Navier–Stokes solver based on a cell‐centre finite volume formulation for unstructured triangular meshes is developed and tested. The solution methodology makes use of pseudocompressibility, whereby the convective terms are computed using a Godunov‐type second‐order upwind finite volume formulation. The evolution of the solution in time is obtained by subiterating the equations in pseudotime for each physical time step, with the pseudotime step set equal to infinity. For flows with a free surface the computational mesh is fitted to the free surface boundary at each time step, with the free surface elevation satisfying a kinematic boundary condition. A ‘leakage coefficient’, ε, is introduced for the calculation of flows with a free surface in order to control the leakage of flow through the free surface. This allows the assumption of stationarity of mesh points to be made during the course of pseudotime iteration. The solver is tested by comparing the output with a wide range of documented published results, both for flows with and without a free surface. The presented results show that the solver is robust. © 1999 John Wiley & Sons, Ltd.  相似文献   

4.
Orbitally shaken bioreactors are an emerging alternative to stirred‐tank bioreactors for large‐scale mammalian cell culture, but their fluid dynamics is still not well defined. Among the theoretical and practical issues that remain to be resolved, the characterization of the liquid free surface during orbital shaking remains a major challenge because it is an essential aspect of gas transfer and mixing in these reactors. To simulate the fluid behavior and the free surface shape, we developed a numerical method based on the finite element framework. We found that the large density ratio between the liquid and the gas phases induced unphysical results for the free surface shape. We therefore devised a new pressure correction scheme to deal with large density ratios. The simulations operated with this new scheme gave values of wave amplitude similar to the ones measured experimentally. These simulations were used to calculate the shear stress and to study the mixing principle in orbitally shaken bioreactors. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

5.
MacCormack's explicit time-marching scheme is used to solve the full Navier–Stokes unsteady, compressible equations for internal flows. The requirement of a very fine grid to capture shock as well as separated flows is circumvented by employing grid clustering. The numerical scheme is applied for axisymmetric as well as two-dimensional flows. Numerical predictions are compared with experimental data and the qualitative as well as the quantitative agreement is found to be quite satisfactory. © 1997 John Wiley & Sons, Ltd.  相似文献   

6.
A three‐dimensional finite element method for incompressible multiphase flows with capillary interfaces is developed based on a (formally) second‐order projection scheme. The discretization is on a fixed (Eulerian) reference grid with an edge‐based local h‐refinement in the neighbourhood of the interfaces. The fluid phases are identified and advected using the level‐set function. The reference grid is then temporarily reconnected around the interface to maintain optimal interpolations accounting for the singularities of the primary variables. Using a time splitting procedure, the convection substep is integrated with an explicit scheme. The remaining generalized Stokes problem is solved by means of a pressure‐stabilized projection. This method is simple and efficient, as demonstrated by a wide range of difficult free‐surface validation problems, considered in the paper. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

7.
A coupling method for numerical calculations of steady free‐surface flows around a body is presented. The fluid domain in the neighbourhood of the hull is divided into two overlapping zones. Viscous effects are taken in account near the hull using Reynolds‐averaged Navier–Stokes equations (RANSE), whereas potential flow provides the flow away from the hull. In the internal domain, RANSE are solved by a fully coupled velocity, pressure and free‐surface elevation method. In the external domain, potential‐flow theory with linearized free‐surface condition is used to provide boundary conditions to the RANSE solver. The Fourier–Kochin method based on the Fourier–Kochin formulation, which defines the velocity field in a potential‐flow region in terms of the velocity distribution at a boundary surface, is used for that purpose. Moreover, the free‐surface Green function satisfying this linearized free‐surface condition is used. Calculations have been successfully performed for steady ship‐waves past a serie 60 and then have demonstrated abilities of the present coupling algorithm. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

8.
Systematic tests have been performed to study the behaviour of a numerical method developed to calculate 2D, steady free surface flows. The Reynolds equations are solved in the physical space by employing a non–orthogonal staggered grid, while the k-ε model is adopted to approximate the Reynolds stresses. The free surface is calculated following an iterative procedure and various parameters that affect convergence and accuracy of the numerical solution have been examined. Calculated results are compared with measured data for two cases, i.e. the wave generation above a bottom topography at various Froude numbers and the free surface formation above a submerged hydrofoil. © 1997 John Wiley & Sons, Ltd.  相似文献   

9.
A previously developed numerical model that solves the incompressible, non‐hydrostatic, Navier–Stokes equations for free surface flow is analysed on a non‐uniform vertical grid. The equations are vertically transformed to the σ‐coordinate system and solved in a fractional step manner in which the pressure is computed implicitly by correcting the hydrostatic flow field to be divergence free. Numerical consistency, accuracy and efficiency are assessed with analytical methods and numerical experiments for a varying vertical grid discretization. Specific discretizations are proposed that attain greater accuracy and minimize computational effort when compared to a uniform vertical discretization. Published in 2007 by John Wiley & Sons, Ltd.  相似文献   

