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Incompressible Flows (incompressible + flow)

Distribution by Scientific Domains
Engineering92%
Mathematics and Statistics7%

Terms modified by Incompressible Flows

  • incompressible flow problem
    		•

    Selected Abstracts

    Pressure boundary condition for the time-dependent incompressible Navier,Stokes equations

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2006
    R. L. Sani
    Abstract In Gresho and Sani (Int. J. Numer. Methods Fluids 1987; 7:1111,1145; Incompressible Flow and the Finite Element Method, vol. 2. Wiley: New York, 2000) was proposed an important hypothesis regarding the pressure Poisson equation (PPE) for incompressible flow: Stated there but not proven was a so-called equivalence theorem (assertion) that stated/asserted that if the Navier,Stokes momentum equation is solved simultaneously with the PPE whose boundary condition (BC) is the Neumann condition obtained by applying the normal component of the momentum equation on the boundary on which the normal component of velocity is specified as a Dirichlet BC, the solution (u, p) would be exactly the same as if the ,primitive' equations, in which the PPE plus Neumann BC is replaced by the usual divergence-free constraint (, · u = 0), were solved instead. This issue is explored in sufficient detail in this paper so as to actually prove the theorem for at least some situations. Additionally, like the original/primitive equations that require no BC for the pressure, the new results establish the same thing when the PPE approach is employed. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    A cut-cell non-conforming Cartesian mesh method for compressible and incompressible flow

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2007
    J. Pattinson
    Abstract This paper details a multigrid-accelerated cut-cell non-conforming Cartesian mesh methodology for the modelling of inviscid compressible and incompressible flow. This is done via a single equation set that describes sub-, trans-, and supersonic flows. Cut-cell technology is developed to furnish body-fitted meshes with an overlapping mesh as starting point, and in a manner which is insensitive to surface definition inconsistencies. Spatial discretization is effected via an edge-based vertex-centred finite volume method. An alternative dual-mesh construction strategy, similar to the cell-centred method, is developed. Incompressibility is dealt with via an artificial compressibility algorithm, and stabilization achieved with artificial dissipation. In compressible flow, shocks are captured via pressure switch-activated upwinding. The solution process is accelerated with full approximation storage (FAS) multigrid where coarse meshes are generated automatically via a volume agglomeration methodology. This is the first time that the proposed discretization and solution methods are employed to solve a single compressible,incompressible equation set on cut-cell Cartesian meshes. The developed technology is validated by numerical experiments. The standard discretization and alternative methods were found equivalent in accuracy and computational cost. The multigrid implementation achieved decreases in CPU time of up to one order of magnitude. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    A CBS-type stabilizing algorithm for the consolidation of saturated porous media

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005
    V. 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]

    Steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility (AC)-based characteristic-based split (CBS) scheme

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005
    P. Nithiarasu
    Abstract In this paper, the explicit characteristic-based split (CBS) scheme has been employed to solve both steady and unsteady flows inside a non-rectangular double driven cavity. This problem is recently suggested as a benchmark problem for incompressible flows. Both unstructured and structured meshes have been employed in the present study to make sure that the predicted results are as close to reality as possible. The results obtained show the existence of steady state at lower Reynolds numbers (,1000) and transient states at higher Reynolds numbers. The flow approaches a turbulent state as the Reynolds number is increased to 10 000. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Quasi-dual reciprocity boundary-element method for incompressible flow: Application to the diffusive,advective equation

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003
    C. F. Loeffler
    Abstract This work presents a new boundary-element method formulation called quasi-dual reciprocity formulation for heat transfer problems, considering diffusive and advective terms. The present approach has some characteristics similar to those of the so-called dual-reciprocity formulation; however, the mathematical developments of the quasi-dual reciprocity approach reduces approximation errors due to global domain interpolation. Some one- and two-dimensional examples are presented, the results being compared against those obtained from analytical and dual-reciprocity formulations. The method convergence is evaluated through analyses where the mesh is successively refined for various Peclet numbers, in order to assess the effect of the advective term. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    A Hermite finite element method for incompressible fluid flow

