Hermitian space-time finite elements for estuarine mass transport

Space-time finite element solutions of the convection–dispersion equation using higher-order nodal continuity and Hermitian polynomial shape functions are described. Five separate elements ranging from a complete linear element with C^0,0 nodal continuity to a complete first-order Hermitian element with C^1,1 nodal continuity are subjected to detailed analysis. Wave deformation analyses identify the source of leading or trailing edge oscillations, trailing edge oscillations being the major source of difficulty. These observations are confirmed by numerical experiments which further demonstrate the potential of higher-order nodal continuity. The performance of the complete first-order Hermitian element is quite satisfactory and measurably superior to the linear element.     

Numerical solutions for solute transport in unconfined aquifers

Two numerical methods for solving the problem of solute transport in unsteady flow in unconfined aquifers are studied. They are the method of characteristics (MOC) based on the finite difference method (FDM), and the finite element method (FEM). The FEM is further subdivided into four schemes: moving mesh, pseudo-Lagrangian (FEM1); stationary mesh, pseudo-Lagrangian (FEM2); pseudo saturated-unsaturated, Eulerian (FEM3); and non-stationary element, Eulerian (FEM4). Experiments on a one-dimensional flow case are performed to illustrate the schemes and to determine the effect of discretization on accuracy. In two-dimensional flow the above methods are compared with experimental results from a sand box model. Results indicate that for a similar degree of accuracy, the FEM requires less computational effort than the MOC. Among the four FEM schemes, FEM4 appears to be most attractive as it is the most efficient and most convenient to apply.     

A survey of some second-order difference schemes for the steady-state convection–diffusion equation

This paper presents a survey of several finite difference schemes for the steady-state convection–diffusion equation in one and two dimensions. Most difference schemes have O(h2) truncation error. The behaviour of these schemes on a one-dimensional model problem is analysed in detail, especially for the case when convection dominates diffusion. It is concluded that none of these schemes is universally second order. One recently proposed scheme is found to yield highly inaccurate solutions for the case of practical interest, i.e. when convection dominates diffusion. Extensions to two and threedimensions are also discussed.     

A transient finite element analysis of natural convection around a horizontal hot cylinder

This paper presents an advanced method for a 2-dimensional analysis of transient natural convection by finite element method. The present method, based on stream function—vorticity formulation, could get rid of numerical errors and constraint of perpendicular mesh subdivision, since we excluded a finite difference approximation of vorticity on no-slip boundaries. A considerable effect of upwind weighting function was examined. The method was successfully applied to a problem of natural convection around a horizontal hot cylinder.     

Fractional step algorithm for estuarine mass transport

A successful and economical fractional step algorithm for the convection-dispersion-reaction equation is described. Exact solutions are adopted for the reaction and convection steps, the latter by the introduction of a moving co-ordinate system. The dispersion step uses an optimized finite difference algorithm which specifically accommodates the grid non-uniformity. The excellent performance of the algorithm is confirmed by numerical experiments together with computations of the Fourier response and integrated square error characteristics.     

Thermal instability of a rotating saturated porous medium heated from below and submitted to rotation

In this work, we study the problem of onset of thermal convection in a rotating saturated porous medium heated from below. The effect of rotation is restricted to the Coriolis force, neglecting thus the centrifugal effects, the porous medium is described by Brinkman's model. The linear eigenvalue problem is solved by means of a modified Galerkin method. The behavior of the critical temperature gradient is discussed in terms of various parameters of the system for both stationary and overstable convections. Finally a weakly nonlinear analysis is provided to derive amplitude equations and to study the onset of Küppers-Lortz instability. Received 24 June 2002 / Received in final form 11 September 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: tdesaive@ulg.ac.be     

The nature of near-wall convection velocity in turbulent channel flow

A novel notion of turbulent structure the local cascade structure-is introduced to study the convection phenomenon in a turbulent channel flow. A space-time cross-correlation method is used to calculate the convection velocity. It is found that there are two characteristic convection speeds near the wall, one associated with small-scale streaks of a lower speed and another with streamwise vortices and hairpin vortices of a higher speed. The new concept of turbulent structure is powerful to illustrate the dominant role of coherent structures in the near-wall convection, and to reveal also the nature of the convection-the propagation of patterns of velocity fluctuations-which is scale-dependent.     

The real meaning of Nernst's steady diffusion layer concept under non-forced hydrodynamic conditions. A simple model based on Levich's seminal view of convection

A model accounting for the role of convection in macroscopically immobile solutions (viz., not submitted to any macroscopic flow or any density gradient) is developed to predict the resulting alterations on electrochemical experiments performed at long time durations. The model is based on a seminal idea introduced by Levich, and shows that in macroscopically still solutions microscopic chaotic motion has the same effect as an apparent diffusion coefficient that depends on the distance from the electrode, x. When the electrochemical perturbation affects only the viscous sub-layer adjacent to the electrode, this apparent diffusion coefficient varies as x⁴. The model remarkably predicts the experimental distortions of chronoamperometric currents from their ideal Cottrellian behavior. The model is thoroughly tested with success by comparing its predictions to experimental results (current and concentration profiles) obtained for the oxidation of Fe(CN)₆⁴⁻ in aqueous KCl.     

MULTIPLICATIVE SCHWARZ ALGORITHM WITH TIME STEPPING ALONG CHARACTERISTIC FOR CONVECTION DIFFUSION EQUATIONS

1. IntroductionMultiplicative SNz method, based on domain decomposition, is a powernd iterationmethods fOr solving elliptic equatinns and other stationaIy problems. A systematic theory hasbeen developed fOr elliptic finite element problerns in the past few y6ars, see l2, 5, 11, 12].But there are little works of dOmain decomPosition methods fOr time-dependence problems.In [111, Lions gives a kind of Schwarz alternating algorithIn in two subdomain case fOr heatequations and gives a converge…     

Boundary-layer flow about a vertical spinning cone under mixed thermal boundary conditions and a magnetic field

A similarity analysis was performed to investigate the laminar boundary-layer flow in the presence of a transverse magnetic field over a down-pointing and spinning cone with mixed thermal boundary conditions. Boundary layer velocity and temperature profiles were determined numerically for various values of the magnetic and spin parameters and the Prandtl number. The spin of the cone compresses the velocity profiles towards the surface by inducing an upward flow and decreases the surface temperature. The magnetic field suppresses the velocity profiles and increases the surface temperature. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter was obtained.