Showing papers on "Incompressible flow published in 2006"
TL;DR: It is demonstrated that a flow algorithm designed to legislate force balance retains an exact balance between surface tension forces and the resulting pressure gradients for both continuous and sharp representations of interfacial surface tension.
676 citations
01 Jan 2006
TL;DR: In this article, the authors describe new benchmark settings for the rigorous evaluation of different methods for fluid-structure interaction problems, which consist of laminar incompressible channel flow around an elastic object which results in self-induced oscillations of the structure.
Abstract: We describe new benchmark settings for the rigorous evaluation of different methods for fluid-structure interaction problems. The configurations consist of laminar incompressible channel flow around an elastic object which results in self-induced oscillations of the structure. Moreover, characteristic flow quantities and corresponding plots are provided for a quantitative comparison.
502 citations
TL;DR: All the numerical experiments show that the present approach can be used to model multiphase flows with large density ratios and its efficiency could be greatly improved, especially in 3D applications.
420 citations
TL;DR: The results show that the immersed interface method implemented here has second-order accuracy in the infinity norm for both the velocity and the pressure, and the method is equally effective in computing flow subject to boundaries with prescribed force or boundaries withcribed motion.
316 citations
TL;DR: The space–time finite element techniques developed for computation of fluid–structure interaction (FSI) problems are described and it is demonstrated that the techniques have increased the scope and accuracy of the methods used in computation of FSI problems.
299 citations
TL;DR: An efficient and accurate numerical scheme is presented and implemented for the coupled nonlinear systems of Navier-Stokes type linear momentum equations and volume preserving Allen-Cahn type phase equations.
228 citations
TL;DR: In this article, a compact approximate model is proposed that predicts the pressure drop for a wide variety of shapes, i.e., area, perimeter, and polar moment of inertia.
Abstract: The pressure drop of fully developed, laminar, incompressible flow in smooth mini- and microchannels of arbitrary cross-section is investigated. A compact approximate model is proposed that predicts the pressure drop for a wide variety of shapes. The model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The proposed model is compared with analytical and numerical solutions for several shapes
212 citations
TL;DR: The method couples a semi-implicit discretization for solving the surfactant transport equation recently developed by Xu and Zhao with the immersed interface method originally developed by LeVeque and Li, for the first time that the level-set method has been used to simulate fluid interfaces with surfactants.
209 citations
TL;DR: An immersed interface method for the incompressible Navier-Stokes equations capable of handling both rigid and flexible boundaries is presented and is second order accurate.
205 citations
TL;DR: In this paper, the authors provide an overview of the solution techniques for the fully discretized equations encountered at every time step in computation of fluid-structure interactions with the space-time techniques.
185 citations
TL;DR: In this paper, the authors compare the accuracy and computational efficiency of two research simulation codes based on the LB and the finite element method (FEM) for two-dimensional incompressible laminar flow problems with complex geometries.
TL;DR: A modified version of the MSFV algorithm is presented that provides a suitable and natural framework to include additional physics and provides accurate solutions for compressible multiphase flow problems.
TL;DR: The velocity boundary condition that must be imposed at an interface between a porous medium and a free fluid is investigated in this article, where a heterogeneous transition zone characterized by rapidly varying properties is introduced between the two homogeneous porous and free fluid regions.
TL;DR: In this article, a nonstandard version of the principle of virtual power is used to develop general balance equations and boundary conditions for second-grade materials, which apply to both solids and fluids as they are independent of constitutive equations.
Abstract: Using a nonstandard version of the principle of virtual power, we develop general balance equations and boundary conditions for second-grade materials. Our results apply to both solids and fluids as they are independent of constitutive equations. As an application of our results, we discuss flows of incompressible fluids at small-length scales. In addition to giving a generalization of the Navier–Stokes equations involving higher-order spatial derivatives, our theory provides conditions on free and fixed boundaries. The free boundary conditions involve the curvature of the free surface; among the conditions for a fixed boundary are generalized adherence and slip conditions, each of which involves a material length scale. We reconsider the classical problem of plane Poiseuille flow for generalized adherence and slip conditions.
TL;DR: Analysis is used to identify two sources of kinetic energy conservation error in the collocated-mesh scheme: errors arising from the interpolations used to estimate the velocity on the cell faces, and errors associated with the slightly inconsistent pressure field used to ensure mass conservation for the cell face volume fluxes.
TL;DR: Using this formulation, the steady 2-D incompressible flow in a driven cavity is solved up to Reynolds number of 20,000 with fourth order spatial accuracy.