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2010
    J. T. Holdeman
    Abstract We describe some Hermite stream function and velocity finite elements and a divergence-free finite element method for the computation of incompressible flow. Divergence-free velocity bases defined on (but not limited to) rectangles are presented, which produce pointwise divergence-free flow fields (,·uh,0). The discrete velocity satisfies a flow equation that does not involve pressure. The pressure can be recovered as a function of the velocity if needed. The method is formulated in primitive variables and applied to the stationary lid-driven cavity and backward-facing step test problems. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Topology optimization of microfluidic mixers

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2009
    Casper Schousboe Andreasen
    Abstract This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering the layout of flow/non-flow regions subject to a constraint on the pressure drop between inlet and outlet. For a square cross-sectioned pipe the mixing is increased by 70% compared with a straight pipe at the cost of a 2.5 fold increase in pressure drop. Another example where only the bottom profile of the channel is a design domain results in intricate herring bone patterns that confirm findings from the literature. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Oscillatory flow of a fourth-order fluid

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009
    T. Hayat
    Abstract This study deals with the incompressible flow of a fourth-order fluid over a porous plate oscillating in its own plane. Numerical solution of the nonlinear problem governing the flow is given. The influence of various parameters of interest on the velocity distribution is shown and discussed with the help of several graphs. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Numerical study of an inviscid incompressible flow through a channel of finite length

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009
    Vasily N. Govorukhin
    Abstract A two-dimensional inviscid incompressible flow in a rectilinear channel of finite length is studied numerically. Both the normal velocity and the vorticity are given at the inlet, and only the normal velocity is specified at the outlet. The flow is described in terms of the stream function and vorticity. To solve the unsteady problem numerically, we propose a version of the vortex particle method. The vorticity field is approximated using its values at a set of fluid particles. A pseudo-symplectic integrator is employed to solve the system of ordinary differential equations governing the motion of fluid particles. The stream function is computed using the Galerkin method. Unsteady flows developing from an initial perturbation in the form of an elliptical patch of vorticity are calculated for various values of the volume flux of fluid through the channel. It is shown that if the flux of fluid is large, the initial vortex patch is washed out of the channel, and when the flux is reduced, the initial perturbation evolves to a steady flow with stagnation regions. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Self-propulsion of oscillating wings in incompressible flow

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2008
    A. Carabineanu
    Abstract In this paper, we show that the oscillatory motion of an airfoil (wing) in an ideal fluid can determine the apparition of thrust. In the framework of the linearized perturbation theory, the pressure jump over the oscillating wing is the solution of a two-dimensional hypersingular integral equation. Using appropriate quadrature formulas, we discretize the oscillatory lifting surface integral equation in order to obtain the jump of the pressure across the surface. Integrating numerically, we obtain the drag coefficient. For some oscillatory motions, if the frequency of the oscillations surpasses a certain value, the drag coefficient becomes negative, i.e. there appears a propulsive force. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Pressure boundary condition for the time-dependent incompressible Navier,Stokes equations

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2006
    R. L. Sani
    Abstract In Gresho and Sani (Int. J. Numer. Methods Fluids 1987; 7:1111,1145; Incompressible Flow and the Finite Element Method, vol. 2. Wiley: New York, 2000) was proposed an important hypothesis regarding the pressure Poisson equation (PPE) for incompressible flow: Stated there but not proven was a so-called equivalence theorem (assertion) that stated/asserted that if the Navier,Stokes momentum equation is solved simultaneously with the PPE whose boundary condition (BC) is the Neumann condition obtained by applying the normal component of the momentum equation on the boundary on which the normal component of velocity is specified as a Dirichlet BC, the solution (u, p) would be exactly the same as if the ,primitive' equations, in which the PPE plus Neumann BC is replaced by the usual divergence-free constraint (, · u = 0), were solved instead. This issue is explored in sufficient detail in this paper so as to actually prove the theorem for at least some situations. Additionally, like the original/primitive equations that require no BC for the pressure, the new results establish the same thing when the PPE approach is employed. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Fourth-order compact formulation of Navier,Stokes equations and driven cavity flow at high Reynolds numbers

