bluuebunny/crossref_metadata_2025_split huggingface dataset:
Semi‐implicit finite difference methods for three‐dimensional shallow water flow
Authors: Casulli Vincenzo , Cheng Ralph T. 
Published: October 2005

AbstractA semi‐implicit finite difference method for the numerical solution of three‐dimensional shallow water flows is presented and discussed. The governing equations are the primitive three‐dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three‐diagonal systems coupled with one five‐diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi‐implicit scheme for solving the corresponding two‐dimensional shallow water equations. The resulting two‐ and three‐dimensional algorithm has been shown to be fast, accurate and mass‐conservative and can also be applied to simulate flooding and drying of tidal mud‐flats in conjunction with three‐dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.
Improved shock‐capturing of Jameson's scheme for the Euler equations
Authors: Van Der Burg J. W. , Kuerten J. G. M. , Zandbergen P. J. 
Published: October 2005

AbstractIt is known that Jameson's scheme is a pseudo‐second‐order‐accurate scheme for solving discrete conservation laws. The scheme contains a non‐linear artificial dissipative flux which is designed to capture shocks. In this paper, it is shown that the, shock‐capturing of Jameson's scheme for the Euler equations can be improved by replacing the Lax‐Friedrichs' type of dissipative flux with Roe's dissipative flux. This replacement is at a moderate expense of the calculation time.
A finite volume approach to large eddy simulation of compressible, homogeneous, isotropic, decaying turbulence
Authors: Vreman A. W. , Geurts B. J. , Kuerten J. G. M. , Zandbergen P. J. 
Published: October 2005

AbstractLarge eddy simulation of compressible, homogeneous, isotropic, decaying turbulence in a rectangular box is performed using finite volume techniques. An analysis of the energy spectra obtained from the simulations shows that an agreement with the Kolmogorov law for the inertial range is found only when an appropriate spatial discretization method is used. This agreement is obtained both for a low (0·05) and a moderate (0·6) Mach number when Smagorinsky's subgrid model is employed.
Numerical solution of transonic full‐potential‐equivalent equations in von Mises co‐ordinates
Authors: An C.‐F. , Barron R. M. 
Published: October 2005

AbstractIn this paper a new approach to calculate transonic flows is developed. A set of full‐potential‐equivalent equations in the von Mises co‐ordinate system is formulated under the irrotationality and isentropic assumptions. The emphasis is placed on supercritical flow, in which the treatment of embedded shock waves is crucial to get convergent solutions. Shock jump conditions are employed and shock point operators (SPOs) are constructed in the body‐fitting streamline co‐ordinate system. SPOs and a type‐dependent difference scheme are applied to solve the ‘main’ equation for the ‘main’ variable, the streamline ordinate y. A number of ‘secondary’ equations are deduced for the corresponding ‘secondary’ variables. An optimal combination for the ‘secondary’ variable, its equation and related difference scheme is selected to be the generalized density R, its linear equation and the Crank‐Nicolson scheme. Numerical results show that the present approach gives good agreement with experimental data and other computational work for NACA0012 and biconvex aerofoils in both subcritical and supercritical ranges.
The behaviour of several stress–velocity–pressure mixed finite elements for Newtonian flows
Authors: Buscaglia Gustavo C. 
Published: October 2005

AbstractThe Q2/P1, P/P1, P2/P0 and Q1/P0 velocity–pressure mixed elements are extended to the stress–velocity–pressure formulation, using the same interpolants for stress and velocity, and tested in the 4‐to‐1 contraction problem for Stokes flow. The comparison shows significant differences among them, which are not present when the velocity–pressure formulation is used.To provide a better understanding of the phenomenon, several variants of the previous elements are introduced, obtained by either changing the pressure space or by enriching the stress space with bubble functions. The formulation exhibits a strong sensitivity to the first alternative, while the second produces only a minor effect. These observations are confirmed by a convergence test effected on a regular problem with the explicit analytical solution. Also, as a result of the whole comparison, the P/P/P1 element looks promising for three‐field calculations.
Shallow flow modelling using curvilinear depth‐averaged stream function and vorticity transport equations
Authors: Borthwick A. G. L. , Kaar E. T. 
Published: October 2005

