Home About us Contact
|
Home About us Contact | ||
|
|
||
Navier
Kinds of Navier Selected AbstractsParallelization and scalability of a spectral element channel flow solver for incompressible Navier,Stokes equationsCONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 10 2007C. W. Hamman Abstract Direct numerical simulation (DNS) of turbulent flows is widely recognized to demand fine spatial meshes, small timesteps, and very long runtimes to properly resolve the flow field. To overcome these limitations, most DNS is performed on supercomputing machines. With the rapid development of terascale (and, eventually, petascale) computing on thousands of processors, it has become imperative to consider the development of DNS algorithms and parallelization methods that are capable of fully exploiting these massively parallel machines. A highly parallelizable algorithm for the simulation of turbulent channel flow that allows for efficient scaling on several thousand processors is presented. A model that accurately predicts the performance of the algorithm is developed and compared with experimental data. The results demonstrate that the proposed numerical algorithm is capable of scaling well on petascale computing machines and thus will allow for the development and analysis of high Reynolds number channel flows. Copyright © 2007 John Wiley & Sons, Ltd. [source] Numerical simulation of drop deformation and breakup in shear flowHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 5 2007Lin Chang-Zhi Abstract Three-dimensional numerical simulation of the deformation and breakup of an isolated liquid drop suspended in immiscible viscous fluid under shear flow was performed with diffuse interface method. The governing equations of the model were described by Navier, Stokes, Cahn, Hilliard equations. The surface tension was treated as a modified stress. In this paper, a uniform staggered Cartesian grid was used. The transient Navier, Stokes equations were solved by an approximation projection method based on pressure increment formulation, while the Cahn, Hilliard equations were solved by a nonlinear full approximation multigrid method. The numerical results of the drop deformation and breakup were in good agreement with the experimental measurements. Therefore, the present model could be perfectly applied to study the mechanism of drop deformation and breakup. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(5): 286, 294, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20160 [source] Numerical simulation of natural convection heat transfer in the open space between two horizontal circular planesHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 6 2001Hideki Tokanai Abstract Numerical simulations were conducted for natural convection heat transfer in a narrow gap between two horizontal plates in air. The lower plate is an infinite plate with a circular heating zone. The upper one is the bottom of a vertical cylinder, which is placed right above the circular heated plate and kept at room temperature. A set of Navier,Stokes equations and an energy equation are analyzed for a variety of combinations of gap clearance and Rayleigh number. The calculated average heat transfer values are shown to be in good agreement with the experimentally obtained ones reported in a previous paper. From the obtained isotherms, streamlines, and local Nusselt numbers, it is found that two types of convection appear in the gap space according to the conditions of Rayleigh number and gap clearance: one is a simple convection due to a single renewal flow which replaces heated air with ambient air and the other is a combined convection due to several vortex flows and a renewal flow. Furthermore, the flow rate of each flow controls the rate of heat transfer from the limited area which is covered by each flow. From this fact, the validity of the previously proposed heat transfer correlation is briefly discussed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(6): 485,502, 2001 [source] Numerical simulation of overbank processes in topographically complex floodplain environmentsHYDROLOGICAL PROCESSES, Issue 4 2003A. P. Nicholas Abstract This article presents results from an investigation of the hydraulic characteristics of overbank flows on topographically-complex natural river floodplains. A two-dimensional hydraulic model that solves the depth-averaged shallow water form of the Navier,Stokes equations is used to simulate an overbank flow event within a multiple channel reach of the River Culm, Devon, UK. Parameterization of channel and floodplain roughness by the model is evaluated using monitored records of main channel water level and point measurements of floodplain flow depth and unit discharge. Modelled inundation extents and sequences are assessed using maps of actual inundation patterns obtained using a Global Positioning System, observational evidence and ground photographs. Simulation results suggest a two-phase model of flooding at the site, which seems likely to be representative of natural floodplains in general. Comparison of these results with previous research demonstrates the complexity of overbank flows on natural river floodplains and