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006
    E. Erturk
    Abstract A new fourth-order compact formulation for the steady 2-D incompressible Navier,Stokes equations is presented. The formulation is in the same form of the Navier,Stokes equations such that any numerical method that solve the Navier,Stokes equations can easily be applied to this fourth-order compact formulation. In particular, in this work the formulation is solved with an efficient numerical method that requires the solution of tridiagonal systems using a fine grid mesh of 601 × 601. Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number with Re = 20 000 fourth-order spatial accuracy. Detailed solutions are presented. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Flow simulation on moving boundary-fitted grids and application to fluid,structure interaction problems

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006
    Martin Engel
    Abstract We present a method for the parallel numerical simulation of transient three-dimensional fluid,structure interaction problems. Here, we consider the interaction of incompressible flow in the fluid domain and linear elastic deformation in the solid domain. The coupled problem is tackled by an approach based on the classical alternating Schwarz method with non-overlapping subdomains, the subproblems are solved alternatingly and the coupling conditions are realized via the exchange of boundary conditions. The elasticity problem is solved by a standard linear finite element method. A main issue is that the flow solver has to be able to handle time-dependent domains. To this end, we present a technique to solve the incompressible Navier,Stokes equation in three-dimensional domains with moving boundaries. This numerical method is a generalization of a finite volume discretization using curvilinear coordinates to time-dependent coordinate transformations. It corresponds to a discretization of the arbitrary Lagrangian,Eulerian formulation of the Navier,Stokes equations. Here the grid velocity is treated in such a way that the so-called Geometric Conservation Law is implicitly satisfied. Altogether, our approach results in a scheme which is an extension of the well-known MAC-method to a staggered mesh in moving boundary-fitted coordinates which uses grid-dependent velocity components as the primary variables. To validate our method, we present some numerical results which show that second-order convergence in space is obtained on moving grids. Finally, we give the results of a fully coupled fluid,structure interaction problem. It turns out that already a simple explicit coupling with one iteration of the Schwarz method, i.e. one solution of the fluid problem and one solution of the elasticity problem per time step, yields a convergent, simple, yet efficient overall method for fluid,structure interaction problems. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Rotating incompressible flow with a pressure Neumann condition

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2006
    Julio R. Claeyssen
    Abstract This work considers the internal flow of an incompressible viscous fluid contained in a rectangular duct subject to a rotation. A direct velocity,pressure algorithm in primitive variables with a Neumann condition for the pressure is employed. The spatial discretization is made with finite central differences on a staggered grid. The pressure and velocity fields are directly updated without any iteration. Numerical simulations with several Reynolds numbers and rotation rates were performed for ducts of aspect ratios 2:1 and 8:1. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Dendritic solidification of binary alloys with free and forced convection

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005
    P. Zhao
    Abstract Dendritic solidification with forced convection and free convection driven by contraction and thermo- solutal buoyancy is simulated in two-dimensional space using a sharp-interface model. Both pure substances and alloys are considered. The model is formulated using the finite element method and works directly with primitive variables. The coupled energy- and solutal concentration-equations, along with the Navier,Stokes equations for incompressible flow, are solved using different meshes. Temperature is solved in a fixed mesh that covers the whole domain (solid + liquid) where the solid,liquid interface is explicitly tracked using marker points. The concentration and momentum equations are solved in the liquid region using an adaptive mesh of triangular elements that conforms to the interface. The velocity boundary conditions are applied directly on the interface. The model is validated using a series of problems that have analytical, experimental and numerical results. Four simulations are presented: (1) crystal growth of succinonitrile with thermal convection under two small undercoolings; (2) dendritic growth into an undercooled pure melt with a uniform forced flow; (3) equiaxial dendritic growth of a pure substance and an alloy with contraction-induced convection; and (4) directional solidification of Pb,0.2 wt% Sb alloy with convection driven by the combined action of contraction, thermal and solutal buoyancy. Some of the simulation results are compared to those reported using other methods including the phase-field method; others are new. In each case, the effects of convection on dendritic solidification are analysed. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Two-dimensional anisotropic Cartesian mesh adaptation for the compressible Euler equations