Abstract: SUMMARY 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 of 20,000 with fourth order spatial accuracy. Detailed solutions are presented.
TL;DR: In this article, the authors used large-eddy simulation (LES) to study the three-dimensional incompressible flow past a rectangular two-dimensional shallow cavity in a channel.
Abstract: The three-dimensional incompressible flow past a rectangular two-dimensional shallow cavity in a channel is investigated using large-eddy simulation (LES). The aspect ratio (length/depth) of the cavity is L/D = 2 and the Reynolds number defined with the cavity depth and the mean velocity in the upstream channel is 3360. The sensitivity of the flow around the cavity to the characteristics of the upstream flow is studied by considering two extreme cases: a developing laminar boundary layer upstream of the cavity and when the upstream flow is fully turbulent. The two simulations are compared in terms of the mean statistics and temporal physics of the flow, including the dynamics of the coherent structures in the region surrounding the cavity. For the laminar inflow case it is found that the flow becomes unstable but remains laminar as it is convected over the cavity. Due to the three-dimensional flow instabilities and the interaction of the jet-like flow inside the recirculation region with the separated shear layer, the spanwise vortices that are shed regularly from the leading cavity edge are disturbed in the spanwise direction and, as they approach the trailing-edge corner, break into an array of hairpin-like vortices that is convected downstream the cavity close to the channel bottom. In the fully turbulent inflow case in which the momentum thickness of the incoming boundary layer is much larger compared to the laminar inflow case, the jittering of the shear layer on top of the cavity by the incoming near-wall coherent structures strongly influences the formation and convection of the eddies inside the separated shear layer. The mass exchange between the cavity and the main channel is investigated by considering the ejection of a passive scalar that is introduced instantaneously inside the cavity. As expected, it is found that the ejection is faster when the incoming flow is turbulent due to the interaction between the turbulent eddies convected from upstream of the cavity with the separated shear layer and also to the increased diffusion induced by the broader range of scales that populate the cavity. In the turbulent case it is shown that the eddies convected from upstream of the cavity can play an important role in accelerating the extraction of high-concentration fluid from inside the cavity. For both laminar and turbulent inflow cases it is shown that the scalar ejection can be described using simple dead-zone theory models in which a single-valued global mass exchange coefficient can be used to describe the scalar mass decay inside cavity over the whole ejection process.
TL;DR: In this paper, a new modeling framework is proposed for describing the flow regime transition utilizing a shock-capturing technique that decouples the hydrostatic pressure from surcharged pressures occurring only in pressurized conditions, effectively overcoming the cited Preissmann slot limitation.
Abstract: Operational problems and system damage have been linked to the flow regime transition between free surface and pressurized flow in rapidly filling stormwater and combined sewer systems. In response, emphasis has been placed on the development of numerical models to describe hydraulic bores and other flow phenomena that may occur in these systems. Current numerical models are based on rigid column analyses, shock-fitting techniques, or shock-capturing procedures employing the Preissmann slot concept. The latter approach is appealing due to the comparative simplicity, but suffers from the inability to realistically describe subatmospheric full-pipe flows. A new modeling framework is proposed for describing the flow regime transition utilizing a shock-capturing technique that decouples the hydrostatic pressure from surcharged pressures occurring only in pressurized conditions, effectively overcoming the cited Preissmann slot limitation. This new approach exploits the identity between the unsteady incompressible flow equations for elastic pipe walls and the unsteady open-channel flow equations, and the resulting numerical implementation is straightforward with only minor modifications to standard free surface flow models required. A comparison is made between the model predictions and experimental data; good agreement is achieved.
TL;DR: In this paper, the spectral element method is employed to carry out two-and three-dimensional simulations of the incompressible flow around pairs of circular cylinders in tandem arrangements, where the simulations are in the Reynolds number (Re) range from 160 to 320, covering the transition in the wake.
TL;DR: The two-dimensional simulation of blood flow between parallel plates demonstrated the capability of the proposed particle method to express the blood flow phenomena observed in experiments, such as the downstream motion of the RBC and the deformation of theRBC into a parachute shape.
TL;DR: The proposed algorithm combines an implicit pressure stabilized finite element method for the solution of incompressible two-phase flow problems with a level set method implemented with a quadrature-free discontinuous Galerkin (DG) method.
TL;DR: Gresho and Sani as discussed by the authors showed that the Navier-Stokes momentum equation can be solved simultaneously with the pressure Poisson equation (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 components of velocity is specified as a Dirichlet BC.
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.