highlights the limitations of laboratory flumes as an analogue for these environments. Despite this complexity, frequency distributions of simulated depth, velocity and unit discharge data closely follow a simple gamma distribution model, and are described by a shape parameter (,) that exhibits clear systematic trends with changing discharge and floodplain roughness. Such statistical approaches have the potential to provide the basis for computationally efficient flood routing and overbank sedimentation models. Copyright © 2002 John Wiley & Sons, Ltd. [source] Numerical solutions for flow in porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2003J.G. Wang Abstract A numerical approach is proposed to model the flow in porous media using homogenization theory. The proposed concept involves the analyses of micro-true flow at pore-level and macro-seepage flow at macro-level. Macro-seepage and microscopic characteristic flow equations are first derived from the Navier,Stokes equation at low Reynolds number through a two-scale homogenization method. This homogenization method adopts an asymptotic expansion of velocity and pressure through the micro-structures of porous media. A slightly compressible condition is introduced to express the characteristic flow through only characteristic velocity. This characteristic flow is then numerically solved using a penalty FEM scheme. Reduced integration technique is introduced for the volumetric term to avoid mesh locking. Finally, the numerical model is examined using two sets of permeability test data on clay and one set of permeability test data on sand. The numerical predictions agree well with the experimental data if constraint water film is considered for clay and two-dimensional cross-connection effect is included for sand. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical modelling of fluid flow in microscopic images of granular materialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2002E. Masad Abstract A program for the simulation of two-dimensional (2-D) fluid flow at the microstructural level of a saturated anisotropic granular medium is presented. The program provides a numerical solution to the complete set of Navier,Stokes equations without a priori assumptions on the viscous or convection components. This is especially suited for the simulation of the flow of fluids with different density and viscosity values and for a wide range of granular material porosity. The analytical solution for fluid flow in a simple microstructure of porous medium is used to verify the computer program. Subsequently, the flow field is computed within microscopic images of granular material that differ in porosity, particle size and particle shape. The computed flow fields are shown to follow certain paths depending on air void size and connectivity. The permeability tensor coefficients are derived from the flow fields, and their values are shown to compare well with laboratory experimental data on glass beads, Ottawa sand and silica sands. The directional distribution of permeability is expressed in a functional form and its anisotropy is quantified. Permeability anisotropy is found to be more pronounced in the silica sand medium that consists of elongated particles. Copyright © 2001 John Wiley & Sons, Ltd. [source] The moment-of-fluid method in actionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2009Hyung Taek Ahn Abstract The moment-of-fluid (MOF) method is a new volume-tracking method that accurately treats evolving material interfaces. The MOF method uses moment data, namely the material volume fraction, as well as the centroid, for a more accurate representation of the material configuration, interfaces and concomitant volume advection. In contrast, the volume-of-fluid method uses only volume fraction data for interface reconstruction and advection. Based on the moment data for each material, the material interfaces are reconstructed with second-order spatial accuracy in a strictly conservative manner. The MOF method is coupled with a stabilized finite element incompressible Navier,Stokes solver for two materials. The effectiveness of the MOF method is demonstrated with a free-surface dam-break and a two-material Rayleigh,Taylor problem. Copyright © 2008 John Wiley & Sons, Ltd. [source] FOIST: Fluid,object interaction subcomputation techniqueINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2009V. Udoewa Abstract Our target is to develop computational techniques for studying aerodynamic interactions between multiple objects. The computational challenge is to predict the dynamic behavior and path of the object, so that separation (the process of objects relatively falling or moving away from each other) is safe and effective. This is a very complex problem because it has an unsteady, 3D nature and requires the solution of complex equations that govern the fluid dynamics (FD) of the object and the aircraft together, with their relative positions changing in time. Large-scale 3D FD simulations require a high computational cost. Not only must one solve the time-dependent Navier,Stokes equations governing the fluid flow, but also one must handle the equations of motion of the object