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2004
    W. A. Keats
    Abstract Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This paper discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible flow. This technique, originally developed for laminar incompressible flow, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this paper, the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Numerical method for calculation of the incompressible flow in general curvilinear co-ordinates with double staggered grid

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2003
    A. Shklyar
    Abstract A solution methodology has been developed for incompressible flow in general curvilinear co-ordinates. Two staggered grids are used to discretize the physical domain. The first grid is a MAC quadrilateral mesh with pressure arranged at the centre and the Cartesian velocity components located at the middle of the sides of the mesh. The second grid is so displaced that its corners correspond to the centre of the first grid. In the second grid the pressure is placed at the corner of the first grid. The discretized mass and momentum conservation equations are derived on a control volume. The two pressure grid functions are coupled explicitly through the boundary conditions and implicitly through the velocity of the field. The introduction of these two grid functions avoids an averaging of pressure and velocity components when calculating terms that are generated in general curvilinear co-ordinates. The SIMPLE calculation procedure is extended to the present curvilinear co-ordinates with double grids. Application of the methodology is illustrated by calculation of well-known external and internal problems: viscous flow over a circular cylinder, with Reynolds numbers ranging from 10 to 40, and lid-driven flow in a cavity with inclined walls are examined. The numerical results are in close agreement with experimental results and other numerical data. Copyright © 2003 John Wiley & Sons, Ltd. [source]

    An approximate projection method for incompressible flow

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2002
    David E. Stevens
    This paper presents an approximate projection method for incompressible flows. This method is derived from Galerkin orthogonality conditions using equal-order piecewise linear elements for both velocity and pressure, hereafter Q1Q1. By combining an approximate projection for the velocities with a variational discretization of the continuum pressure Poisson equation, one eliminates the need to filter either the velocity or pressure fields as is often needed with equal-order element formulations. This variational approach extends to multiple types of elements; examples and results for triangular and quadrilateral elements are provided. This method is related to the method of Almgren et al. (SIAM J. Sci. Comput. 2000; 22: 1139,1159) and the PISO method of Issa (J. Comput. Phys. 1985; 62: 40,65). These methods use a combination of two elliptic solves, one to reduce the divergence of the velocities and another to approximate the pressure Poisson equation. Both Q1Q1 and the method of Almgren et al. solve the second Poisson equation with a weak error tolerance to achieve more computational efficiency. A Fourier analysis of Q1Q1 shows that a consistent mass matrix has a positive effect on both accuracy and mass conservation. A numerical comparison with the widely used Q1Q0 (piecewise linear velocities, piecewise constant pressures) on a periodic test case with an analytic solution verifies this analysis. Q1Q1 is shown to have comparable accuracy as Q1Q0 and good agreement with experiment for flow over an isolated cubic obstacle and dispersion of a point source in its wake. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Injection/suction boundary conditions for fluid,structure interaction simulations in incompressible flow

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2002
    G. Medic
    Abstract This paper presents the analysis of injection/suction boundary conditions in the context of the fluid,structure interactions simulation of the incompressible turbulent flow. First, the equations used in the modelling of the fluid and the structure are presented, as well as the numerical methods used in the corresponding solvers. Injection/suction boundary conditions are then presented with details of different implementation alternatives. Arbitrary Lagrangian,Eulerian (ALE) approach was also implemented in order to test the injection/suction boundary conditions. Numerical tests are performed where injection/suction boundary conditions are compared to ALE simulations. These tests include forced movement of the structure and two-degrees-of-freedom structure model simulations. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Towards entropy detection of anomalous mass and momentum exchange in incompressible fluid flow