TL;DR: In this article, the wall roughness is assumed to posses a Gaussian isotropic distribution, and a novel analytical model is developed that predicts the increase in pressure drop due to wall rougheness in microtubes.
Abstract: The characteristics of fully-developed, laminar, pressure-driven, incompressible flow in rough circular microchannels are studied. A novel analytical model is developed that predicts the increase in pressure drop due to wall roughness in microtubes. The wall roughness is assumed to posses a Gaussian isotropic distribution. The present model is compared with experimental data, collected by other researchers and good agreement is observed.
TL;DR: The resulting discretization approach, which is a type of the CIP/multi-moment finite volume method and called VSIAM3 (volume/surface integrated average-based multi-moments method), is combined with a pressure-based projection formulation for the time integration to enable the simulations for both compressible and incompressible flows.
TL;DR: In this paper, a small augmentation is proposed which allows to overcome the dilemma of incompressibility and fixed boundary velocities by introducing the volume constraint on the structural system of equations.
Abstract: In a subset of fluid–structure interaction (FSI) problems of incompressible flow and highly deformable structures all popular partitioned approaches fail to work. This also holds for recently quite popular strong coupling approaches based on Dirichlet–Neumann substructuring. This subset can be described as the special case where the fluid domain is entirely enclosed by Dirichlet boundary conditions, i.e. prescribed velocities. A vivid simple example would be a balloon with prescribed inflow rate. In such cases the incompressibility of the fluid cannot be satisfied during standard alternating FSI iterations as the deformation of the coupling surface is determined by the structural displacement that usually does not know about the current constraint on the fluid field. By analyzing this deficiency of the partitioned algorithm a small augmentation is proposed which allows to overcome the dilemma of incompressibility and fixed boundary velocities by introducing the volume constraint on the structural system of equations. In contrast to the original accelerated strong coupling partitioned method, the relaxation which ensures convergence of the iteration over the different fields has now to be performed on the coupling forces rather than on the displacements. In addition, two alternative approaches are discussed for the solution of the dilemma. The capability of the proposed method to deal with largely changing volumes of enclosed fluid is demonstrated by means of numerical examples.
TL;DR: In this paper, a volume of fluid (VOF) technique was developed and coupled with an incompressible Euler/Navier-Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures.
TL;DR: In this article, an incompressible MRT-LBGK model has been proposed to recover the Navier-Stokes equations without artificial compressible effects, and the numerical simulation results agree well with the analytical solutions or the existing results.
TL;DR: In this article, an implicit algorithm for incompressible fluid flow solution using the arbitrary Lagrangian-Eulerian (ALE) formulation is presented, where the penalty method is utilized to eliminate the pressure on the element level.
TL;DR: In this paper, the local multiquadric differential quadrature (LMQDQ) method is applied on three-dimensional incompressible flow problems, where the radial basis functions (RBFs) are used as the trial functions instead of high-order polynomials.
TL;DR: This work rigorously establishes the well‐posedness of the proposed model for designing domains for incompressible Navier–Stokes flows, and proposes changes in the optimization model that allow it to overcome the two key difficulties.
Abstract: We consider the problem of optimal design of flow domains for Navier–Stokes flows in order to minimize a given performance functional. We attack the problem using topology optimization techniques, or control in coefficients, which are widely known in structural optimization of solid structures for their flexibility, generality, and yet ease of use and integration with existing FEM software. Topology optimization rapidly finds its way into other areas of optimal design, yet until recently it has not been applied to problems in fluid mechanics. The success of topology optimization methods for the minimal drag design of domains for Stokes fluids (see the study of Borrvall and Petersson [12]) has lead to attempts to use the same optimization model for designing domains for incompressible Navier–Stokes flows. We show that the optimal control problem obtained as a result of such a straightforward generalization is ill-posed, at least if attacked by the direct method of calculus of variations. We illustrate the two key difficulties with simple numerical examples and propose changes in the optimization model that allow us to overcome these difficulties. Namely, to deal with impenetrable inner walls that may appear in the flow domain we slightly relax the incompressibility constraint as typically done in penalty methods for solving the incompressible Navier–Stokes equations. In addition, to prevent discontinuous changes in the flow due to very small impenetrable parts of the domain that may disappear, we consider so-called filtered designs, that has become a “classic” tool in the topology optimization toolbox. Technically, however, our use of filters differs significantly from their use in the structural optimization problems in solid mechanics, owing to the very unlike design parametrizations in the two models. We rigorously establish the well-posedness of the proposed model and then discuss related computational issues.