as well as the treatment of the moving domain usually treated as a type of pseudo-solid. These costs include mesh update methods, distortion-limiting techniques, and remeshing and projection tactics. To save computational costs, point force calculations have been performed in the past. This paper presents a hybrid between full mesh-moving simulations and the point force calculation. This mesh-moving alternative is called FOIST: fluid,object subcomputation interaction technique. Copyright © 2009 John Wiley & Sons, Ltd. [source] A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2007V. G. Ferreira Abstract This paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier,Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110:171,186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199,210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Numerical prediction of the hydrodynamic performance of a centrifugal pump in cavitating flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2007Jun Li Abstract A computational modelling for the prediction of the hydrodynamic performance of a centrifugal pump in cavitating flows is presented in this paper. The cavitation model is implemented in a viscous Reynolds-averaged Navier,Stokes solver. The cavity interface and shape are determined using an iterative procedure matching the cavity surface to a constant pressure boundary. The pressure distribution, as well as its gradient on the wall, is taken into account in updating the cavity shape iteratively. Numerical validation of the present cavitation model and algorithms is performed on different headform/cylinder bodies for a range of cavitation numbers through comparing with the experimental data. Flow characteristics trends associated with off-design flow and twin cavities in the blade channel are observed using the presented cavitation prediction. The rapid drop in head coefficient at low cavitation number is captured for two different flow coefficients. Local flow field solution illustrates the principle physical mechanisms associated with the onset of breakdown. Copyright © 2006 John Wiley & Sons, Ltd. [source] Numerical stability of unsteady stream-function vorticity calculationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2003E. Sousa Abstract The stability of a numerical solution of the Navier,Stokes equations is usually approached by con- sidering the numerical stability of a discretized advection,diffusion equation for either a velocity component, or in the case of two-dimensional flow, the vorticity. Stability restrictions for discretized advection,diffusion equations are a very serious constraint, particularly when a mesh is refined in an explicit scheme, so an accurate understanding of the numerical stability of a discretization procedure is often of equal or greater practical importance than concerns with accuracy. The stream-function vorticity formulation provides two equations, one an advection,diffusion equation for vorticity and the other a Poisson equation between the vorticity and the stream-function. These two equations are usually not coupled when considering numerical stability. The relation between the stream-function and the vorticity is linear and so has, in principle, an exact inverse. This allows an algebraic method to link the interior and the boundary vorticity into a single iteration scheme. In this work, we derive a global time-iteration matrix for the combined system. When applied to a model problem, this matrix formulation shows differences between the numerical stability of the full system equations and that of the discretized advection,diffusion equation alone. It also gives an indication of how the wall vorticity discretization affects stability. Despite the added algebraic complexity, it is straightforward to use MATLAB to carry out all the matrix operations. Copyright © 2003 John Wiley & Sons, Ltd. [source] Simulation technique for wave generationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2003S. Aliabadi Abstract In this paper, we present a new finite element technique for simulation of water waves impacting on floating structures. The emphasis will be on the numerical methods for water wave generation and propagation. In our approach, the governing equations are the Navier,Stokes equations written for two incompressible fluids. An interface function with two distinct values serves as a marker identifying the location of the free-surface. This function is transported throughout the computational domain with a time-dependent advection equation. The stabilized finite element formulations are written and integrated in an arbitrary Lagrangian,Eulerian domain. This allows us to handle the motion of the physical boundaries, such as the wave generator surface by moving the computational nodes. In the mesh-moving scheme, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements for each computational node. The numerical examples include 3D wave generation and wave breaking as they approach the coast, and the waves impacting on near-shore support columns. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical stability and error analysis for the incompressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2002S. Prudhomme Abstract This paper describes a strategy to control errors in finite element approximations of the time-dependent incompressible Navier,Stokes equations. The approach involves estimating the errors due to the discretization in space, using information from the residuals in the momentum and continuity equations. Following a numerical stability analysis of channel flows past a cylinder, it is concluded that the errors due to the residual in the continuity equation should be carefully controlled since it appears to be the source of unphysical perturbations artificially created by the spatial discretization. The performance of the adaptive strategy is then tested for lid-driven oblique cavity flows. Copyright © 2002 John Wiley & Sons, Ltd. [source] A priori pivoting in solving the Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002S. Ų. Wille Abstract Mixed finite element formulations of incompressible Navier,Stokes Equations leads to non-positive definite algebraic systems inappropriate for iterative solution techniques. However, introducing a suitable preconditioner, the mixed finite element equation system becomes positive definite and solvable by iterative techniques. The present work suggests a priori pivoting sequences for parallel and serial implementations of incomplete Gaussian factorization. Tests are performed for the driven cavity problem in two and three dimensions. Copyright © 2002 John Wiley & Sons, Ltd. [source] Adaptive ICT procedure for non-linear seepage flows with free surface in porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2002N. H. Sharif Abstract This paper focuses on adaptive finite element (FE)-methods for computation of the motion of viscous fluid interfaces fundamentally encountered in multiphase flow problems in porous media. An interface capturing technique (ICT)-procedure is formulated with a stabilized finite element scheme in a Eulerian framework to solve the two-dimensional (2D) and three-dimensional (3D) Navier,Stokes equation in porous media. Global mesh refinements of the discretized domain and local mesh refinements in the vicinity of the interface are used for the spatial discretization. The ICT is embedded into the finite element scheme by adding an extra advection equation and an additional unbounded degree of freedom to the number of the unknowns. Problems of non-linear free surface seepage flow in earth-fill dams are simulated in order to validate the performance of the FE-ICT. Computations for steady non-linear seepage flows in 2D and 3D are obtained for homogenous, isotropic and isothermal porous media. Copyright © 2002 John Wiley & Sons, Ltd. [source] CBS versus GLS stabilization of the incompressible Navier,Stokes equations and the role of the time step as stabilization parameterINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2002R. Codina Abstract In this work we compare two apparently different stabilization procedures for the finite element approximation of the incompressible Navier,Stokes equations. The first is the characteristic-based split (CBS). It combines the characteristic Galerkin method to deal with convection dominated flows with a classical splitting technique, which in some cases allows us to use equal velocity,pressure interpolations. The second approach is the Galerkin-least-squares (GLS) method, in which a least-squares form of the element residual is added to the basic Galerkin equations. It is shown that both formulations display similar stabilization mechanisms, provided the stabilization parameter of the GLS method is identified with the time step of the CBS approach. This identification can be understood from a formal Fourier analysis of the linearized problem. Copyright © 2001 John Wiley & Sons, Ltd. [source] A control analysis of interaction problem by fluid forceINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2001Shoichiro Kato Abstract This paper presents a control analysis of displacement for a building. To control the vertical displacement of the building, control device of multi-balloons with water inside is introduced on the friction piles. Coupling through the water, soil, balloon and pile, the interaction problem is numerically solved. The soil is assumed to be a linear elastic body. The balloon and pile are also modelled as linear elastic truss and rigid-frame components. The water is assumed to be the two-dimensional incompressible Navier,Stokes flow. All components are discretized by the finite element method in space. The control analysis of vertical displacement by fluid force is performed for the purpose of keeping the building horizontal. One of the optimal control theory, the so-called Sakawa,Shindo method, is applied for the control analysis. Using this method, control flux of the water is determined so that position at the top of the balloon comes to be close to the objective position. Copyright © 2001 John Wiley & Sons, Ltd. [source] Comparison of three second-order accurate reconstruction schemes for 2D Euler and Navier,Stokes compressible flows on unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2001N. P. C. Marques Abstract This paper reports an intercomparison of three second-order