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Two-dimensional Flow (two-dimensional + flow)
Selected AbstractsPhysically-based modelling of double-peak discharge responses at Slapton Wood catchmentHYDROLOGICAL PROCESSES, Issue 10 2008Stephen J Birkinshaw Abstract Heavy winter rainfall produces double-peak hydrographs at the Slapton Wood catchment, Devon, UK. The first peak is saturation-excess overland flow in the hillslope hollows and the second (i.e. the delayed peak) is subsurface stormflow. The physically-based spatially-distributed model SHETRAN is used to try to improve the understanding of the processes that cause the double peaks. A three-stage (multi-scale) approach to calibration is used: (1) water balance validation for vertical one-dimensional flow at arable, grassland and woodland plots; (2) two-dimensional flow for cross-sections cutting across the stream valley; and (3) three-dimensional flow in the full catchment. The main data are for rainfall, stream discharge, evaporation, soil water potential and phreatic surface level. At each scale there was successful comparison with measured responses, using as far as possible parameter values from measurements. There was some calibration but all calibrated values at one scale were used at a larger scale. A large proportion of the subsurface runoff enters the stream from three dry valleys (hillslope hollows), and previous studies have suggested convergence of the water in the three large hollows as being the major mechanism for the production of the delayed peaks. The SHETRAN modelling suggests that the hillslopes that drain directly into the stream are also involved in producing the delayed discharges. The model shows how in the summer most of the catchment is hydraulically disconnected from the stream. In the autumn the catchment eventually ,wets up' and shallow subsurface flows are produced, with water deflected laterally along the soil-bedrock interface producing the delayed peak in the stream hydrograph. Copyright © 2007 John Wiley & Sons, Ltd. [source] Numerical stability of unsteady stream-function vorticity calculationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2003E. Sousa Abstract The stability of a numerical solution of the Navier,Stokes equations is usually approached by con- sidering the numerical stability of a discretized advection,diffusion equation for either a velocity component, or in the case of two-dimensional flow, the vorticity. Stability restrictions for discretized advection,diffusion equations are a very serious constraint, particularly when a mesh is refined in an explicit scheme, so an accurate understanding of the numerical stability of a discretization procedure is often of equal or greater practical importance than concerns with accuracy. The stream-function vorticity formulation provides two equations, one an advection,diffusion equation for vorticity and the other a Poisson equation between the vorticity and the stream-function. These two equations are usually not coupled when considering numerical stability. The relation between the stream-function and the vorticity is linear and so has, in principle, an exact inverse. This allows an algebraic method to link the interior and the boundary vorticity into a single iteration scheme. In this work, we derive a global time-iteration matrix for the combined system. When applied to a model problem, this matrix formulation shows differences between the numerical stability of the full system equations and that of the discretized advection,diffusion equation alone. It also gives an indication of how the wall vorticity discretization affects stability. Despite the added algebraic complexity, it is straightforward to use MATLAB to carry out all the matrix operations. Copyright © 2003 John Wiley & Sons, Ltd. [source] Permeable and non-reflecting boundary conditions in SPHINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2009Martin Lastiwka Abstract Inflow and outflow boundary conditions are essential for the application of computational fluid dynamics to many engineering scenarios. In this paper we present a new boundary condition implementation that enables the simulation of flow through permeable boundaries in the Lagrangian mesh-free method, smoothed particle hydrodynamics (SPH). Each permeable boundary is associated with an inflow or outflow zone outside the domain, in which particles are created or removed as required. The analytic boundary condition is applied by prescribing the appropriate variables for particles in an inflow or outflow zone, and extrapolating other variables from within the domain. Characteristic-based non-reflecting boundary conditions, described in the literature for mesh-based methods, can be implemented within this framework. Results are presented for simple one-dimensional flows, quasi-one-dimensional compressible nozzle flow, and two-dimensional flow around a cylinder at Reynolds numbers of 40 and 100 and a Mach number of 0.1. These results establish the capability of SPH to model flows through open domains, opening a broad new class of applications. Copyright © 2008 John Wiley & Sons, Ltd. [source] Influence of inertia, topography and gravity on transient axisymmetric thin-film flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004Roger E. Khayat Abstract This study examines theoretically the development of early transients for axisymmetric flow of a thin film over a stationary cylindrical substrate of arbitrary shape. The fluid is assumed to emerge from an annular tube as it is driven by a pressure gradient maintained inside the annulus, and/or by gravity in the axial direction. The interplay between inertia, annulus aspect ratio, substrate topography and gravity is particularly emphasized. Initial conditions are found to have a drastic effect on the ensuing flow. The flow is governed by the thin-film equations of the ,boundary-layer' type, which are solved by expanding the flow field in terms of orthonormal modes in the radial direction. The formulation is validated upon comparison with the similarity solution of Watson (J. Fluid Mech 1964; 20:481) leading to an excellent agreement when only 2,3 modes are included. The wave and flow structure are examined for high and low inertia. It is found that low-inertia