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Convective Terms (convective + term)
Selected AbstractsAssessment of acceleration modelling for fluid-filled porous media subjected to dynamic loadingINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2008B. Lenhof Abstract The purpose of this paper is to examine the importance of different possible simplifying approximations when performing numerical simulations of fluid-filled porous media subjected to dynamic loading. In particular, the relative importance of the various acceleration terms for both the solid and the fluid, especially the convective contribution, is assessed. The porous medium is modelled as a binary mixture of a solid phase, in the sense of a porous skeleton, and a fluid phase that represents both liquid and air in the pores. The solid particles are assumed to be intrinsically incompressible, whereas the fluid is assigned a finite intrinsic compressibility. Finite element (FE) simulations are carried out while assuming material properties and loading conditions representative for a road structure. The results show that, for the range of the material data used in the simulations, omitting the relative acceleration gives differences in the solution of the seepage velocity field, whereas omitting only the convective term does not lead to significant differences. Copyright © 2007 John Wiley & Sons, Ltd. [source] A CBS-type stabilizing algorithm for the consolidation of saturated porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005V. A. Salomoni Abstract The presented method stems from the works by Zienkiewicz and co-workers for coupled fluid/thermal problems starting from the early 1990s. They propose algorithms to overcome the difficulties connected to the application of the FEM to the area of fluid mechanics, which include the problems of singular behaviour in incompressibility and the problems connected to convective terms. The major step forward was to introduce the concept of characteristic lines (the particle paths in a simple convection situation): for a class of problems with a single scalar variable, the equations in the characteristic co-ordinates regain self-adjointness. The procedure is called characteristic based split algorithm (CBS). We use here a CBS-type procedure for a saturated deformable elastic porous medium, in which the fluid velocity is governed by Darcy's equation (which comes directly from Navier,Stokes ones). The physical,mathematical model is a fully coupled one and is here used to study an incompressible flow inside a continuum with incompressible solid grains. The power of the adopted algorithm is to treat the basic equations in their strong form and to transform a usual ,u,p' problem into a ,u,v,p' one, where u generally indicates the displacement of the solid matrix and p and v the pressure and velocity of the fluid, respectively. Attention is focused on the expression of Darcy's velocity which is considered as the starting point of the algorithm. The accuracy of the scheme is checked by comparing the present predictions in a typical consolidation test with available analytical and numerical u,p solutions. A good fitting among different results has been obtained. It is further shown that the procedure eliminates the oscillations at the onset of consolidation, typical for many schemes. The FEM code Ed-Multifield has been used for implementing and testing the procedure. Copyright © 2005 John Wiley & Sons, Ltd. [source] Performance of very-high-order upwind schemes for DNS of compressible wall-turbulenceINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2010G. A. Gerolymos Abstract The purpose of the present paper is to evaluate very-high-order upwind schemes for the direct numerical simulation (DNS) of compressible wall-turbulence. We study upwind-biased (UW) and weighted essentially nonoscillatory (WENO) schemes of increasingly higher order-of-accuracy (J. Comp. Phys. 2000; 160:405,452), extended up to WENO17 (AIAA Paper 2009-1612, 2009). Analysis of the advection,diffusion equation, both as ,x,0 (consistency), and for fixed finite cell-Reynolds-number Re,x (grid-resolution), indicates that the very-high-order upwind schemes have satisfactory resolution in terms of points-per-wavelength (PPW). Computational results for compressible channel flow (Re,[180, 230]; M,CL,[0.35, 1.5]) are examined to assess the influence of the spatial order of accuracy and the computational grid-resolution on predicted turbulence statistics, by comparison with existing compressible and incompressible DNS databases. Despite the use of baseline O(,t2) time-integration and O(,x2) discretization of the viscous terms, comparative studies of various orders-of-accuracy for the convective terms demonstrate that very-high-order upwind schemes can reproduce all the DNS details obtained by pseudospectral schemes, on computational grids of only slightly higher density. Copyright © 2009 John Wiley & Sons, Ltd. [source] Two-dimensional prediction of time dependent, turbulent flow around a square cylinder confined in a channelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2010M. Raisee Abstract This paper presents two-dimensional and unsteady RANS computations of time dependent, periodic, turbulent flow around a square block. Two turbulence models are used: the Launder,Sharma low-Reynolds number k,, model and a non-linear extension sensitive to the anisotropy of turbulence. The Reynolds number based on the free stream velocity and obstacle side is Re=2.2×104. The present numerical results have been obtained using a