Showing papers on "Incompressible flow published in 2001"
TL;DR: In this article, the authors consider the accuracy of projection method approximations to the initial-boundary-value problem for the incompressible Navier-Stokes equations and present an improved projection algorithm which is fully second-order accurate.
841 citations
TL;DR: This work provides a comprehensive review of the strategy of the CIP method, which has a compact support and subcell resolution, including a front-capturing algorithm with functional transformation, a pressure-based algorithm, and other miscellaneous physics such as the elastic–plastic effect and surface tension.
690 citations
TL;DR: In this paper, a three-dimensional, incompressible, multiphase particle-in-cell method for dense particle flows is presented, which solves the governing equations of the fluid phase using a continuum model and those of the particle phase using Lagrangian model.
586 citations
TL;DR: In this article, a mathematical model for turbulent flow in porous media following the second path, or say, space-integrating the equations for turbulent flows in clear fluid is presented.
305 citations
TL;DR: A finite element formulation for the numerical solution of the stationary incompressible Navier–Stokes equations including Coriolis forces and the permeability of the medium using the algebraic version of the sub-grid scale approach.
259 citations
TL;DR: In this article, the truly meshless local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations and the local weak form is modi- fied in a very careful way so as to ovecome the Babuska-Brezzi conditions.
Abstract: The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modi- fied in a very careful way so as to ovecome the so-called Babuska-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline direction. Numerical results for benchmark problems show that the MLPG method is very promising to solve the convection dominated fluid mechanics problems. keyword: MLPG, MLS, Babuconditions, upwinding scheme, incompressible flow, Navier-Stokes equations.
213 citations
TL;DR: It is shown that the bulk flow region of time periodic electroosmotic flows are rotational when the diffusion length scales are comparable to and less than the half channel height, and the instantaneous Helmholtz-Smoluchowski velocity is the appropriate electroOSmotic slip condition even for high-frequency excitations.
Abstract: Analytical solutions of time periodic electroosmotic flows in two-dimensional straight channels are obtained as a function of a nondimensional parameter κ, which is based on the electric double-layer (EDL) thickness, kinematic viscosity, and frequency of the externally applied electric field. A parametric study as a function of κ reveals interesting physics, ranging from oscillatory “pluglike” flows to cases analogous to the oscillating flat plate in a semi-infinite flow domain (Stokes' second problem). The latter case differs from the Stokes' second solution within the EDL, since the flow is driven with an oscillatory electric field rather than an oscillating plate. The analogous case of plate oscillating with the Helmholtz−Smoluchowski velocity matches our analytical solution in the bulk flow region. This indicates that the instantaneous Helmholtz−Smoluchowski velocity is the appropriate electroosmotic slip condition even for high-frequency excitations. The velocity profiles for large κ values show infl...
167 citations
TL;DR: A new numerical method for treating two-phase incompressible flow where one phase is being converted into the other, e.g., the vaporization of liquid water, which admits a sharp interface representation similar to the method proposed in Helenbrook et al. (1999).
156 citations
TL;DR: In this paper, the history of particle deposition in symmetric double-bifurcation airway models is described, assuming spherical noninteracting aerosols that stick to the wall when touching the surface.
Abstract: The flow theory and air flow structures in symmetric double-bifurcation airway models assuming steady laminar, incompressible flow, unaffected by the presence of aerosols, has been described in a companion paper (Part 1). The validated computer simulation results showed highly vortical flow fields, especially around the second bifurcations, indicating potentially complex particle distributions and deposition patterns. In this paper (Part 2), assuming spherical non-interacting aerosols that stick to the wall when touching the surface, the history of depositing particles is described. Specifically, the finite-volume code CFX (AEA Technology) with user-enhanced FORTRAN programs were validated with experimental data of particle deposition efficiencies as a function of the Stokes number for planar single and double bifurcations. The resulting deposition patterns, particle distributions, trajectories and time evolution were analysed in the light of the air flow structures for relatively low (Re D1 = 500) and high (Re D1 = 2000) Reynolds numbers and representative Stokes numbers, i.e. St D1 = 0.04 and St D1 = 0.12. Particle deposition patterns and surface concentrations are largely a function of the local Stokes number, but they also depend on the fluid-particle inlet conditions as well as airway geometry factors. While particles introduced at low inlet Reynolds numbers (e.g. Re D1 = 500) follow the axial air flow, secondary and vortical flows become important at higher Reynolds numbers, causing the formation of particle-free zones near the tube centres and subsequently elevated particle concentrations near the walls. Sharp or mildly rounded carinal ridges have little effect on the deposition efficiencies but may influence local deposition patterns. In contrast, more drastic geometric changes to the basic double-bifurcation model, e.g. the 90°-non-planar configuration, alter both the aerosol wall distributions and surface concentrations considerably.