AbstractMost receiving water, such as lakes and open reservoirs, have large plan dimensions with respect to their depth. In such cases, the flow may be nearly two‐dimensional and the depth‐averaged Reynolds equations are appropriate. This paper presents a new version of the governing equations in curvilinear depth‐averaged stream function and vorticity transport (ψ, ω) form appropriate for non‐orthogonal computational meshes. The equations are discretized using finite differences and solved using successive over‐relaxation for the depth‐averaged stream function equation and an alternating direction implicit scheme for the vorticity transport equation. Results from the numerical model are validated against data from flow past a backward facing step and jet‐forced flow in a circular reservoir. The results indicate that the (ψ, ω) form of the shallow water equations may be useful for applications where the free surface can either be assumed horizontal, or is know a priori.
Is the steady viscous incompressible two‐dimensional flow over a backward‐facing step at Re = 800 stable?
Authors: Gresho Philip M. , Gartling David K. , Torczynski J. R. , Cliffe K. A. , Winters K. H. , Garratt T. J. , Spence A. , Goodrich John W. 
Published: October 2005

AbstractA detailed case study is made of one particular solution of the 2D incompressible Navier–Stokes equations. Careful mesh refinement studies were made using four different methods (and computer codes): (1) a high‐order finite‐element method solving the unsteady equations by time‐marching; (2) a high‐order finite‐element method solving both the steady equations and the associated linear‐stability problem; (3) a second‐order finite difference method solving the unsteady equations in streamfunction form by time‐marching; and (4) a spectral‐element method solving the unsteady equations by time‐marching. The unanimous conclusion is that the correct solution for flow over the backward‐facing step at Re = 800 is steady—and it is stable, to both small and large perturbations.
An adaptive multigrid finite‐volume scheme for incompressible Navier–Stokes equations
Authors: Lin San‐Yih , Wu Tsuen‐Muh 
Published: October 2005

AbstractAn algorithm for the solutions of the two‐dimensional incompressible Navier–Stokes equations is presented. The algorithm can be used to compute both steady‐state and time‐dependent flow problems. It is based on an artificial compressibility method and uses higher‐order upwind finite‐volume techniques for the convective terms and a second‐order finite‐volume technique for the viscous terms. Three upwind schemes for discretizing convective terms are proposed here. An interesting result is that the solutions computed by one of them is not sensitive to the value of the artificial compressibility parameter. A second‐order, two‐step Runge–Kutta integration coupling with an implicit residual smoothing and with a multigrid method is used for achieving fast convergence for both steady‐ and unsteady‐state problems. The numerical results agree well with experimental and other numerical data. A comparison with an analytically exact solution is performed to verify the space and time accuracy of the algorithm.
The numerical solution of the flow in a general bifurcating channel at moderately high Reynolds number using boundary‐fitted co‐ordinates, primitive variables and Newton iteration
Authors: Hunt Roland 
Published: October 2005

AbstractA numerical code has been implemented for the numerical solution of the steady, incompressible Navier–Stokes equations using primitive variables in a bifurcating channel. A boundary‐fitted, numerically generated grid is placed onto the domain of the channel which is transformed into either a rectilinear C‐ or T‐shaped region. The differenced equations are solved using Newton's iteration which makes upwinding at high Reynolds number unnecessary. Practical implications of inverting the huge Jacobian matrix of Newton's method are discussed. The results have relative error of 2–3 × 10−3 at Reynolds number 100, with T‐geometry being marginally but significantly more accurate than C‐geometry. Results have been obtained for Reynolds numbers up to 1000 for three bifurcations one of which models the carotid arterial bifurcation in the human head. For this latter bifurcation the wall shear stress is calculated in connection with the onset of atherosclerosis. Finally, the results of flows having different daughter tube end pressures are presented.
Integral transform analysis of natural convection in porous enclosures
Authors: Baohua Cai , Cotta R. M. 
Published: October 2005

AbstractA hybrid numerical‐analytical solution for steady‐state natural convection in a porous cavity is proposed, based on application of the ideas in the generalized integral transform technique. The integral transformation process reduces the original coupled partial differential equations, for temperature and stream function, into an infinite system of non‐linear ordinary differential equations for the transformed potentials, which is adaptively truncated and numerically solved through well‐established algorithms. The approach is applied to a vertical rectangular enclosure subjected to uniform internal heat generation. The convergence characteristics of the explicit inversion formulae are illustrated and critical comparisons with previously reported purely numerical solutions are performed.
Boundary element method for steady 2D high‐Reynolds‐number flow
Authors: Rek Z. , Škerget L. 
Published: October 2005

AbstractThis 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.
Computation of unsteady laminar viscous flow past an aerofoil using the CPI method
Authors: Deng G. B. , Guilmineau E. , Piquet J. , Queutey P. , Visonneau M. 
Published: October 2005

