Showing papers on "Incompressible flow published in 2003"
TL;DR: An adaptive mesh projection method for the time-dependent incompressible Euler equations is presented and second-order convergence in space and time is demonstrated on regular, statically and dynamically refined grids.
1,122 citations
Book•
02 Jun 2003
TL;DR: An introduction to monotonicity-preserving schemes and other stabilization techniques and new trends in fluid dynamics, and main issues in incompressible flow problems.
Abstract: Preface. 1. Introduction and preliminaries. Finite elements in fluid dynamics. Subjects covered. Kinematical descriptions of the flow field. The basic conservation equations. Basic ingredients of the finite element method. 2. Steady transport problems. Problem statement. Galerkin approximation. Early Petrov-Galerkin methods. Stabilization techniques. Other stabilization techniques and new trends. Applications and solved exercises. 3. Unsteady convective transport. Introduction. Problem statement. The methods of characteristics. Classical time and space discretization techniques. Stability and accuracy analysis. Taylor-Galerkin Methods. An introduction to monotonicity-preserving schemes. Least-squares-based spatial discretization. The discontinuous Galerkin method. Space-time formulations. Applications and solved exercises. 4. Compressible Flow Problems. Introduction. Nonlinear hyperbolic equations. The Euler equations. Spatial discretization techniques. Numerical treatment of shocks. Nearly incompressible flows. Fluid-structure interaction. Solved exercises. 5. Unsteady convection-diffusion problems. Introduction. Problem statement. Time discretization procedures. Spatial discretization procedures. Stabilized space-time formulations. Solved exercises. 6. Viscous incompressible flows. Introduction Basic concepts. Main issues in incompressible flow problems. Trial solutions and weighting functions. Stationary Stokes problem. Steady Navier-Stokes problem. Unsteady Navier-Stokes equations. Applications and Solved Exercices. References. Index.
1,035 citations
TL;DR: A hierarchy of low-dimensional Galerkin models is proposed for the viscous, incompressible flow around a circular cylinder building on the pioneering works of Stuart (1958), Deane et al. (1991), and Ma & Karniadakis (2002) as mentioned in this paper.
Abstract: A hierarchy of low-dimensional Galerkin models is proposed for the viscous, incompressible flow around a circular cylinder building on the pioneering works of Stuart (1958), Deane et al. (1991), and Ma & Karniadakis (2002). The empirical Galerkin model is based on an eight-dimensional Karhunen–Loeve decomposition of a numerical simulation and incorporates a new ‘shift-mode’ representing the mean-field correction. The inclusion of the shift-mode significantly improves the resolution of the transient dynamics from the onset of vortex shedding to the periodic von Karman vortex street. In addition, the Reynolds-number dependence of the flow can be described with good accuracy. The inclusion of stability eigenmodes further enhances the accuracy of fluctuation dynamics. Mathematical and physical system reduction approaches lead to invariant-manifold and to mean-field models, respectively. The corresponding two-dimensional dynamical systems are further reduced to the Landau amplitude equation.
989 citations
TL;DR: A phase field model for the mixture of two incompressible fluids is presented in this article, which is based on an energetic variational formulation, consisting of a Navier-Stokes system coupled with a Cahn-Hilliard equation through an extra stress term and the transport term.
612 citations
TL;DR: In this paper, a family of acoustic perturbation equations for the simulation of flow-induced acoustic fields in time and space is derived, which are excited by source terms determined from a simulation of the compressible or the incompressible flow problem.
584 citations
TL;DR: Numerical experiments showed that the simplified thermal model can keep the same order of accuracy as the thermal energy distribution model, but it requires much less computational effort.
Abstract: Considering the fact that the compression work done by the pressure and the viscous heat dissipation can be neglected for the incompressible flow, and its relationship with the gradient term in the evolution equation for the temperature in the thermal energy distribution model, a simplified thermal energy distribution model is proposed. This thermal model does not have any gradient term and is much easier to be implemented. This model is validated by the numerical simulation of the natural convection in a square cavity at a wide range of Rayleigh numbers. Numerical experiments showed that the simplified thermal model can keep the same order of accuracy as the thermal energy distribution model, but it requires much less computational effort.