accurate reconstruction schemes to predict 2D steady-state compressible Euler and Navier,Stokes flows on unstructured meshes. The schemes comprise one monotone slope limiter (Barth and Jespersen, A1AA Paper 89-0366, 1989) and two approximately monotone methods: the slope limiter due to Venkatakrishnan and a data-dependent weighting least-squares procedure (Gooch, Journal of Computational Physics, 1997; 133:6,17). In addition to the 1D scalar wave problem, comparisons were performed under two inviscid test cases: a supersonic 10° ramp and a supersonic bump; and two viscous laminar compressible flow cases: the Blasius boundary layer and a double-throated nozzle. The data-dependent oscillatory behaviour is found to be dependent on a user-supplied constant. The three schemes are compared in terms of accuracy and computational efficiency. The results show that the data-dependent procedure always returns a numerical steady-state solution, more accurate than the ones returned by the slope limiters. Its use for Navier,Stokes flow calculations is recommended. Copyright © 2001 John Wiley & Sons, Ltd. [source] An embedded Dirichlet formulation for 3D continuaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2010A. Gerstenberger Abstract This paper presents a new approach for imposing Dirichlet conditions weakly on non-fitting finite element meshes. Such conditions, also called embedded Dirichlet conditions, are typically, but not exclusively, encountered when prescribing Dirichlet conditions in the context of the eXtended finite element method (XFEM). The method's key idea is the use of an additional stress field as the constraining Lagrange multiplier function. The resulting mixed/hybrid formulation is applicable to 1D, 2D and 3D problems. The method does not require stabilization for the Lagrange multiplier unknowns and allows the complete condensation of these unknowns on the element level. Furthermore, only non-zero diagonal-terms are present in the tangent stiffness, which allows the straightforward application of state-of-the-art iterative solvers, like algebraic multigrid (AMG) techniques. Within this paper, the method is applied to the linear momentum equation of an elastic continuum and to the transient, incompressible Navier,Stokes equations. Steady and unsteady benchmark computations show excellent agreement with reference values. The general formulation presented in this paper can also be applied to other continuous field problems. Copyright © 2009 John Wiley & Sons, Ltd. [source] Fixed-grid fluid,structure interaction in two dimensions based on a partitioned Lattice Boltzmann and p -FEM approachINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009S. Kollmannsberger Abstract Over the last decade the Lattice Boltzmann method, which was derived from the kinetic gas theory, has matured as an efficient approach for solving Navier,Stokes equations. The p -FEM approach has proved to be highly efficient for a variety of problems in the field of structural mechanics. Our goal is to investigate the validity and efficiency of coupling the two approaches to simulate transient bidirectional Fluid,Structure interaction problems with geometrically non-linear structural deflections. A benchmark configuration of self-induced large oscillations for a flag attached to a cylinder can be accurately and efficiently reproduced within this setting. We describe in detail the force evaluation techniques, displacement transfers and the algorithm used to couple these completely different solvers as well as the results, and compare them with a benchmark reference solution computed by a monolithic finite element approach. Copyright © 2009 John Wiley & Sons, Ltd. [source] Fast single domain,subdomain BEM algorithm for 3D incompressible fluid flow and heat transferINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009Jure Ravnik Abstract In this paper acceleration and computer memory reduction of an algorithm for the simulation of laminar viscous flows and heat transfer is presented. The algorithm solves the velocity,vorticity formulation of the incompressible Navier,Stokes equations in 3D. It is based on a combination of a subdomain boundary element method (BEM) and single domain BEM. The CPU time and storage requirements of the single domain BEM are reduced by implementing a fast multipole expansion method. The Laplace fundamental solution, which is used as a special weighting function in BEM, is expanded in terms of spherical harmonics. The computational domain and its boundary are recursively cut up forming a tree of clusters of boundary elements and domain cells. Data sparse representation is used in parts of the matrix, which correspond to boundary-domain clusters pairs that are admissible for expansion. Significant reduction of the complexity is achieved. The paper presents results of testing of the multipole expansion algorithm by exploring its effect on the accuracy of the solution and its influence on the non-linear convergence properties of the solver. Two 3D benchmark numerical examples are used: the lid-driven cavity and the onset of natural convection in a differentially heated enclosure. Copyright © 2008 John Wiley & Sons, Ltd. [source] Numerical