138 citations
TL;DR: In this article, a degenerate elliptic-parabolic partial differential system was proposed to describe the flow of two incompressible, immiscible fluids in porous media, and it was shown that this weak solution is unique under physically reasonable hypotheses on the data.
TL;DR: In this paper, the combination of hysteretic and dynamic effects in the capillary relationship has not been considered yet, and thermodynamic considerations are employed to ensure the admissibility of the new relationships.
Abstract: It is well known that the relationship between capillary pressure and saturation, in two- phase flow problems demonstrates memory effects and, in particular, hysteresis. Explicit represent- ation of full hysteresis with a myriad of scanning curves in models of multiphase flow has been a difficult problem. A second complication relates to the fact that P c -S relationships, determined under static conditions, are not necessarily valid in dynamics. There exist P c -S relationships which take into account dynamic effects. But the combination of hysteretic and dynamic effects in the capillary relationship has not been considered yet. In this paper, we have developed new models of capillary hysteresis which also include dynamic effects. In doing so, thermodynamic considerations are employed to ensure the admissibility of the new relationships. The simplest model is constructed around main imbibition and drainage curves and assumes that all scanning curves are vertical lines. The dynamic effect is taken into account by introducing a damping coefficient in P c -S equation. A second-order model of hysteresis with inclined scanning curves is also developed. The simplest version of proposed models is applied to two-phase incompressible flow and an example problem is solved.
TL;DR: In this article, a finite-difference solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite plate with uniform heat and mass flux is presented.
Abstract: A finite-difference solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite plate with uniform heat and mass flux is presented here, taking into account the homogeneous chemical reaction of first order. The velocity profiles are compared with the available theoretical solution and are found to be in good agreement. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first order chemical reaction the velocity decreases with increasing values of the chemical reaction parameter. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.
TL;DR: In this article, vortex-induced oscillations of a rigid body in viscous incompressible flow are studied and a new formulation for two-dimensional fluid-rigid body interaction problems is developed.
TL;DR: In this paper, the authors established rigorous lower bounds on the speed of traveling fronts and on the bulk burning rate in reaction-diffusion equation with passive advection, where nonlinearity is assumed to be of either KPP or ignition type.
Abstract: We establish rigorous lower bounds on the speed of traveling fronts and on the bulk burning rate in reaction-diffusion equation with passive advection. The non-linearity is assumed to be of either KPP or ignition type. We consider two main classes of flows. Percolating flows, which are characterized by the presence of long tubes of streamlines mixing hot and cold material, lead to strong speed-up of burning which is linear in the amplitude of the flow, U. On the other hand the cellular flows, which have closed streamlines, are shown to produce weaker increase in reaction. For such flows we get a lower bound which grows as U1/5 for a large amplitude of the flow.
TL;DR: In this paper, a new collocated finite-volume-based solution procedure for predicting viscous compressible and incompressible flows is presented, which is equally applicable in the subsonic, transonic, and supersonic regimes.
TL;DR: In this paper, the effects of different inlet Reynolds and Stokes numbers in a triple bifurcation of the human respiratory system were simulated for several combinations of relatively high and low inlet numbers, and it was shown that preferential concentration of particles can be induced by the secondary vortical flow in the tubes when the inlet number is high enough.
Abstract: Considering steady laminar incompressible flow in a triple bifurcation, which represents generations three to six of the human respiratory system, air flow fields and micron-particle transport have been simulated for several combinations of relatively high and low inlet Reynolds and Stokes numbers. While the upstream bifurcations are hardly affected by the third bifurcation, complex air and particle flow fields occur in the daughter tubes leading to the third dividers. Variations in Reynolds number, 500≤Re≤2000, and Stokes number, 0.04≤St≤0.12, cause locally changing vortical air flows as well as irregular particle motions. Preferential concentration of particles can be induced by the secondary vortical flow in the tubes when the inlet Reynolds number is high enough. The air and particle velocity profiles in the third daughter tubes are still quite different from those in the upstream tubes, which indicates that additional downstream effects are possible. This work may contribute to respiratory dose estimation in health risk assessment studies, as well as the analyses of drug aerosol delivery.
TL;DR: In this paper, a finite volume method is used to calculate the steady incompressible flow in rectangular cavities, where the flow is driven by two opposing cavity side walls which move with constant velocities tangentially to themselves.