AbstractThe present work is a discussion of the computation of unsteady laminar incompressible two‐dimensional viscous flow past complex geometries. A new physically consistent method is presented for the reconstruction of velocity fluxes which arise from the mass and momentum balance discrete equations. This closure method for fluxes makes possible the use of a cell‐centred grid in which velocity and pressure unknowns share the same location while circumventing the occurrence of spurious pressure modes. The method is validated using the impulsively started cylinder problem for circular or aerofoil‐like shapes at several Reynolds numbers of the order of 103–104.
An element level zero‐divergence finite element approach
Authors: Mack A. N. F. 
Published: October 2005

AbstractAn innovative idea for the solution of viscous incompressible flows, in which the equation for conservation of mass is satisfied at the element level, is termed the solenoidal finite element approach. The term ‘solenoidal’ derives from the fact that the velocity components need to be solenoidal, i.e. to have zero divergence. The difficulty with this idea centres on the construction of a specialized element in which the velocity components are constrained to be solenoidal by the nature of their interpolation functions. If such an element can be constructed, then the pressure is suppressed from the prime solution. This has obvious attractions, although recourse to another novel idea is needed for its eventual retrieval. The validity of these ideas is demonstrated herein by the results for some classical benchmark problems. Where possible, comparisons are made with other results, both from other codes and from the literature.
Prediction of turbulent wall shear flows directly from wall
Authors: Jaw Shenq‐Yuh , Hwang Robert R. 
Published: October 2005

AbstractThe fully elliptic Reynolds‐averaged Navier–Stokes equations have been used together with Lam and Bremhorst's low‐Reynolds‐number model, Chen and Patel's two‐layer model and a two‐point wall function method incorporated into the standard k‐ϵ model to predict channel flows and a backward‐facig step flow. These flows enable the evaluation of the performance of different near‐wall treatments in flows involving streamwise and normal pressure gradients, flows with separation and flows with non‐equilibrium turbulence characteristics. Direct numerical simulation (DNS) of a channel flow with Re =3200 further provides the detailed budgets of each modelling term of the k and ϵ‐transport equations. Comparison of model results with DNS data to evaluate the performance of each modelling term is also made in the present study. It is concluded that the low‐Reynolds‐number model has wider applicability and performs better than the two‐layer model and wall function approaches. Comparison with DNS data further shows that large discrepancies exist between the DNS budgets and the modelled production and destruction terms of the ϵ equation. However, for simple channel flow the discrepancies are similar in magnitude but opposite in sign, so they are cancelled by each other. This may explain why, even when employing such an inaccurately modelled ϵ‐equation, one can still predict satisfactorily some simple turbulent flows.
Damped artificial compressibility iteration scheme for implicit calculations of unsteady incompressible flow
Authors: McHugh P. R. , Ramshaw J. D. 
Published: October 2005

AbstractPeyret (J. Fluid Mech., 78, 49–63 (1976)) and others have described artificial compressibility iteration schemes for solving implicit time discretizations of the unsteady incompressible Navier‐Stokes equations. Such schemes solve the implicit equations by introduing derivatives with respect to a pseudo‐time variable τ and marching out to a steady state in τ. The pseudo‐time evolution equation for the pressure p takes the form ∂p/∂ = −a2∂∇.u, where a is an artificial compressibility parameter and u is the fluid velocity vector. We present a new scheme of this type in which convergence is accelerated by a new procedure for setting a and by introducing an artificial bulk viscosity b into the momentum equation. This scheme is used to solve the non‐linear equations resulting from a fully implicit time differencing scheme for unsteady incompressible flow. We find that the best values of a and b are generally quite different from those in the analogous scheme for steady flow (J. D. Ramshaw and V. A. Mousseau, Comput. Fluids, 18, 361–367 (1990)), owing to the previously unrecognized fact that the character of the system is profoundly altered by the pressence of the physical time derivative terms. In particular, a Fourier dispersion analysis shows that a no longer has the significance of a wave speed for finite values of the physical time step δt,. Inded, if on sets a ˜ |u| as usual, the artificial sound waves cease to exist when δt is small and this adversely affects the iteration convergence rate. Approximate analytical expressions for a and b are proposed and the benefits of their use relative to the conventional values a ∼ |u| and b = 0 are illustrated in simple test calculations.
An h4 accurate vorticity‐velocity formulation for calculating flow past a cylinder
Authors: Dennis S. C. R. , Hudson J. D. 
Published: October 2005

AbstractA method of solution for the two‐dimensional Navier‐Stokes equations for incompressible flow past a cylinder is given in which the euquation of continuity is solved by a step‐by‐step integration procedure at each stage of an interative process. Thus the formulation involves the solution of one first‐order and one second‐order equation for the velocity components, together with the vorticity transport equation. the equations are solved numerically by h4‐accurate methods in the case of steady flow past a circular cylinder in the Reynolds number range 10–100. Results are in satisfactory agreement with recent h4‐accurate calculations. An improved approximation to the boundary conditions at large distance is also considered.
An investigation of artificial dissipation for the cell‐vertex finite volume method
Authors: Mackenzie J. A. 
Published: October 2005