385 citations
TL;DR: The method developed in this paper is motivated by Peskin's immersed boundary (IB) method, and allows one to model the motion of flexible membranes or other structures immersed in viscous incompressible fluid using a fluid solver on a fixed Cartesian grid.
Abstract: The method developed in this paper is motivated by Peskin's immersed boundary (IB) method, and allows one to model the motion of flexible membranes or other structures immersed in viscous incompressible fluid using a fluid solver on a fixed Cartesian grid. The IB method uses a set of discrete delta functions to spread the entire singular force exerted by the immersed boundary to the nearby fluid grid points. Our method instead incorporates part of this force into jump conditions for the pressure, avoiding discrete dipole terms that adversely affect the accuracy near the immersed boundary. This has been implemented for the two-dimensional incompressible Navier--Stokes equations using a high-resolution finite-volume method for the advective terms and a projection method to enforce incompressibility. In the projection step, the correct jump in pressure is imposed in the course of solving the Poisson problem. This gives sharp resolution of the pressure across the interface and also gives better volume conservation than the traditional IB method. Comparisons between this method and the IB method are presented for several test problems. Numerical studies of the convergence and order of accuracy are included.
355 citations
TL;DR: The finite element approximation can capture the discontinuities at the interface without requiring the mesh to conform to the interface, eliminating the need for remeshing.
Abstract: An extended finite element method with arbitrary interior discontinuous gradients is applied to two-phase immiscible flow problems. The discontinuity in the derivative of the velocity field is introduced by an enrichment with an extended basis whose gradient is discontinuous across the interface. Therefore, the finite element approximation can capture the discontinuities at the interface without requiring the mesh to conform to the interface, eliminating the need for remeshing. The equations for incompressible flow are solved by a fractional step method where the advection terms are stabilized by a characteristic Galerkin method. The phase interfaces are tracked by level set functions which are discretized by the same finite element mesh and are updated via a stabilized conservation law. The method is demonstrated in several examples
300 citations
TL;DR: In this paper, a hybrid LES-RANS modeling approach is proposed, where RANS is used in the near wall regions (y ≤ 60), and the turbulence is modelled with a κ-ω model.
Abstract: A hybrid LES-RANS modelling approach is proposed. RANS is used in the near wall regions (y ≤ 60), and the turbulence is modelled with a κ-ω model. LES is used in the remaining part of the flow, and the SGS turbulence is modelled with a one-equation κ sgs model. The same continuity and momentum equations are solved throughout the domain, the only difference being that the turbulent viscosity is taken from the κ-ω model in the RANS region, and from the one-equation κ sgs model in the LES region. The new modelling approach is applied to two incompressible flow test cases. They are fully developed flow in a plane channel and the flow over a 2D-hill in a channel
191 citations
TL;DR: In this paper, a direct, exact, and complete numerical solution of the flow in porous media is given for arbitrary distributions of permeabilities in the porous matrix and in the fracture network.
Abstract: [1] Flow in fractured porous media was first investigated by Barenblatt and Zheltov [1960] and Barenblatt et al. [1960] by means of the double-porosity model. A direct, exact, and complete numerical solution of the flow in such media is given in this paper for arbitrary distributions of permeabilities in the porous matrix and in the fracture network. The fracture network and the porous matrix are automatically meshed; the flow equations are discretized by means of the finite volume method. This code has been so far applied to incompressible fluids and to statistically homogeneous media which are schematized as spatially periodic media. Some results pertaining to random networks of polygonal fractures are presented and discussed; they show the importance of the percolation threshold of the fracture network and possibly of the porous matrix. Moreover, the influence of the fracture shape can be taken into account by means of the excluded volume.
180 citations
TL;DR: In this article, an artificial compressibility scheme using the finite element method is introduced, which takes advantage of good features from both velocity correction and standard artificial compressible schemes and works on a variety of grids and gives results for a wide range of Reynold's numbers.