Abstract: The two-dimensional steady incompressible flow in rectangular cavities is calculated numerically by a finite volume method. The flow is driven by two opposing cavity side walls which move with constant velocities tangentially to themselves. Depending on the cavity aspect ratio and the two side-wall Reynolds numbers different flow states exist. Their range of existence and the bifurcations between different states are investigated by a continuation method accurately locating the bifurcation points. When both side walls move in opposite directions up to seven solutions are found to exist for the same set of parameters. Three of these are point-symmetric and four are asymmetric with respect to the center of the cavity, if the side-wall Reynolds numbers have the same magnitude. When the walls move in the same direction, up to five different flow states are found. In this case only a single mirror symmetric solution exists for equal Reynolds numbers.
TL;DR: In this paper, the authors consider a model of nonhomogeneous diphasic incompressible flow where the densities of the phases are different and show the existence of a global weak solution and a unique local strong solution.
Abstract: In this paper we are interested in the study of a model of nonhomogeneous diphasic incompressible flow. More precisely we consider a coupling of a Cahn–Hilliard and an incompressible Navier–Stokes equations where the densities of the phases are different. For this general model we can only show the local existence of a unique very regular solution and the existence of weaker solutions is still an open problem. But, if we look at the behavior of the system when the densities tends to be equal (slightly nonhomogeneous case), we show the existence of a global weak solution and of a unique local strong solution (which is in fact global in 2D). Finally, an asymptotic stability result for the metastable states is shown in this slightly nonhomogeneous case.
TL;DR: Computable a posteriori error bounds and related adaptive meshrefining algorithms are provided for the numerical treatment of monotone stationary flow problems with a quite general class of conforming and non-conforming finite element methods.
Abstract: Computable a posteriori error bounds and related adaptive meshrefining algorithms are provided for the numerical treatment of monotone stationary flow problems with a quite general class of conforming and non-conforming finite element methods. A refined residual-based error estimate generalises the works of Verfurth; Dari, Duran and Padra; Bao and Barrett. As a consequence, reliable and efficient averaging estimates can be established on unstructured grids. The symmetric formulation of the incompressible flow problem models certain nonNewtonian flow problems and the Stokes problem with mixed boundary conditions. A Helmholtz decomposition avoids any regularity or saturation assumption in the mathematical error analysis. Numerical experiments for the partly nonconforming method analysed by Kouhia and Stenberg indicate efficiency of related adaptive mesh-refining algorithms.
TL;DR: In this paper, the authors considered the unsteady flow of incompressible micropolar fluid between two parallel porous plates when there is a periodic suction at the lower plate and injection at the upper plate.
TL;DR: In this paper, the transition of natural convection in an annulus between horizontal concentric cylinders is investigated theoretically by assuming two-dimensional and incompressible flow fields, and it is confirmed by numerical simulations that dual stable steady solutions exist for Rayleigh numbers larger than a critical value.
TL;DR: In this article, the authors proposed the Taylor relaxed states of a single-fluid magnetohydrodynamic (MHD) plasma, where the energy condensates into a single Beltrami magnetic field resulting in the self-organization of a force-free equilibrium.
Abstract: A general solenoidal vector field, such as a magnetic field or an incompressible flow, can be decomposed into an orthogonal sum of Beltrami fields (eigenfunctions of the curl operator). Nonlinear dynamics of a plasma induces complex couplings among these Beltrami fields. In a single-fluid magnetohydrodynamic (MHD) plasma, however, the energy condensates into a single Beltrami magnetic field resulting in the self-organization of a force-free equilibrium, that is, the Taylor relaxed state. By relating the velocity and the magnetic fields, the Hall term in the two-fluid model leads to a singular perturbation that enables the formation of an equilibrium given by a pair of two different Beltrami fields. This new set of relaxed states, despite the simple mathematical structure, includes a variety of plasma states that could explain a host of interesting phenomena. The H-mode (high-confinement) boundary layer, where a diamagnetic structure is self-organized under the coupling of the magnetic field, flow, electri...
TL;DR: A numerical scheme for incompressible viscous flow, formulated as an equation for the stream function that obviates the difficulty associated with vorticity boundary conditions and is implemented with a high-resolution central scheme that remains stable and accurate in the presence of large gradients.
Abstract: We present a numerical scheme for incompressible viscous flow, formulated as an equation for the stream function. The pure stream function formulation obviates the difficulty associated with vorticity boundary conditions. The resulting biharmonic equation is discretized with a compact scheme and solved with an algebraic multigrid solver. The advection of vorticity is implemented with a high-resolution central scheme that remains stable and accurate in the presence of large gradients. The accuracy and robustness of the method are demonstrated for high Reynolds number flows in a lid-driven cavity.