simulations of a transient injection flow at low Mach number regimeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008A. Beccantini Abstract In this paper, a transient injection flow at low Mach number regime is investigated. Three different methods are used and analyzed. Two of them are based on asymptotic models of the Navier,Stokes equations valid for small Mach numbers, whereas the other is based on the full compressible Navier,Stokes equations, with particular care given to the discretization at low Mach numbers. Numerical solutions are computed both with or without the gravity force. Finally, the performance of the solvers in terms of CPU-time consumption is investigated, and the sensitivity of the solution to some parameters, which affect CPU time is also performed. Copyright © 2008 John Wiley & Sons, Ltd. [source] An updated interactive boundary layer method for high Reynolds number flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2006F. Įlvarez Abstract The quasi-simultaneous interactive boundary layer (IBL) method is improved with the iterative correction of an inviscid operator. The updated interactive boundary layer method (UIBL) presented in this work, uses the Hess,Smith panel method (HSPM) as an inviscid operator to update the outer flow calculation and the inviscid velocity in the interaction law (IL). The discretization of the Hilbert integral (HI) from the original method is modified to reduce the error introduced by the calculation of the HI in a restricted domain. The method is tested on a flat plate with a small indentation for two-dimensional, steady, incompressible and laminar flow. The UIBL method is capable to predict the flow separation and reattachment with good accuracy. The accuracy of the results is competitive with the numerical solution of the Navier,Stokes equations (NSE). Copyright © 2005 John Wiley & Sons, Ltd. [source] A discrete splitting finite element method for numerical simulations of incompressible Navier,Stokes flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005Kenn K. Q. Zhang Abstract The presence of the pressure and the convection terms in incompressible Navier,Stokes equations makes their numerical simulation a challenging task. The indefinite system as a consequence of the absence of the pressure in continuity equation is ill-conditioned. This difficulty has been overcome by various splitting techniques, but these techniques incur the ambiguity of numerical boundary conditions for the pressure as well as for the intermediate velocity (whenever introduced). We present a new and straightforward discrete splitting technique which never resorts to numerical boundary conditions. The non-linear convection term can be treated by four different approaches, and here we present a new linear implicit time scheme. These two new techniques are implemented with a finite element method and numerical verifications are made. Copyright © 2005 John Wiley & Sons, Ltd. [source] Investigation of nanoscale electrohydrodynamic transport phenomena in charged porous materialsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005P. Pivonka Abstract Depending on the permeability of porous materials, different mass transport mechanisms have to be distinguished. Whereas mass transport through porous media characterized by low permeabilities is governed by diffusion, mass transport through highly permeable materials is governed by advection. Additionally a large number of porous materials are characterized by the presence of surface charge which affects the permeability of the porous medium. Depending on the ion transport mechanism various phenomena such as co-ion exclusion, development of diffusion,exclusion potentials, and streaming potentials may be encountered. Whereas these various phenomena are commonly described by means of different transport models, a unified description of these phenomena can be made within the framework of electrohydrodynamics. In this paper the fundamental equations describing nanoscale multi-ion transport are given. These equations comprise the generalized Nernst,Planck equation, Gauss' theorem of electrostatics, and the Navier,Stokes equation. Various phenomena such as the development of exclusion potentials, diffusion,exclusion potentials, and streaming potentials are investigated by means of finite element analyses. Furthermore, the influence of the surface charge on permeability and ion transport are studied in detail for transient and steady-state problems. The nanoscale findings provide insight into events observed at larger scales in charged porous materials. Copyright © 2005 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] A computational stream function method for two-dimensional incompressible viscous flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005Marcelo H. Kobayashi Abstract This work concerns the development of a numerical method based on the stream function formulation of the Navier,Stokes equations to simulate two-dimensional,plane or axisymmetric,viscous flows. The main features of the proposed method are: the use of the high order finite-difference compact method for the discretization of the stream function equation, the