Abstract: In this paper, an artificial compressibility scheme using the finite element method is introduced. 2002 Zienkiewicz Silver Medal and Prize winning paper. The multi-purpose CBS scheme is implemented in its fully explicit form to solve incompressible fluid dynamics problems. It is important to note that the scheme developed here includes split and velocity correction. The proposed method takes advantage of good features from both velocity correction and standard artificial compressibility schemes. Unlike many other artificial compressibility schemes, the proposed one works on a variety of grids and gives results for a wide range of Reynold's numbers. The paper presents some bench mark two- and three-dimensional steady and unsteady incompressible flow solutions obtained from the proposed scheme. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this paper, strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids in R 3 have been derived independent of the lower bound of the density.
Abstract: We study strong solutions of the Navier–Stokes equations for nonhomogeneous incompressible fluids in Ω ⊂ R 3. Deriving higher a priori estimates independent of the lower bounds of the density, we p...
TL;DR: In this paper, a tangent line to the adiabatic pressure-volume curve is used as an approximation to the curve itself, which can be applied to flows with velocities approaching that of sound, whereas the theory of Demtchenko and Busemann only gives an approximation for flows with velocity smaller than one half of the sound velocity.
Abstract: The basic concept of the present paper is to use a tangent line to the adiabatic pressure-volume curve as an approximation to the curve itself. First, the general characteristics of such a fluid are shown. Then in Section I a theory is developed which can be applied to flows with velocities approaching that of sound, whereas the theory of Demtchenko and Busemann only give an approximation for flows with velocities smaller than one-half of the sound velocity. This is done by a generalization of the method of approximation to the adiabatic relation by a tangent line, conceived jointly by Th. von Karman and the author. The theory is put into a form by which, knowing the incompressible flow over a body, the compressible flow over a similar body can be calculated. The theory is then applied to calculate the flow over elliptic cylinders. In Section II the work of H. Bateman is applied to this approximate adiabatic fluid and the results obtained are essentially the same as those obtained in Section I.
TL;DR: In this paper, a single time scale, multiple space scale asymptotic analysis is used to gain insight into the limit behavior of the compressible flow equations as the Mach number vanishes.
TL;DR: In this article, a mathematical analysis of the quasilinear effects arising in a hyperbolic system of partial differential equations modelling blood flow through large compliant vessels is presented, which is derived using asymptotic reduction of the incompressible Navier-Stokes equations in narrow, long channels.
Abstract: In this paper, we present a mathematical analysis of the quasilinear effects arising in a hyperbolic system of partial differential equations modelling blood flow through large compliant vessels. The equations are derived using asymptotic reduction of the incompressible Navier–Stokes equations in narrow, long channels.
To guarantee strict hyperbolicity we first derive the estimates on the initial and boundary data which imply strict hyperbolicity in the region of smooth flow. We then prove a general theorem which provides conditions under which an initial–boundary value problem for a quasilinear hyperbolic system admits a smooth solution. Using this result we show that pulsatile flow boundary data always give rise to shock formation (high gradients in the velocity and inner vessel radius). We estimate the time and the location of the first shock formation and show that in a healthy individual, shocks form well outside the physiologically interesting region (2.8m downstream from the inlet boundary). In the end we present a study of the influence of vessel tapering on shock formation. We obtain a surprising result: vessel tapering postpones shock formation. We provide an explanation for why this is the case. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this article, the analysis of the incompressible laminar shear driven flow in a channel of which one of the walls carries a macro roughness pattern while the opposite one has a parallel velocity is discussed from the standpoint of lubrication theory and it is shown that the usual simplified models as the Reynolds or the Stokes equations are not applicable.
Abstract: The present work deals with the analysis of the incompressible laminar shear driven flow in a channel of which one of the walls carries a macro roughness pattern while the opposite one has a parallel velocity. The problem is discussed from the standpoint of lubrication theory and it is shown that the usual simplified models as the Reynolds or the Stokes equations are not applicable. Numerical results are presented for three types of two dimensional macro-roughness and two versions of a three dimensional one. It is shown that a pressure generation effect occurs with increasing the relative importance of convective inertia. Previous analyses found in the literature discussed only the increase of the shear stress due to the presence of the macro roughness but the lift effect due to the pressure generation has never been enlightened up to now. It is further discussed that, extrapolated to a very large number of macro roughness characterizing a textured surface, this new effect could be added to the other lift generating mechanisms of the lubrication theory. It could thus bring a different light on inertia effects stemming from the use of textured surfaces.
