bluuebunny/crossref_metadata_2025_split huggingface dataset:
A one‐dimensional moving grid solution for the coupled non‐linear equations governing multiphase flow in porous media. 1: Model development
Authors: Gamliel Amir , Abriola Linda M. 
Published: August 2005

AbstractA straightforward moving grid finite element method is developed to solve the one‐dimensional coupled system of non‐linear partial differential equations (PDEs) governing two‐ and three‐phase flow in porous media. The method combines features from a number of self‐adaptive grid techniques. These techniques are the equidistribution, the moving grid finite element and the local grid refinement/coarsening methods. Two equidistribution criteria, based on solution gradient and curvature, are employed and nodal distributions are computed iterativcly. Using the developed approach, an intermingle‐free nodal distribution is guaranteed. The method involves examination of a single representative gradient to facilitate the application of moving grid algorithms to solve a non‐linear coupled set of PDEs and includes a feature to limit mass balance error during nodal redistribution. The finite element part of the developed algorithm is verified against an existing finite difference model. A numerical simulation example involving a single‐front two‐phase flow problem is presented to illustrate model performance. Additional simulation examples are given in Part 2 of this paper. These examples include single and double moving fronts in two‐ and three‐phase flow systems incorporating source/sink terms. Simulation sensitivity to the moving grid parameters is also explored in Part 2.
A one‐dimensional moving grid solution for the coupled non‐linear equations governing multiphase flow in porous media. 2: Example simulations and sensitivity analysis
Authors: Gamliel Amir , Abriola Linda M. 
Published: August 2005

AbstractThis paper presents numerical examples for the moving grid finite element algorithm derived in Part Ito solve the non‐linear coupled set of PDEs governing immiscible multiphase flow in porous media in one dimension. Examples include single‐ and double‐front simulations for two‐ and three‐phase flow regimes and incorporating a mass sink. The modelling approach is shown to achieve significant savings in computation time and memory allocation when compared with fixed grid solutions of equivalent accuracy. This work includes sensitivity analyses for the parameters which are incorporated in the grid adaptation method, including the curvature weights, artificial viscosity and artificial repulsive force. It is found that the curvature weights are exponential functions of the negative ratio of the square root of the domain length to the number of discrete nodes. These weighting parameters are also shown to depend upon the shape of the front. On the basis of the examined simulations, it is recommended that artificial viscosity be neglected in the solution of the coupled non‐linear set of PDEs governing multiphase flow in porous media. Similarly, use of a repulsive force is found to be unnecessary in simulations involving the migration of two liquid phases. For multiphase flows incorporating a gas phase it is recommended to use a non‐zero value for the repulslive force to avoid development of an ill‐conditioned nodal distribution matrix. An equation to evaluate the repulsive force under these circumstances is suggested.
A comparison of spatial grids for numerical modelling of flows in near‐coastal seas
Authors: Lardner R. W. , Song Y. 
Published: August 2005

AbstractThree‐dimensional algorithms for the numerical computation of flows caused by tides or meteorological forcing are developed for four of Arakawa's spatial grid types using a spectral method in the vertical dimension. Three of the grids, in which the velocity components are computed at the same grid points, offer potential advantages over the commonly used C‐grid. The computed results from the four grids are compared for three test problems based on the linearized hydrodynamical equations. It is concluded that the B‐grid provides a viable alternative to the C‐grid, with significant advantages when a spectral method is used.
Surface tension and buoyancy‐driven flow in a non‐isothermal liquid bridge
Authors: Zhang Yiqiang , Alexander J. Iwan D. 
Published: August 2005