AbstractThis paper is concerned with an investigation of artificial dissipation models that are used with the cell‐vertex finite volume approximation of the compressible Euler and Navier‐Stokes equations. Based on the observation that first and second‐order upwind schemes can be written as a central discretization plus an appropriately scaled dissipative flux, a matrix scaling of second and fourth‐differences is implemented in an artificial dissipation model that also uses a procedure to limit the applicability of shock‐capturing dissipation. Analysis of the model and the associated boundary conditions is given to determine the effect on accuracy. Numerical results are given for transonic Euler flow past a NACA0012 aerofoil profile which demonstrate the improved shock‐capturing capability of the model. Results for laminar subsonic viscous flow over a flat plate show that the matrix‐dissipation model reduces the amount of spurious artificial dissipation within boundary layers.
An application of Roe's flux‐difference splitting for k‐ϵ turbulence model
Authors: Siikonen Timo 
Published: October 2005

AbstractIn this paper Roe's flux‐difference splitting is applied for the solution of Reynolds‐averaged Navier‐Stokes equations. Turbulence is modelled using a low‐Reynolds number form of the k‐ϵ tubulence model. The coupling between the turbulence kinetic energy equation and the inviscid part of the flow equations is taken into account. The equations are solved with a diagonally dominant alternating direction implicit (DDADI) factorized implicit time integration method. A multigrid algorithm is used to accelerate the convergence. To improve the stability some modifications are needed in comparison with the application of an algebraic turbulence model. The developed method is applied to three different test cases. These cases show the efficiency of the algorithm, but the results are only marginally better than those obtained with algebraic models.
Numerical modelling of ice jam resistance to main channel flow
Authors: Saadé Raafat G. , Amruthur  , Ramamurthy S. , Troitsky Michael S. 
Published: October 2005

AbstractIn northern countries, subfreezing temperatures during the winter season result in the formation of ice covers on most rivers. Towards the end of the winter season, during the spring break‐up period, stationary ice covers become weak in strength and break up. The resulting broken ice pieces or ice floes are significantly larger in thickness and have a rougher undersurface relative to sheet ice and impose higher hydraulic resistance. The downstream movement of the ice floes may be arrested under conditions such as an intact ice cover, bridge piers or channel constrictions, among others, thereby initiating a break‐up ice jam. These ice jams most often have been observed to cause very high water stages. Detrimental effects caused by these high water levels encompass those of operational and design‐related problems such as the flooding of communities due to ice‐jam‐induced backwater, flood risk assessments, altering of the open water flow regime, bed scour and flooding of bridges.The ability to predict the influence of an ice jam on the main flow is of considerable importance in river engineering and can be viewed upon by its effects on the variation in the water surface levels. All other information is dependent on the foregoing. The ice jam influence on the main flow can be regarded with respect to local and global standpoints.The primary objective of this study is to formulate the influence of the ice jam on the main channel flow. The formulation is then coupled with a two‐dimensional numerical model for the simulation of the water flow regime. The data from different laboratory experiments on ice jams are reproduced numerically. Various simulations are then carried out to compute the water surface levels and velocities in channels under ice jam conditions. The numerical results are then compared with the laboratory data.Results show that the mathematical formulation developed to predict the water surface levels and velocities along the ice jam length as well as upstream and downstream of its leading and trailing edges respectively gives satisfactory predictions.
Implementation of some higher‐order convection schemes on non‐uniform grids
Authors: Li Yuguo , Baldacchino Lisa 
Published: October 2005

AbstractA generalized formulation is applied to implement the quadratic upstream interpolation (QUICK) scheme, the second‐order upwind (SOU) scheme and the second‐order hybrid scheme (SHYBRID) on non‐uniform grids. The implementation method is simple. The accuracy and efficiency of these higher‐order schemes on non‐uniform grids are assessed. Three well‐known bench mark convection‐diffusion problems and a fluid flow problem are revisited using non‐uniform grids. These are: (1) transport of a scalar tracer by a uniform velocity field; (2) heat transport in a recirculating flow; (3) two‐dimensional non‐linear Burgers equations; and (4) a two‐dimensional incompressible Navier‐Stokes flow which is similar to the classical lid‐driven cavity flow. The known exact solutions of the last three problems make it possible to thoroughly evaluate accuracies of various uniform and non‐uniform grids. Higher accuracy is obtained for fewer grid points on non‐uniform grids. The order of accuracy of the examined schemes is maintained for some tested problems if the distribution of non‐uniform grid points is properly chosen.