TL;DR: In this article, the Navier-Stokes equations are reduced to a single, nonlinear, ordinary differential equation, and the resulting equation is then solved both numerically and asymptotically, using perturbations in the crossflow Reynolds number R.
Abstract: We consider in this paper the incompressible laminar flow in a porous channel with expanding or contracting walls. While the head-end is closed by a compliant membrane, the downstream end is left unobstructed. For symmetric injection or suction along the uniformly expanding porous walls, the Navier-Stokes equations are reduced to a single, nonlinear, ordinary differential equation. The latter is obtained via similarity transformations in both time and space. The resulting equation is then solved both numerically and asymptotically, using perturbations in the crossflow Reynolds number R. Two separate approaches are presented for each of the injection and suction cases, respectively. For the large injection case, the governing equation is first integrated and the resulting third-order differential equation is solved using the method of variation of parameters. For the large suction case, the governing equation is first simplified near the wall and then solved using successive approximations. Results are then correlated and compared for variations in R and the dimensionless wall expansion rate α. For injection-induced flow, the asymptotic solution becomes more accurate when R/α is increased. Its deviation from the classic sinusoidal profile arising in nonexpanding channels becomes less significant with successive increases in R. For suction-induced flows, faster wall contractions increase the effective Reynolds number -(α + R), thus leading to more precise approximations. For the same absolute value of R, the suction-flow approximation tends to be the most accurate of the two and the least sensitive to variations in α. As - (α + R) is increased, the suction profile approaches the linear form anticipated in nonexpanding channels. By comparison with the injection-induced flow, suction is characterized by improved accuracy, sharper flow turning, and larger shear.
TL;DR: Analytical expressions for axial velocity, fluid acceleration, flow rate and shear stress have been obtained inulsatile flow of blood through a stenosed porous medium under the influence of body acceleration.
TL;DR: The local discontinuous Galerkin method is introduced and analyzed for a class of shape-regular meshes with hanging nodes and optimal a priori estimates for the errors in the velocity and the pressure in L 2 - and negative-order norms are derived.
Abstract: We introduce and analyze the local discontinuous Galerkin method for the Oseen equations of incompressible fluid flow. For a class of shape-regular meshes with hanging nodes, we derive optimal a priori estimates for the errors in the velocity and the pressure in L 2 - and negative-order norms. Numerical experiments are presented which verify these theoretical results and show that the method performs well for a wide range of Reynolds numbers.
TL;DR: In this article, a comprehensive numerical investigation of incompressible flow about fixed cylinder pairs is performed, including tandem, side-by-side, and staggered and Reynolds numbers of 80 and 1000.
TL;DR: In this paper, a moving staggered mesh discretization for the numerical simulation of incompressible flow problems involving free-surfaces is presented, which uses the staggered mesh to obtain speed and conservation properties.
TL;DR: In this article, the feasibility of taking advantage of bend-induced vortices to stir the fluid and enhance the mixing process was evaluated theoretically and experimentally, and a prototype of a stirrer was fabricated with low temperature co-fired ceramic tapes.
TL;DR: In this paper, a new free surface tracking algorithm based on the donor-acceptor scheme has been proposed, which can be easily implemented in any irregular non-uniform grid systems usually encountered in the finite element method (FEM).
Abstract: Numerical simulation of fluid flow with moving free surface has been performed. For the free surface flow, a volume of fluid (VOF)-based algorithm utilizing a fixed grid system has been investigated. In order to reduce numerical smearing at the free surface represented on a fixed grid system, a new free surface-tracking algorithm based on the donor–acceptor scheme has been proposed. Novel features of the proposed algorithm are characterized by two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed algorithm can be easily implemented in any irregular non-uniform grid systems usually encountered in the finite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3D free surface flow problems without additional efforts. For computation of unsteady incompressible flow, a finite element approximation based on the explicit fractional step method has been adopted. In addition, the streamline upwind/Petrov–Galerkin (SUPG) method has been implemented to deal with convection dominated flows. Combination of the proposed free surface-tracking scheme and the explicit fractional step formulation resulted in an efficient solution algorithm. Validity of the present solution algorithm was demonstrated from its application to the broken dam and the solitary wave propagation problems. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this paper, a two-dimensional numerical study on the laminar incompressible flow past a rotating circular cylinder in the Reynolds number range 60-Re⩽200 and at rotational rates 0-6 was carried out.