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002
    G. F. Naterer
    An entropy-based approach is presented for assessment of computational accuracy in incompressible flow problems. It is shown that computational entropy can serve as an effective parameter in detecting erroneous or anomalous predictions of mass and momentum transport in the flow field. In the present paper, the fluid flow equations and second law of thermodynamics are discretized by a Galerkin finite-element method with linear, isoparametric triangular elements. It is shown that a weighted entropy residual is closely related to truncation error; this relationship is examined in an application problem involving incompressible flow through a converging channel. In particular, regions exhibiting anomalous flow behaviour, such as under-predicted velocities, appear together with analogous trends in the weighted entropy residual. It is anticipated that entropy-based error detection can provide important steps towards improved accuracy in computational fluid flow. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    On non-stationary viscous incompressible flow through a cascade of profiles

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2006
    Miloslav Feistauer
    Abstract The paper deals with theoretical analysis of non-stationary incompressible flow through a cascade of profiles. The initial-boundary value problem for the Navier,Stokes system is formulated in a domain representing the exterior to an infinite row of profiles, periodically spaced in one direction. Then the problem is reformulated in a bounded domain of the form of one space period and completed by the Dirichlet boundary condition on the inlet and the profile, a suitable natural boundary condition on the outlet and periodic boundary conditions on artificial cuts. We present a weak formulation and prove the existence of a weak solution. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2007
    V. 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]

    Local volume-conserving free surface smoothing

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2007
    F. S. Sousa
    Abstract Removing high-frequency undulations in surfaces is a problem that appears in different fields, such as computer graphics and computational fluid mechanics. This problem is typically handled by surface smoothing techniques, such as Laplacian filters, that eliminate high-frequency undulations but degrade the volume encompassed by the surface. The need for conserving volume (or mass) rules out the use of such techniques in several application, as for example incompressible flows. In this work we present a smoothing technique that suppresses undulations while conserving local volumes, ensuring that the global mass is conserved. The effectiveness of the proposed technique is illustrated in synthetic datasets as well as in free surface flows simulation. Comparisons between our smoothing approach and the well-known Laplacian filter are also presented. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Computation of mould filling processes with a moving Lagrangian interface technique

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2002
    Marcela Cruchaga
    Abstract Computation of non-isothermal flow problems involving moving interfaces is presented. A Lagrangian interface technique, defined in the context of a fixed-mesh finite element formulation for incompressible flows, is employed to update the interface position. A global mass-corrector algorithm is used to accurately enforce the global mass conservation. The Navier,Stokes equations are solved with an improved sub-element integration technique to more accurately account for sudden changes in the fluid properties across the interface. The method described is applied to two mould filling problems. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Performance of parallel preconditioners for adaptive hp FEM discretization of incompressible flows

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2002
    Andrew C. Bauer
    Abstract Adaptive hp finite element (FEM) approximations of incompressible flow make special demands on parallel solution algorithms. We report here on the performance of standard algebraic preconditioning techniques for the efficient solution of such problems. We employ a Schur complement scheme to eliminate the ,bubble' degrees of freedom associated with the velocity field, thus removing the zeros from the diagonals and enabling the use of standard algebraic techniques. Using new data management strategies and the PETSc library of iterative solvers for linear systems, numerical results for Jacobi, Block Jacobi and Additive Schwartz preconditioners are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Stabilized finite element formulation of buoyancy driven incompressible flows

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2002
    S. Aliabadi
    Abstract Streamline-upwind/Petrov,Galerkin finite element method is developed for buoyancy-driven incom-pressible flows with heat and mass transfer. The stabilized finite element formulations are implemented in parallel using message passing interface libraries. To measure the accuracy of the method, we solve a 2D numerical example of natural convection flows at moderate to high Rayleigh numbers. The 3D applications include the dispersion of smoke from a chimney and within a stadium. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    Steady and unsteady incompressible flow in a double driven cavity using the artificial compressibility (AC)-based characteristic-based split (CBS) scheme