10.
We study here the numerical analysis of a hydrodynamic contact in a particular configuration: the 3D incompressible viscous flow of a fluid dragged by a smooth plate over a rough surface. The mathematical model takes into account and discretizes the local topography of the rough profile. The simulation outcome will be the 3D velocity and pressure fields of the fluid film within the contact borders. This work is limited to the study of numerical resolution methods working solely in finite differences. The algorithms will be tested by analysing and comparing their results with analytically known flows. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

11.
A three‐dimensional, non‐hydrostatic pressure, numerical model with kε equations for small amplitude free surface flows is presented. By decomposing the pressure into hydrostatic and non‐hydrostatic parts, the numerical model uses an integrated time step with two fractional steps. In the first fractional step the momentum equations are solved without the non‐hydrostatic pressure term, using Newton's method in conjunction with the generalized minimal residual (GMRES) method so that most terms can be solved implicitly. This method only needs the product of a Jacobian matrix and a vector rather than the Jacobian matrix itself, limiting the amount of storage and significantly decreasing the overall computational time required. In the second step the pressure–Poisson equation is solved iteratively with a preconditioned linear GMRES method. It is shown that preconditioning reduces the central processing unit (CPU) time dramatically. In order to prevent pressure oscillations which may arise in collocated grid arrangements, transformed velocities are defined at cell faces by interpolating velocities at grid nodes. After the new pressure field is obtained, the intermediate velocities, which are calculated from the previous fractional step, are updated. The newly developed model is verified against analytical solutions, published results, and experimental data, with excellent agreement. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

12.
Conjunctive modelling of free/porous flows provides a powerful and cost‐effective tool for designing industrial filters used in the process industry and also for quantifying surface–subsurface flow interactions, which play a significant role in urban flooding mechanisms resulting from sea‐level rise and climate changes. A number of well‐established schemes are available in the literature for simulation of such regimes; however, three‐dimensional (3D) modelling of such flow systems still presents numerical and practical challenges. This paper presents the development of a fully 3D, transient finite element model for the prediction and quantitative analyses of the hydrodynamic behaviour encountered in industrial filtrations and environmental flows represented by coupled flows. The weak‐variational formulation in this model is based on the use of C0 continuous equal‐order Lagrange polynomial functions for velocity and pressure fields represented by 3D hexahedral finite elements. A mixed UVWP finite element scheme based on the standard Galerkin technique satisfying the Ladyzhenskaya–Babuska–Brezzi stability criterion through incorporation of an artificial compressibility term in the continuity equation has been employed for the solution of coupled partial differential equations. We prove that the discretization generates unified stabilization for both the Navier–Stokes and Darcy equations and preserves the geometrical flexibility of the computational grids. A direct node‐linking procedure involving the rearrangement of the global stiffness matrix for the interface elements has been developed by the authors, which is utilized to couple the governing equations in a single model. A variety of numerical tests are conducted, indicating that the model is capable of yielding theoretically expected and accurate results for free, porous and coupled free/porous problems encountered in industrial and environmental engineering problems representing complex filtration (dead‐end and cross‐flow) and interacting surface–subsurface flows. The model is computationally cost‐effective, robust, reliable and easily implementable for practical design of filtration equipments, investigation of land use for water resource availability and assessment of the impacts of climatic variations on environmental catastrophes (i.e. coastal and urban floods). The model developed in this work results from the extension of a multi‐disciplinary project (AEROFIL) primarily sponsored by the European aerospace industries for development of a computer simulation package (Aircraft Cartridge Filter Analysis Modelling Program), which was successfully utilized and deployed for designing hydraulic dead‐end filters used in Airbus A380.Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

13.
A numerical investigation of laminar flow over a three-dimensional backward-facing step is presented with comparisons with detailed experimental data, available in the literature, serving to validate the numerical results. The continuity constraint method, implemented via a finite element weak statement, was employed to solve the unsteady three-dimensional Navier–Stokes equations for incompressible laminar isothermal flow. Two-dimensional numerical simulations of this step geometry underestimate the experimentally determined extent of the primary separation region for Reynolds numbers Re greater than 400. It has been postulated that this disagreement between physical and computational experiments is due to the onset of three-dimensional flow near Re ≈ 400. This paper presents a full three-dimensional simulation of the step geometry for 100⩽ Re⩽ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three-dimensionality. Previous numerical studies have discussed possible instability modes which could induce a sudden onset of three-dimensional flow at certain critical Reynolds numbers. The current study explores the influence of the sidewall on the development of three-dimensional flow for Re greater than 400. Of particular interest is the characterization of three-dimensional vortices in the primary separation region immediately downstream of the step. The complex interaction of a wall jet, located at the step plane near the sidewall, with the mainstream flow reveals a mechanism for the increasing penetration (with increasing Reynolds number) of three-dimensional flow structures into a region of essentially two-dimensional flow near the midplane of the channel. The character and extent of the sidewall-induced flow are investigated for 100⩽Re⩽ 800. © 1997 John Wiley & Sons, Ltd.  相似文献   