AbstractThe Navier–Stokes–Boussinesq equations governing the transport of momentum, mass and heat in a non‐isothermal liquid bridge with a temperature‐dependent surface tension are solved using a vorticity‐stream‐function formulation together with a non‐orthogonal co‐ordinate transformation. The equations are discretized using a pseudo‐unsteady semi‐implicit finite difference scheme and are solved by the ADI method. A Picard‐type iteration is adopted which consists of inner and outer iterative processes. The outer iteration is used to update the shape of the free surface. Two schemes have been used for the outer iteration; both use the force balance normal to the free surface as the distinguished boundary condition. The first scheme involves successive approximation by the direct solution of the distinguished boundary condition. The second scheme uses the artificial force imbalance between the fluid pressure, viscous and capillary forces at the free surface which arises when the boundary condition for force balance normal to the surface is not satisfied. This artificial imbalance is then used to change the surface shape until the distinguished boundary condition is satisfied. These schemes have been used to examine a variety of model liquid bridge situations including purely thermocapillary‐driven flow situations and mixed thermocapillary‐ and bouyancy‐driven flow.
A numerical study of bifurcation in laminar flow in curved ducts
Authors: Jayanti S. , Hewitt G. F. 
Published: August 2005

AbstractThe bifurcation phenomenon whereby multiple‐vortex secondary flow occurs in place of the normal two‐vortex flow in laminar flow in curved ducts has previously been studied numerically by several researchers. However, the various results have been conflicting on many points. The present paper describes a set of numerical experiments conducted to study the effect of numerical accuracy on the solution. The results show that the transition from two‐ to four‐vortex structure depends strongly on the differencing scheme and to a lesser extent on the grid size. The study also shows that as the Reynolds number of the flow increases, a two‐vortex structure is re‐established via a path which involves strongly asymmetric secondary flow patterns. These results are in agreement, at least qualitatively, with recent experimental theoretical and numerical results.
Compressible gas flow between closely spaced plates
Authors: Mourelatos Zissimos P. 
Published: August 2005

AbstractA theoretical analysis is presented to solve numerically the steady state Navier–Stokes equations, continuity equation and energy equation for a compressible ideal gas flow between two closely spaced, in general nonparallel, infinitely wide plates (siider bearing). The analysis includes the gas inertia effect and covers both non‐choked and choked flows. The results of the present analysis compare very well with both analytical and experimental results of compressible flow in a slider bearing comprised of two parallel and stationary plates. It was found that for choked flow the gas inertia effect is important, while the consideration of the energy equation does not affect the accuracy of the calculated flow substantially. Finally, the stiffness of a slider bearing is presented for different geometrical characteristics of the bearing.
Numerical prediction of vortex shedding behind a square cylinder
Authors: Kelkar Kanchan M. , Patankar Suhas V. 
Published: August 2005

AbstractIt is common knowledge that flow around bluff bodies exhibits oscillatory behaviour. The aim of the present study is to compute the steady two‐dimensional flow around a square cylinder at different Reynolds numbers and to determine the onset of unsteadiness through a linear stability analysis of the steady flow. Stability of the steady flow to small two‐dimensional perturbations is analysed by computing the evolution of these perturbations. An analysis of various time‐stepping techniques is carried out to select the most appropriate technique for predicting the growth of the perturbations and hence the stability of the flow. The critical Reynolds number is determined from the growth rate of the perturbations. Computations are then made for periodic unsteady flow at a Reynolds number above the critical value. The predicted Strouhal number agrees well with experimental data. Heat transfer from the cylinder is also studied for the unsteady laminar flow.
An accurate computation for rapidly varied flow in an open channel
Authors: Yang Jinn‐Chuang , Chen Kun‐Nan , Lee Hong‐Yuan 
Published: August 2005

AbstractA new method combining the Preissmann four‐point scheme and the Holly–Preissmann reach‐back scheme is introduced to solve the rapidly varied flow problem in an open channel. The Preissmann four‐point scheme is well known for the computation of one‐dimensional unsteady flow. The Holly–Preissmann reach‐back scheme integrates the Holly‐Preissmann two‐point scheme with the concept of reach‐back characteristics, which allows the characteristics to project several time steps beyond the current time level. A spontaneous surge formation case is used to demonstrate and evaluate the applicability of the new method. It has been found that the results from this method are quite compatible with those of Preissmann four‐point scheme. In addition, with the appropriate choice of the number of reach‐back time steps, this new method can always avoid the numerical oscillation which usually exists when one uses the Preissmann four‐point scheme for the condition of Courant number not close to unity.
Computation of two‐dimensional dam‐break flood flows
Authors: Soulis Johannes Vassiliou 
Published: August 2005

