Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. and third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,

Some aspects of lubrication in heavy regimes: thermal effects, stability and turbulence

In this work, a combination of numerical methods applied to thermohydrodynamic lubrication problems with cavitation is presented. It should be emphasized the difficulty of the nonlinear mathematical coupled model involving a free boundary problem, but also the simplicity of the algorithms employed to solve it. So, finite element discretizations for the hydrodynamic and thermal equations combined with upwind techniques for the convection terms and duality methods for nonlinear features are proposed. Additionally, a model describing the movement of the shaft is provided. Considering the shaft as a rigid body this model will consist of an ODE system relating acceleration of the center of gravity and external and pressure loads. The numerical experiments of mechanical stability try to clarify the position of the neutral stability curve. Finally, a rotating machine for ship propulsion involving both axial and radial bearings operating with nonconventional lubricants (seawater to avoid environmental pollution) is analyzed by using laminar and turbulent inertial flows.

Heat transfer and entropy generation optimization of forced convection in a porous-saturated duct of rectangular cross-section

We investigate analytically the first and the second law characteristics of fully developed forced convection inside a porous-saturated duct of rectangular cross-section. The Darcy-Brinkman flow model is employed. Three different types of thermal boundary conditions are examined. Expressions for the Nusselt number, the Bejan number, and the dimensionless entropy generation rate are presented in terms of the system parameters. The conclusions of this analytical study will make it possible to compare, evaluate, and optimize alternative rectangular duct design options in terms of heat transfer, pressure drop, and entropy generation. (c) 2006 Elsevier Ltd. All rights reserved.

Commentary: Using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyanaa in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application. (C) 2000 Wiley-Liss Inc. and the American Pharmaceutical Association J Pharm Sci 89:1579-1586, 2000.

Anisotropic convection model for the earth's mantle

The paper presents a theory for modeling flow in anisotropic, viscous rock. This theory has originally been developed for the simulation of large deformation processes including the folding and kinking of multi-layered visco-elastic rock (Muhlhaus et al. [1,2]). The orientation of slip planes in the context of crystallographic slip is determined by the normal vector - the director - of these surfaces. The model is applied to simulate anisotropic mantle convection. We compare the evolution of flow patterns, Nusselt number and director orientations for isotropic and anisotropic rheologies. In the simulations we utilize two different finite element methodologies: The Lagrangian Integration Point Method Moresi et al [8] and an Eulerian formulation, which we implemented into the finite element based pde solver Fastflo (www.cmis.csiro.au/Fastflo/). The reason for utilizing two different finite element codes was firstly to study the influence of an anisotropic power law rheology which currently is not implemented into the Lagrangian Integration point scheme [8] and secondly to study the numerical performance of Eulerian (Fastflo)- and Lagrangian integration schemes [8]. It turned out that whereas in the Lagrangian method the Nusselt number vs time plot reached only a quasi steady state where the Nusselt number oscillates around a steady state value the Eulerian scheme reaches exact steady states and produces a high degree of alignment (director orientation locally orthogonal to velocity vector almost everywhere in the computational domain). In the simulations emergent anisotropy was strongest in terms of modulus contrast in the up and down-welling plumes. Mechanisms for anisotropic material behavior in the mantle dynamics context are discussed by Christensen [3]. The dominant mineral phases in the mantle generally do not exhibit strong elastic anisotropy but they still may be oriented by the convective flow. Thus viscous anisotropy (the main focus of this paper) may or may not correlate with elastic or seismic anisotropy.

Theoretical and numerical study of thermomagnetic convection in magnetic fluids

In this thesis, the magnetic field control of convection instabilities and heat and mass transfer processesin magnetic fluids have been investigated by numerical simulations and theoretical considerations. Simulation models based on finite element and finite volume methods have been developed. In addition to standard conservation equations, themagnetic field inside the simulation domain is calculated from Maxwell equations and the necessary terms to take into account for the magnetic body force and magnetic dissipation have been added to the equations governing the fluid motion.Numerical simulations of magnetic fluid convection near the threshold supportedexperimental observations qualitatively. Near the onset of convection the competitive action of thermal and concentration density gradients leads to mostly spatiotemporally chaotic convection with oscillatory and travelling wave regimes, previously observed in binary mixtures and nematic liquid crystals. In many applications of magnetic fluids, the heat and mass transfer processes including the effects of external magnetic fields are of great importance. In addition to magnetic fluids, the concepts and the simulation models used in this study may be applied also to the studies of convective instabilities in ordinary fluids as well as in other binary mixtures and complex fluids.