14.
In this paper, the mesh‐free least square‐based finite difference (MLSFD) method is applied to numerically study the flow field around two circular cylinders arranged in side‐by‐side and tandem configurations. For each configuration, various geometrical arrangements are considered, in order to reveal the different flow regimes characterized by the gap between the two cylinders. In this work, the flow simulations are carried out in the low Reynolds number range, that is, Re=100 and 200. Instantaneous vorticity contours and streamlines around the two cylinders are used as the visualization aids. Some flow parameters such as Strouhal number, drag and lift coefficients calculated from the solution are provided and quantitatively compared with those provided by other researchers. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

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A two‐dimensional quadrilateral spectral multidomain penalty method (SMPM) model has been developed for the simulation of high Reynolds number incompressible stratified flows. The implementation of higher‐order quadrilateral subdomains renders this model a nontrivial extension of a one‐dimensional subdomain SMPM model built for the simulation of the same type of flows in vertically nonperiodic domains (Diamessis et al., J. Comp. Phys, 202 :298‐322, 2005). The nontrivial aspects of this extension consist of the implementation of subdomain corners, the penalty formulation of the pressure Poisson equation (PPE), and, most importantly, the treatment of specific challenges that arise in the iterative solution of the SMPM‐discretized PPE. The two primary challenges within the framework of the iterative solution of the PPE are its regularization to ensure the consistency of the associated linear system of equations and the design of an appropriate two‐level preconditioner. A qualitative and quantitative assessment of the accuracy, efficiency, and stability of the quadrilateral SMPM solver is provided through its application to the standard benchmarks of the Taylor vortex, lid‐driven cavity, and double shear layer. The capacity of the flow solver for the study of environmental stratified flow processes is shown through the simulation of long‐distance propagation of an internal solitary wave of depression in a manner that is free of numerical dispersion and dissipation. The methods and results presented in this paper make it a point of reference for future studies oriented toward the reliable application of the quadrilateral SMPM model to more complex environmental stratified flow process studies. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

17.
We present a projection scheme whose end‐of‐step velocity is locally pointwise divergence free, using a continuous ?1 approximation for the velocity in the momentum equation, a first‐order Crouzeix–Raviart approximation at the projection step, and a ?0 approximation for the pressure in both steps. The analysis of the scheme is done only for grids that guarantee the existence of a divergence free conforming ?1 interpolant for the velocity. Optimal estimates for the velocity error in L2‐ and H1‐norms are deduced. The numerical results demonstrate that these estimates should also hold on grids on which the continuous ?1 approximation for the velocity locks. Since the end‐of‐step velocity is locally solenoidal, the scheme is recommendable for problems requiring good mass conservation. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

18.
A new numerical approach based on consistent operator splitting is presented for computing compressible, highly stratified flows in astrophysics. The algorithm is particularly designed to search for steady or almost steady solutions for the time-dependent Navier–Stokes equations, describing viscous flow under the influence of a strong gravitational field. The algorithm proposed is multidimensional and works in Cartesian, cylindrical or spherical co-ordinates. It uses a second-order finite volume scheme with third-order upwinding and a second-order time discretization. An adaptive time step control and monotonic multilevel grid distribution has been incorporated to speed up convergence. This method has been incorporated into a hydrodynamical code by which, for the first time, for two-dimensional models the dynamics of the boundary layer in the accretion disk around a compact star could be computed over the whole viscous time scale. © 1998 John Wiley & Sons, Ltd.  相似文献   

19.
In this paper a new type of transient multidimensional two-fluid model has been applied to simulate intermittent or slug flow problems. Three different approaches to modelling interfacial friction, including an interfacial tracking scheme, have been investigated. The numerial method is based on an implicit finite difference scheme, solved directly in two steps applying a separate equation for the pressure. 2D predictions of Taylor bubble propagation in horizontal and inclined channels have been compared with experimental data and analytical solutions. The 2D model has also been applied to investigate a number of special phenomena in slug flow, including slug initiation, bubble turning in downflow and the bubble centring process at large liquid flow rates.  相似文献   

20.
This paper describes a method for simulation of viscous flows with a free surface around realistic hull forms with a transom, which has been developed based on a FINFLO RANS solver with a moving mesh. A dry‐transom model is proposed and implemented for the treatment of flows off the transom. The bulk RANS flow with the artificial compressibility is solved by a cell‐centred finite volume multigrid scheme and the free surface deformed by wave motions is tracked by satisfying the kinematic and dynamic free‐surface boundary conditions on the actual location of the surface. The effects of turbulence on flows are evaluated with the Baldwin–Lomax turbulence model without a wall function. A test case is modern container ship model with a transom, the Hamburg Test Case. The calculated results are validated and they agree well with the measured results in terms of the free‐surface waves and the total resistance coefficient. Furthermore, the numerical solutions successfully captured many important features of the complicated interaction of the free surface with viscous flows around transom stern ships. In addition, the convergence performance and the grid refinement studies are also investigated. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

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