implicit pseudo-transient Newton,Krylov-multigrid matrix free method for the stationary stream function equation and the fourth order Runge,Kutta method for the integration of non-stationary flows. Copyright © 2005 John Wiley & Sons, Ltd. [source] Efficient preconditioning techniques for finite-element quadratic discretization arising from linearized incompressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2010A. El Maliki Abstract We develop an efficient preconditioning techniques for the solution of large linearized stationary and non-stationary incompressible Navier,Stokes equations. These equations are linearized by the Picard and Newton methods, and linear extrapolation schemes in the non-stationary case. The time discretization procedure uses the Gear scheme and the second-order Taylor,Hood element P2,P1 is used for the approximation of the velocity and the pressure. Our purpose is to develop an efficient preconditioner for saddle point systems. Our tools are the addition of stabilization (penalization) term r,(div(·)), and the use of triangular block matrix as global preconditioner. This preconditioner involves the solution of two subsystems associated, respectively, with the velocity and the pressure and have to be solved efficiently. Furthermore, we use the P1,P2 hierarchical preconditioner recently proposed by the authors, for the block matrix associated with the velocity and an additive approach for the Schur complement approximation. Finally, several numerical examples illustrating the good performance of the preconditioning techniques are presented. Copyright © 2009 John Wiley & Sons, Ltd. [source] Finite element and sensitivity analysis of thermally induced flow instabilitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2010Jean-Serge Gigučre Abstract This paper presents a finite element algorithm for the simulation of thermo-hydrodynamic instabilities causing manufacturing defects in injection molding of plastic and metal powder. Mold-filling parameters determine the flow pattern during filling, which in turn influences the quality of the final part. Insufficiently, well-controlled operating conditions may generate inhomogeneities, empty spaces or unusable parts. An understanding of the flow behavior will enable manufacturers to reduce or even eliminate defects and improve their competitiveness. This work presents a rigorous study using numerical simulation and sensitivity analysis. The problem is modeled by the Navier,Stokes equations, the energy equation and a generalized Newtonian viscosity model. The solution algorithm is applied to a simple flow in a symmetrical gate geometry. This problem exhibits both symmetrical and non-symmetrical solutions depending on the values taken by flow parameters. Under particular combinations of operating conditions, the flow was stable and symmetric, while some other combinations leading to large thermally induced viscosity gradients produce unstable and asymmetric flow. Based on the numerical results, a stability chart of the flow was established, identifying the boundaries between regions of stable and unstable flow in terms of the Graetz number (ratio of thermal conduction time to the convection time scale) and B, a dimensionless ratio indicating the sensitivity of viscosity to temperature changes. Sensitivities with respect to flow parameters are then computed using the continuous sensitivity equations method. We demonstrate that sensitivities are able to detect the transition between the stable and unstable flow regimes and correctly indicate how parameters should change in order to increase the stability of the flow. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical simulation of free-surface flow using the level-set method with global mass correctionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010Yali Zhang Abstract A new numerical method that couples the incompressible Navier,Stokes equations with the global mass correction level-set method for simulating fluid problems with free surfaces and interfaces is presented in this paper. The finite volume method is used to discretize Navier,Stokes equations with the two-step projection method on a staggered Cartesian grid. The free-surface flow problem is solved on a fixed grid in which the free surface is captured by the zero level set. Mass conservation is improved significantly by applying a global mass correction scheme, in a novel combination with third-order essentially non-oscillatory schemes and a five stage Runge,Kutta method, to accomplish advection and re-distancing of the level-set function. The coupled solver is applied to simulate interface change and flow field in four benchmark test cases: (1) shear flow; (2) dam break; (3) travelling and reflection of solitary wave and (4) solitary wave over a submerged object. The computational results are in excellent agreement with theoretical predictions, experimental data and previous numerical simulations using a RANS-VOF method. The simulations reveal some interesting free-surface phenomena such as the free-surface vortices, air entrapment and wave deformation over a submerged object. Copyright © 2009 John Wiley & Sons, Ltd. [source] | ||||||||||||||||