A generalized 1D particle transport method for convection diffusion reaction model

This work is devoted to the development of numerical method to deal with convection diffusion dominated problem with reaction term, non - stiff chemical reaction and stiff chemical reaction. The technique is based on the unifying Eulerian - Lagrangian schemes (particle transport method) under the framework of operator splitting method. In the computational domain, the particle set is assigned to solve the convection reaction subproblem along the characteristic curves created by convective velocity. At each time step, convection, diffusion and reaction terms are solved separately by assuming that, each phenomenon occurs separately in a sequential fashion. Moreover, adaptivities and projection techniques are used to add particles in the regions of high gradients (steep fronts) and discontinuities and transfer a solution from particle set onto grid point respectively. The numerical results show that, the particle transport method has improved the solutions of CDR problems. Nevertheless, the method is time consumer when compared with other classical technique e.g., method of lines. Apart from this advantage, the particle transport method can be used to simulate problems that involve movingsteep/smooth fronts such as separation of two or more elements in the system.

Les oscillations torsionnelles dans la zone de convection solaire

Nous analysons les oscillations torsionnelles se développant dans une simulation magnétohydrodynamique de la zone de convection solaire produisant des champs magnétiques de type solaire (champs axisymétriques subissant des inversions de polarités régulières sur des échelles temporelles décadaires). Puisque ces oscillations sont également similaires à celles observées dans le Soleil, nous analysons les dynamiques zonales aux grandes échelles. Nous séparons donc les termes aux grandes échelles (force de Coriolis exercée sur la circulation méridienne et les champs magnétiques aux grandes échelles) de ceux aux petites échelles (les stress de Reynolds et de Maxwell). En comparant les flux de moments cinétiques entre chacune des composantes, nous nous apercevons que les oscillations torsionnelles sont maintenues par l’écoulement méridien aux grandes échelles, lui même modulé par les champs magnétiques. Une analyse d’échange d’énergie confirme ce résultat, puisqu’elle montre que seul le terme comprenant la force de Coriolis injecte de l’énergie dans l’écoulement. Une analyse de la dynamique rotationnelle ayant lieu à la limite de la zone stable et de la zone de convection démontre que celle-ci est fortement modifiée lors du passage de la base des couches convectives à la base de la fine tachocline s’y formant juste en-dessous. Nous concluons par une discussion au niveau du mécanisme de saturation en amplitude dans la dynamo s’opérant dans la simulation ainsi que de la possibilité d’utiliser les oscillations torsionnelles comme précurseurs aux cycles solaires à venir.

Precipitating convection in cold air: virtual potential temperature structure

Simulations of precipitating convection are used to illustrate the importance of the turbulent kinetic energy (TKE) budget in determining the virtual potential-temperature structure of the convecting atmosphere. Two sets of simulations are presented: in one the surface temperature was increased to simulate cold air flowing over a warmer surface and in the second a cooling profile, representing cold-air advection, was imposed. It is shown that the terms in the TKE budgets for both sets of simulations scale in the same way, but that the non-dimensional profiles are different. It is suggested that this is associated with the effects of sublimation of ice. It is shown that the magnitudes of the transport and precipitation terms in the virtual potential temperature budget are determined by the scaling of the TKE budget. Some implications of these results for parametrizations of moist convection are discussed. Copyright © 2007 Royal Meteorological Society

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.

Plasma structure within poleward-moving cusp/cleft auroral transients: EISCAT Svalbard radar observations and an explanation in terms of large local time extent of events

We report high-resolution observations of the southward-IMF cusp/cleft ionosphere made on December 16th 1998 by the EISCAT (European incoherent scatter) Svalbard radar (ESR), and compare them with observations of dayside auroral luminosity, as seen at a wavelength of 630 nm by a meridian scanning photometer at Ny Alesund, and of plasma flows, as seen by the CUTLASS (co-operative UK twin location auroral sounding system) Finland HF radar. The optical data reveal a series of poleward-moving transient red-line (630 nm) enhancements, events that have been associated with bursts in the rate of magnetopause reconnection generating new open flux. The combined observations at this time have strong similarities to predictions of the effects of soft electron precipitation modulated by pulsed reconnection, as made by Davis and Lockwood (1996); however, the effects of rapid zonal flow in the ionosphere, caused by the magnetic curvature force on the newly opened field lines, are found to be a significant additional factor. In particular, it is shown how enhanced plasma loss rates induced by the rapid convection can explain two outstanding anomalies of the 630 nm transients, namely how minima in luminosity form between the poleward-moving events and how events can re-brighten as they move poleward. The observations show how cusp/cleft aurora and transient poleward-moving auroral forms appear in the ESR data and the conditions which cause enhanced 630 nm emission in the transients: they are an important first step in enabling the ESR to identify these features away from the winter solstice when supporting auroral observations are not available.