finite volume code that solves the governing equations in a vertical plane, located at the lateral mid-point of the channel. The pressure field is obtained with the SIMPLE algorithm. A bounded version of the third-order QUICK scheme is used for the convective terms. Comparisons of the numerical results with the experimental data indicate that a preliminary steady solution of the governing equations using the linear k,, does not lead to correct flow field predictions in the wake region downstream of the square cylinder. Consequently, the time derivatives of dependent variables are included in the transport equations and are discretized using the second-order Crank,Nicolson scheme. The unsteady computations using the linear and non-linear k,, models significantly improve the velocity field predictions. However, the linear k,, shows a number of predictive deficiencies, even in unsteady flow computations, especially in the prediction of the turbulence field. The introduction of a non-linear k,, model brings the two-dimensional unsteady predictions of the time-averaged velocity and turbulence fields and also the predicted values of the global parameters such as the Strouhal number and the drag coefficient to close agreement with the data. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010Roberto Croce Abstract In this paper we present a three-dimensional Navier,Stokes solver for incompressible two-phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third-order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second-order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first-order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three-dimensional results with those of quasi-two-dimensional and two-dimensional simulations. This comparison clearly shows the need for full three-dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. Copyright © 2009 John Wiley & Sons, Ltd. [source] Systematic derivation of an asymptotic model for the dynamics of curved viscous fibersMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2008Satyananda Panda Abstract This paper presents a slender body theory for the dynamics of a curved inertial viscous Newtonian fiber. Neglecting surface tension and temperature dependence, the fiber flow is modeled as a three-dimensional free boundary value problem in terms of instationary incompressible Navier,Stokes equations. From regular asymptotic expansions in powers of the slenderness parameter, leading-order balance laws for mass (cross-section) and momentum are derived that combine the unrestricted motion of the fiber centerline with the inner viscous transport. The physically reasonable form of the one-dimensional fiber model results thereby from the introduction of the intrinsic velocity that characterizes the convective terms. For the numerical investigation of the viscous, gravitational and rotational effects on the fiber dynamics, a finite volume approach on a staggered grid with implicit upwind flux discretization is applied. Copyright © 2007 John Wiley & Sons, Ltd. [source] A simulation of the non-isothermal resin transfer molding processPOLYMER ENGINEERING & SCIENCE, Issue 12 2000Vincenza Antonucci A simulation of the non-isothermal resin transfer molding manufacturing process accounting for both the filling and the consolidation stage has been developed. The flow of an exothermally reactive resin through a porous medium has been analyzed with reference to the Darcy law, allowing for the chemorheological properties of the reacting resin. Thermal profile calculations have been extended to a three phase domain, namely the mold, the dry preform and the filled preform. The mold has been included in order to evaluate the thermal inertial effects. The energy balance equation includes the reaction term together with the conductive and convective terms, and particular attention has been devoted to setting the thermal boundary condition at the flow front surface. The moving boundary condition has been derived by a jump equation. The simulation performance has been tested by comparing the predicted temperature profiles with experimental data from literature. Further numerical analysis assessed the relevance of using the jump equation at the flow front position for both filling time and thermal profile determination. [source] A new update procedure for internal variables in an ALE-description of rolling contactPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005M. Ziefle In FEM analysis of rolling contact problems Arbitrary Lagrangian-Eulerian (ALE) methods are the state of the art. These methods allow mesh refinements concentrated to the contact region and offer a time independent formulation of stationary elastic rolling. The relative-kinematic description of rolling leads to a relative motion between the finite element mesh and the material points. Thus in the case of inelastic material behavior history dependent constitutive equations contain convective terms. The handling of these convective terms is performed by a so called fractional step method. A material step is followed by a convection step. In the first step the nonlinear solid contact problem is resolved by neglecting the convective terms. In the following step the internal variables are transported on the streamlines of the material particles by solving the advection equation via a time-discontinuous Galerkin method. This update procedure is demonstrated on a typical FEM-tire model. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [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] | ||||||||||