TL;DR: In this paper, it was shown that a regular tube convected by a 3D incompressible flow cannot collapse to zero thickness in finite time, and the concept of regular tube was introduced.
Abstract: We define the notion of a “regular tube”, and prove that a regular tube convected by a 3D incompressible flow cannot collapse to zero thickness in finite time.
TL;DR: Some iterative schemes to perform the uncoupling of the pressure gradient projection (PGP) from the calculation of the velocity and the pressure, both for the stationary and the transient Navier–Stokes equations are discussed.
Abstract: We discuss in this paper some implementation aspects of a finite element formulation for the incompressible Navier-Stokes equations which allows the use of equal order velocity-pressure interpolations. The method consists in introducing the projection of the pressure gradient and adding the difference between the pressure Laplacian and the divergence of this new field to the incompressibility equation, both multiplied by suitable algorithmic parameters. The main purpose of this paper is to discuss how to deal with the new variable in the implementation of the algorithm. Obviously, it could be treated as one extra unknown, either explicitly or as a condensed variable. However, we take for granted that the only way for the algorithm to be efficient is to uncouple it from the velocity-pressure calculation in one way or another. Here we discuss some iterative schemes to perform this uncoupling of the pressure gradient projection (PGP) from the calculation of the velocity and the pressure, both for the stationary and the transient Navier-Stokes equations. In the first case, the strategies analyzed refer to the interaction of the linearization loop and the iterative segregation of the PGP, whereas in the second the main dilemma concerns the explicit or implicit treatment of the PGP.
TL;DR: This paper analyzes a pressure stabilized, finite element method for the unsteady, incompressible Navier–Stokes equations in primitive variables and provides some error estimates for the fully discrete solution which show that the velocity is first order accurate in the time step and attains optimal order accuracy in the mesh size for the given spatial interpolation.
TL;DR: In this article, an analytic solution for the incompressible third-grade fluctuating flow over an infinite porous plate in a rotating medium is obtained, and the resulting velocity profile, drag and the lateral stress on the plate are calculated.
Abstract: Analytic solution for the incompressible third-grade fluctuating flow over an infinite porous plate in a rotating medium is obtained. The resulting velocity profile, drag and the lateral stress on the plate are calculated. Some comments on symmetric and asymmetric nature of the solutions are given in the conclusion.
TL;DR: A finite element approximation for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media is considered.
Abstract: This is the third paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial differential system which describes the flow of two incompressible, immiscible fluids in porous media In this paper we consider a finite element approximation for this system The elliptic equation for the pressure and velocity is approximated by a mixed finite element method, while the degenerate parabolic equation for the saturation is approximated by a Galerkin finite element method A fully discrete approximation is analyzed Sharp error estimates in energy norms are obtained for this approximation The error analysis does not use any regularization of the saturation equation; the error estimates are derived directly from the degenerate equation Also, the analysis does not impose any restriction on the nature of degeneracy Finally, it respects the minimal regularity on the solution of the differential system
TL;DR: In this paper, a pipeline inspection gauge (PIG) with bypass flow control in natural gas pipeline is modeled and simulation results for PIG with bypass control are presented. And the simulation results show that the derived mathematical model and the proposed computational scheme are effective for estimating the position and velocity of the PIG under given operational conditions of pipeline.
Abstract: This paper introduces modeling and simulation results for pipeline inspection gauge (PIG) with bypass flow control in natural gas pipeline. The dynamic behaviour of the PIG depends on the different pressure across its body and the bypass flow through it. The system dynamics includes: dynamics of driving gas flow behind the PIG, dynamics of expelled gas in front of the PIG, dynamics of bypass flow, and dynamics of the PIG. The bypass flow across the PIG is treated as incompressible flow with the assumption of its Mach number smaller than 0.45. The governing nonlinear hyperbolic partial differential equations for unsteady gas flows are solved by method of characteristics (MOC) with the regular rectangular grid under appropriate initial and boundary conditions. The Runge-Kuta method is used for solving the steady flow equations to get initial flow values and the dynamic equation of the PIG. The sampling time and distance are chosen under Courant-Friedrich-Lewy (CFL) restriction. The simulation is performed with a pipeline segment in the Korea Gas Corporation (KOGAS) low pressure system, Ueijungboo-Sangye line. Simulation results show us that the derived mathematical model and the proposed computational scheme are effective for estimating the position and velocity of the PIG with bypass flow under given operational conditions of pipeline.