AbstractSudden total collapse of a dam holding back a reservoir of water, whenever it occurs, becomes formidably impressive in the extent of destruction with which it is associated. The movement on a dry bed of a two‐dimensional flood wave resulting from the break of a dam has been one of the most important and challenging subjects in rapidly varied unsteady flows from the computational point of view. An implicit time‐marching finite volume numerical scheme was developed and subsequently applied for the solution of the two‐dimensional unsteady open channel flow equations written in conservation form. In order to avoid the problems associated with a conventional grid system, a body‐fitted non‐orthogonal local co‐ordinate system was utilized. The proposed numerical technique was applied to determine the stage hydrographs, water surface profiles and velocities of flood flows resulting from suddenly breached storage dams. Predictions were compared with an analytical solution, with available numerical solutions using MacCormack's two‐step explicit scheme and with experimental measurements. Agreement between predictions and measurements regarding the wave front advancement and stage hydrographs is considered to be satisfactory.
Numerical method for unsteady viscous hydrodynamical problem with free boundaries
Authors: Shopov Peter J. , Minev Peter D. , Bazhlekov Ivan B. 
Published: August 2005

AbstractA finite element method for the transient incompressible Navier–Stokes equations with the ability to handle multiple free boundaries is presented. Problems of liquid–liquid type are treated by solving two coupled Navier–Stokes problems for two separate phases. The possibility to solve problems of liquid–gas, liquid–liquid–gas or liquid–liquid–liquid type is demonstrated too. Surface tension effects are included at deformable interfaces.The method is of Lagrangian type with mesh redefinition. A predictor‐corrector scheme is used to compute the position of the deformable interface with automatic control of its accuracy and smoothness. The method is provided with an automatic choice of the time integration step and an optional spline filtration of the truncation error at the free surface. In order to show the accuracy of the method, tests and comparisons are presented. Numerical examples include motion of bubbles and multiple drops.
A modified adaptive grid method for recirculating flows
Authors: Lee D. , Tsuei Y. M. 
Published: August 2005

AbstractIn this study a method of equidistribution of a weight function for grid adaption is modified to produce a smoother grid which yields a more accurate solution. In the original scheme the weight function was estimated on each grid independently and a large variation in the values of the, weight function could generate a highly skewed and non‐uniform grid which produced large errors. In this study the weight function is smoothed by coupling neighbouring weight functions. Abrupt changes in the weight function are alleviated and a smoother grid distribution is obtained. With relatively minor modifications of the original weight function it is demonstrated in this study that the solution can be improved. The test cases presented are the one‐dimensional convection‐diffusion equation, a laminar polar cavity flow, a laminar backwardfacing step flow and a turbulent reacting sudden expansion pipe flow. Numerical efficiencies ranging from factors of five to 10 are achieved over uniform grid methods.
A finite element solutionof three‐dimensional mixed convection gas flows in horizontal chnnels using preconditioned iterative metrix methods
Authors: Einset Erik O. , Jensen Klavs F. 
Published: August 2005