Ionospheric convection response to slow, strong variations in a northward interplanetary magnetic field: A case study for January 14, 1988

We analyze ionospheric convection patterns over the polar regions during the passage of an interplanetary magnetic cloud on January 14, 1988, when the interplanetary magnetic field (IMF) rotated slowly in direction and had a large amplitude. Using the assimilative mapping of ionospheric electrodynamics (AMIE) procedure, we combine simultaneous observations of ionospheric drifts and magnetic perturbations from many different instruments into consistent patterns of high-latitude electrodynamics, focusing on the period of northward IMF. By combining satellite data with ground-based observations, we have generated one of the most comprehensive data sets yet assembled and used it to produce convection maps for both hemispheres. We present evidence that a lobe convection cell was embedded within normal merging convection during a period when the IMF By and Bz components were large and positive. As the IMF became predominantly northward, a strong reversed convection pattern (afternoon-to-morning potential drop of around 100 kV) appeared in the southern (summer) polar cap, while convection in the northern (winter) hemisphere became weak and disordered with a dawn-to-dusk potential drop of the order of 30 kV. These patterns persisted for about 3 hours, until the IMF rotated significantly toward the west. We interpret this behavior in terms of a recently proposed merging model for northward IMF under solstice conditions, for which lobe field lines from the hemisphere tilted toward the Sun (summer hemisphere) drape over the dayside magnetosphere, producing reverse convection in the summer hemisphere and impeding direct contact between the solar wind and field lines connected to the winter polar cap. The positive IMF Bx component present at this time could have contributed to the observed hemispheric asymmetry. Reverse convection in the summer hemisphere broke down rapidly after the ratio |By/Bz| exceeded unity, while convection in the winter hemisphere strengthened. A dominant dawn-to-dusk potential drop was established in both hemispheres when the magnitude of By exceeded that of Bz, with potential drops of the order of 100 kV, even while Bz remained northward. The later transition to southward Bz produced a gradual intensification of the convection, but a greater qualitative change occurred at the transition through |By/Bz| = 1 than at the transition through Bz = 0. The various convection patterns we derive under northward IMF conditions illustrate all possibilities previously discussed in the literature: nearly single-cell and multicell, distorted and symmetric, ordered and unordered, and sunward and antisunward.

Dayside ionospheric convection changes in response to long-period interplanetary Magnetic field oscillations: Determination of the ionospheric phase velocity

Ground magnetic field perturbations recorded by the CANOPUS magnetometer network in the 7 to 13 MLT sector are used to examine how reconfigurations of the dayside polar ionospheric flow take place in response to north-south changes of the IMF. During the 6-hour interval in question IMF Bz oscillates between ±7 nT with about a 1-hour period. Corresponding variations in the ground magnetic disturbance are observed which we infer are due to changes in ionospheric flow. Cross correlation of the data obtained from two ground stations at 73.5° magnetic latitude, but separated by ∼2 hours in MLT, shows that changes in the flow are initiated in the prenoon sector (∼10 MLT) and then spread outward toward dawn and dusk with a phase speed of ∼5 km s−1 over the longitude range ∼8 to 12 MLT, slowing to ∼2 km s−1 outside this range. Cross correlating the data from these ground stations with IMP 8 IMF Bz records produces a MLT variation in the ground response delay relative to the IMF which is compatible with these deduced phase speeds. We interpret these observations in terms of the ionospheric response to the onset, expansion and decay of magnetic reconnection at the dayside magnetopause.

On flow reversal boundaries and transpolar voltage in average models of high-latitude convection

The implications of polar cap expansions, contractions and movements for empirical models of high-latitude plasma convection are examined. Some of these models have been generated by directly averaging flow measurements from large numbers of satellite passes or radar scans; others have employed more complex means to combine data taken at different times into large-scale patterns of flow. In all cases, the models have implicitly adopted the assumption that the polar cap is in steady state: they have all characterized the ionospheric flow in terms of the prevailing conditions (e.g. the interplanetary magnetic field and/or some index of terrestrial magnetic activity) without allowance for their history. On long enough time scales, the polar cap is indeed in steady state but on time scales shorter than a few hours it is not and can oscillate in size and position. As a result, the method used to combine the data can influence the nature of the convection reversal boundary and the transpolar voltage in the derived model. This paper discusses a variety of effects due to time-dependence in relation to some ionospheric convection models which are widely applied. The effects are shown to be varied and to depend upon the procedure adopted to compile the model.