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005
    P. Nithiarasu
    Abstract In this paper, the explicit characteristic-based split (CBS) scheme has been employed to solve both steady and unsteady flows inside a non-rectangular double driven cavity. This problem is recently suggested as a benchmark problem for incompressible flows. Both unstructured and structured meshes have been employed in the present study to make sure that the predicted results are as close to reality as possible. The results obtained show the existence of steady state at lower Reynolds numbers (,1000) and transient states at higher Reynolds numbers. The flow approaches a turbulent state as the Reynolds number is increased to 10 000. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Multi-material incompressible flow simulation using the moment-of-fluid method,

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2010
    Samuel P. Schofield
    Abstract This paper compares the numerical performance of the moment-of-fluid (MOF) interface reconstruction technique with Youngs, LVIRA, power diagram (PD), and Swartz interface reconstruction techniques in the context of a volume-of-fluid (VOF) based finite element projection method for the numerical simulation of variable-density incompressible viscous flows. In pure advection tests with multiple materials MOF shows dramatic improvements in accuracy compared with the other methods. In incompressible flows where density differences determine the flow evolution, all the methods perform similarly for two material flows on structured grids. On unstructured grids, the second-order MOF, LVIRA, and Swartz methods perform similarly and show improvement over the first-order Youngs' and PD methods. For flow simulations with more than two materials, MOF shows increased accuracy in interface positions on coarse meshes. In most cases, the convergence and accuracy of the computed flow solution was not strongly affected by interface reconstruction method. Published in 2009 by John Wiley & Sons, Ltd. [source]

    A two-step Taylor-characteristic-based Galerkin method for incompressible flows and its application to flow over triangular cylinder with different incidence angles

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2010
    Yan Bao
    Abstract An alternative characteristic-based scheme, the two-step Taylor-characteristic-based Galerkin method is developed based on the introduction of multi-step temporal Taylor series expansion up to second order along the characteristic of the momentum equation. Contrary to the classical characteristic-based split (CBS) method, the current characteristic-based method does not require splitting the momentum equation, and segregate the calculation of the pressure from that of the velocity by using the momentum,pressure Poisson equation method. Some benchmark problems are used to examine the effectiveness of the proposed algorithm and to compare with the original CBS method, and the results show that the proposed method has preferable accuracy with less numerical dissipation. We further applied the method to the numerical simulation of flow around equilateral triangular cylinder with different incidence angles in free stream. In this numerical investigation, the flow simulations are carried out in the low Reynolds number range. Instantaneous streamlines around the cylinder are used as a means to visualize the wake region behind, and they clearly show the flow pattern around the cylinder in time. The influence of incidence angle on flow characteristic parameters such as Strouhal number, Drag and Lift coefficients are discussed quantitatively. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    Numerical implementation of Aristov,Pukhnachev's formulation for axisymmetric viscous incompressible flows

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2010
    N. P. Moshkin
    Abstract In the present work a finite-difference technique is developed for the implementation of a new method proposed by Aristov and Pukhnachev (Doklady Phys. 2004; 49(2):112,115) for modeling of the axisymmetric viscous incompressible fluid flows. A new function is introduced that is related to the pressure and a system similar to the vorticity/stream function formulation is derived for the cross-flow. This system is coupled to an equation for the azimuthal velocity component. The scheme and the algorithm treat the equations for the cross-flow as an inextricably coupled system, which allows one to satisfy two conditions for the stream function with no condition on the auxiliary function. The issue of singularity of the matrix is tackled by adding a small parameter in the boundary conditions. The scheme is thoroughly validated on grids with different resolutions. The new numerical tool is applied to the Taylor flow between concentric rotating cylinders when the upper and lower lids are allowed to rotate independently from the inner cylinder, while the outer cylinder is held at rest. The phenomenology of this flow is adequately represented by the numerical model, including the hysteresis that takes place near certain specific values of the Reynolds number. Thus, the present results can be construed to demonstrate the viability of the new model. The success can be attributed to the adequate physical nature of the auxiliary function. The proposed technique can be used in the future for in-depth investigations of the bifurcation phenomena in rotating flows. Copyright © 2009 John Wiley & Sons, Ltd. [source]