fluids tend to accumulate near the annulus exit, exhibiting a standing wave that grows with time. This behaviour clearly illustrates the difficulty faced with coating high-viscosity fluids. The annulus aspect is found to be influential only when inertia is significant; there is less flow resistance for a film over a cylinder of smaller diameter. For high inertia, the free surface evolves similarly to two-dimensional flow. The substrate topography is found to have a significant effect on transient behaviour, but this effect depends strongly on inertia. It is observed that the flow of a high-inertia fluid over a step-down exhibits the formation of a secondary wave that moves upstream of the primary wave. Gravity is found to help the film (coating) flow by halting or prohibiting the wave growth. The initial film profile and velocity distribution dictate whether the fluid will flow downstream or accumulate near the annulus exit. Copyright © 2004 John Wiley & Sons, Ltd. [source] Verification testing in computational fluid dynamics: an example using Reynolds-averaged Navier,Stokes methods for two-dimensional flow in the near wake of a circular cylinderINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2003Jennifer Richmond-Bryant Abstract Verification testing was performed for various Reynolds-averaged Navier,Stokes methods for uniform flow past a circular cylinder at Re= 5232. The standard and renormalized group (RNG) versions of the k,, method were examined, along with the Boussinesq, Speziale and Launder constitutive relationships. Wind tunnel experiments for flow past a circular cylinder were also performed to obtain a comparative data set. Preliminary studies demonstrate poor convergence for the Speziale relationship. Verification testing with the standard and RNG k,, models suggests that the simulations exhibit global monotonic convergence for the Boussinesq models. However, the global order of accuracy of the methods was much lower than the expected order of accuracy of 2. For this reason, pointwise convergence ratios and orders of accuracy were computed to show that not all sampling locations had converged (standard k,, model: 19% failed to converge; RNG k,, model: 14% failed to converge). When the non-convergent points were removed from consideration, the average orders of accuracy are closer to the expected value (standard k,, model: 1.41; RNG k,, model: 1.27). Poor iterative and global grid convergence was found for the RNG k,,/Launder model. The standard and RNG k,, models with the Boussinesq relationship were compared with experimental data and yielded results significantly different from the experiments. Copyright © 2003 John Wiley & Sons, Ltd. [source] The design of improved smoothing operators for finite volume flow solvers on unstructured meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2001Benjamin de Foy Abstract Spatial operators used in unstructured finite volume flow solvers are analysed for accuracy using Taylor series expansion and Fourier analysis. While approaching second-order accuracy on very regular grids, operators in common use are shown to have errors resulting in accuracy of only first-, zeroth- or even negative-order on three-dimensional tetrahedral meshes. A technique using least-squares optimization is developed to design improved operators on arbitrary meshes. This is applied to the fourth-order edge sum smoothing operator. The improved numerical dissipation leads to a much more accurate prediction of the Strouhal number for two-dimensional flow around a cylinder and a reduction of a factor of three in the loss coefficient for inviscid flow over a three-dimensional hump. Copyright © 2001 John Wiley & Sons, Ltd. [source] Simulation and analysis of flow through microchannelASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 4 2009Madhusree Kundu Abstract One-dimensional and two-dimensional models for microchannel flow with noncontinuum (slip flow) boundary conditions have been presented here. This study presents an efficient numerical procedure using pressure-correction-based iterative SIMPLE algorithm with QUICK scheme in convective terms to simulate a steady incompressible two-dimensional flow through a microchannel. In the present work, the slip flow of liquid through a microchannel has been modeled using a slip length assumption instead of using conventional Maxwell's slip flow model, which essentially utilizes the molecular mean free path concept. The models developed, following this approach, lend an insight into the physics of liquid flow through microchannels. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd. [source] Shape reconstruction of an inverse boundary value problem of two-dimensional Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010Wenjing Yan Abstract This paper is concerned with the problem of the shape reconstruction of two-dimensional flows governed by the Navier,Stokes equations. Our objective is to derive a regularized Gauss,Newton method using the corresponding operator equation in which the unknown is the geometric domain. The theoretical foundation for the Gauss,Newton method is given by establishing the differentiability of the initial boundary value problem with respect to the boundary curve in the sense of a domain derivative. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. Copyright © 2009 John Wiley & Sons, Ltd. [source] Passive control of the flow around a square cylinder using porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004Charles-Henri Bruneau Abstract The passive control of bluff body flows using porous media is investigated by means of the penalization method. This method is used to create intermediate porous media between solid obstacles and the fluid in order to modify the boundary layer behaviour. The study covers a wide range of two-dimensional flows from low transitional flow to fully established turbulence by direct numerical simulation of incompressible Navier,Stokes equations. A parametric study is performed to illustrate the effect of the porous layer permeability and thickness on the passive control. The numerical results reveal the ability of porous media to both regularize the flow and to reduce the drag forces up to 30%. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||