AbstractAn algorithm is presented for the finite element solution of three‐dimensional mixed convection gas flows in channels heated from below. The algorithm uses Newton's method and iterative matrix methods. Two iterative solution algorithms, conjugate gradient squared (CGS) and generalized minimal residual (GMERS), are used in conjunction with a preconditioning technique that is simple to implement. The preconditioner is a subset of the full Jacobian matrix centered around the main diagonal but retaining the most fundamental axial coupling of the residual equations. A domain‐renumbering scheme that enhances the overall algorithm performance is proposed on the basis of and analysis of the preconditioner. Comparison with the frontal elimination method demonstrates that the iterative method will be faster when the front width exceeds approximately 500. Techniques for the direct assembly f the problem into a compressed sparse row storage format are demonstrated. Elimination of fixed boundary conditions is shown to decrease the size of the matrix problem by up to 30%. Finally, fluid flow solutions obtained with the numerical technique are presented. These solutions reveal complex three‐dimensional mixed convection fluid flow phenomena at low Reynolds numbers, including the reversal of the direction of longitudinal rolls in the presence of a strong recirculation in the entrance region of the channel.
Influence of skirt radius on performance of circular clarifier with density stratification
Authors: Zhou Siping , McCorquodale John A. 
Published: August 2005

AbstractA numerical model for predicting the velocity field and suspended solids distribution in a secondary circular clarifier with density difference is evaluated. The density effects are characterized by the inlet densimetric Froude number. This study focuses on the role of the reaction baffle position in the performance of the clarifiers. For a large‐radius baffle and low densimetric Froude number an important phenomenon known as the density waterfall occurs in the inlet zone of the clarifiers. This was predicted by the numerical model and confirmed by the physical model tests. This model consists of a series of conservation equations for fluid mass and momentum and sediment concentration. The turbulent stresses are calculated by use of the eddy viscosity concept and the κ–ϵ. turbulence model. The study showed that the density waterfall results in high entrainment and high recirculation. A comparison of the solids concentration distribution for a tank with a small skirt radius to that with a large skirt radius shows that small skirt radius reduces the density waterfall effect and significantly improves the clarifier performance at low densimetric Froude numbers.
An extension of Osher's Riemann solver for chemical and vibrational non‐equilibrium gas flows
Authors: Abgrall R. , Fezoui L. , Talandier J. 
Published: August 2005

AbstractIn this paper we study an extension of Osher's Riemann solver to mixtures of perfect gases whose equation of state is of the form encountered in hypersonic applications. As classically, one needs to compute the Riemann invariants of the system to evaluate Osher's numerical flux. For the case of interest here it is impossible in general to derive simple enough expressions which can lead to an efficient calculation of fluxes. The key point here is the definition of approximate Riemann invariants to alleviate this difficulty.Some of the properties of this new numerical flux are discussed. We give 1D and 2D applications to illustrate the robustness and capability of this new solver. We show by numerical examples that the main properties of Osher's solver are preserved; in particular, no entropy fix is needed even for hypersonic applications.
A numerical simulation of boundary layer effects in a shock tube
Authors: Badcock K. J. 
Published: August 2005

AbstractA numerical scheme is used to investigate boundary layer effects in a shock tube. The method consists of a mixture of Roe's approximate Riemann solver and central differences for the convective fluxes and central differences for the viscous fluxes and is implicit in one space dimension. Comparisons are made with experimental data and with solutions obtained via boundary layer equations. Examination of the calculated flow field explains the observed behaviour and highlights the approximate nature of boundary layer solutions.
A general numerical method for solution of gravity wave problems. Part 2: Steady nonlinear gravity waves
Authors: Liao S. J. 
Published: August 2005

AbstractA type of numerical scheme for 2D and 3D steady non‐linear water wave problems is described. It is based on the finite process method and is insensitive to initial solutions. The relationship between the finite process method and iterative techniques is discussed. As a numerical example the flow past a submerged vortex is solved and the results are compared with those of other authors.
Improved artificial dissipation schemes for the Euler equations
Authors: Thomadakis M. P. , Tsangaris S. 
Published: August 2005

AbstractThe influence of artificial dissipation schemes on the accuracy and stability of the numerical solution of compressible flow is extensively examined. Using an implicit central difference factored scheme, an improved form of artificial dissipation is introduced which highly reduces the errors due to numerical viscosity. A function of the local Mach number is used to scale the amount of numerical damping added into the solution according to the character of the flow in several flow regimes. The resulting scheme is validated through several inviscid flow test cases.
Adaptive h‐refinement on 3D unstructured grids for transient problems
Authors: Löhner Rainald , Baum Joseph D. 
Published: August 2005

AbstractAn adaptive finite element scheme for transient problems is presented. The classic h‐enrichment/coarsening is employed in conjunction with a tetrahedral finite element discretization in three dimensions. A mesh change is performed every n time steps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved by pre‐sorting the elements and then performing the refinement/coarsening groupwise according to the case at hand. Further reductions in CPU requirements arc realized by optimizing the identification and sorting of elements for refinement and deletion. The developed technology has been used extensively for shock‐shock and shock‐object interaction runs in a production mode. A typical example of this class of problems is given.
Navier‐Stokes computations past a prolate spheroid at incidence. II: High incidence case
Authors: Piquet J. , Queutey P. 
Published: August 2005

AbstractThe computation of incompressible three‐dimensional viscous flow is investigated. An iterative fully decoupled technique based on the fully elliptic mode is applied to the Reynolds‐averaged‐Navier‐Stokes equations (RANSE) written down in a non‐orthogonal curvilinear body‐fitted co‐ordinate system. Results of the computations are compared with experimental data past a prolate spheroid at 30° incidence.
An efficient three‐dimensional semi‐implicit finite element scheme for simulation of free surface flows
Authors: Li Y. S. , Zhan J. M. 
Published: August 2005

AbstractAn efficient semi‐implicit finite element model is proposed for the simulation of three‐dimensional flows in stratified seas. The body of water is divided into a number of layers and the two horizontal momentum equations for each layer of water are first integrated vertically. Nine‐node Lagrangian quadratic isoparametric elements are employed for spatial discretization in the horizontal domain. The time derivatives are approximated using a second‐order‐accurate semi‐implicit time‐stepping scheme. The distinguishing feature of the proposed numerical scheme is that only nodal values on the same vertical line are coupled. Two test cases for which analytic solutions are available are employed to test the proposed scheme. The test results show that the scheme is efficient and stable. A numerical experiment is also included to compare the proposed scheme with a finite difference scheme.
Computation of turbulent asymmetric wake
Authors: Tulapurkara E. G. , Vengadesan S. , Lakshminarasimhan J. 
Published: August 2005

AbstractThe development of asymmetric wake behind an aerofoil in turbulent incompressible flow has been computed using finite volume scheme for solving two‐dimensional Navier‐Stokes equations along with the k‐ε model of turbulence. The results are compared with available experimental data. It is observed that the computed shift of the point of minimum velocity with distance is sensitive to the prescribed value of the normal component of velocity at the trailing edge of the aerofoil. Making the model constant Cu as a function of streamline curvature and changing the production term in the equation for ε, has only marginal influence on the results.
Analysis of erosion behaviour in a turbocharger radial turbine
Authors: Benim A. C. , Neuhoff H. G. 
Published: August 2005

AbstractAn analysis of the erosion behaviour of a turbocharger radial turbine is presented. The solution domain includes both sides of the radial turbine scroll with double intake and the rotor channel. In the analysis a dilute gas‐particle flow assumption is employed. The gas turbulence is defined by the k‐ε model. In solving the gas phase equation, the computer code Harwell‐FLOW3D is employed, which is based on a finite volume formulation using non‐orthogonal body‐fitted structured gridding and a pressure correction method. The particle phase is described by a Lagrangian approach, while particle paths are computed deterministically, neglecting the turbulent dispersion. For the computation of particle trajectories the code PTRACK is employed, which has been developed at ABB. Computations are carried out for several particle size classes. The results show that particles are thrown back into the scroll by the rotor at high rates. This seems to be the main source of erosion effects in the scroll. It has been observed that particles are unequally distributed between the scroll sides on their re‐entry, resulting in greater erosion on one of the scroll sides. The maximum erosion along the scroll is found to be likely to occur near the scroll end.