Abstract: To examine in detail the behavior of a new vortex shedding mode found in a previous investigation [Phys. Fluids 14, 3160 (2002)], a two-dimensional numerical study on the laminar incompressible flow past a rotating circular cylinder in the Reynolds number range 60⩽Re⩽200 and at rotational rates 0⩽α⩽6 was carried out. The results obtained clearly confirm the existence of the second shedding mode for the entire Reynolds number range investigated. A complete bifurcation diagram α(Re) was compiled defining both kind of shedding modes. The unsteady periodic flow in the second mode is characterized by a frequency much lower than that known for classical von Karman vortex shedding of the first mode. The corresponding Strouhal number shows a strong dependence on the rotational velocity of the cylinder, while only a weak dependence is observed for the Reynolds number. Furthermore, the amplitudes of the fluctuating lift and drag coefficients are much larger than those characterizing classical vortex shedding behind...
TL;DR: This paper compares both lattice Boltzmann method and gas-kinetic BGK scheme in the isothermal low-Mach number flow simulations and chooses to use the 2D cavity flow since it is one of the most extensively studied cases.
TL;DR: In this paper, the authors studied the transition to turbulence in the incompressible flow around a NACA0012 wing at high incidence in the Reynolds number range 800-10000 and identified two main routes for the two-dimensional transition mechanisms: that to aperiodicity beyond the von Karman mode via a period doubling scenario and the development of a shear-layer instability, forced by the fundamental oscillation of the separation point downstream of the leading edge.
Abstract: The transition to turbulence in the incompressible flow around a NACA0012 wing at high incidence is studied by DNS in the Reynolds number range 800–10000. Two main routes are identified for the two-dimensional transition mechanisms: that to aperiodicity beyond the von Karman mode via a period-doubling scenario and the development of a shear-layer instability, forced by the fundamental oscillation of the separation point downstream of the leading edge. The evolution of the global parameters as well as the variation law of the shear-layer instability wavelength are quantified. The history of the three-dimensional transition mechanisms from a nominally two-dimensional flow structure is identified beyond the first bifurcation, as well as the preferred spanwise wavelengths.
01 Jan 2003
TL;DR: A Lattice Bhatager-Gross-Krook (LBGK) model to simulate incompressible flow is developed and the numerical results are found to be in excellent agreement with theory and the results of previous studies.
Abstract: In this paper a Lattice Bhatager-Gross-Krook (LBGK) model to simulate incompressible flow is developedThe basic idea is to explicitly eliminate the compressible effect, due to the density fluctuation in the existing LBGK modelsIn the proposed incompressible LBGK model, the pressure p instead of the constant mass density ρ0 is the independent dynamic variableThe incompressible Navier-Stokes equations are exactly derived from this incompressible LBGK modelIn order to test the LBGK model, the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as the 2-D Womersley flow are simulatedThe numerical results are found to be in excellent agreement with theory and the results of previous studies
TL;DR: A fourth order finite difference method is presented for the 2D unsteady viscous incompressible Boussinesq equations in vorticity-stream function formulation, which is especially suitable for moderate to large Reynolds number flows.
Abstract: A fourth order finite difference method is presented for the 2D unsteady viscous incompressible Boussinesq equations in vorticity-stream function formulation. The method is especially suitable for moderate to large Reynolds number flows. The momentum equation is discretized by a compact fourth order scheme with the no-slip boundary condition enforced using a local vorticity boundary condition. Fourth order long-stencil discretizations are used for the temperature transport equation with one-sided extrapolation applied near the boundary. The time stepping scheme for both equations is classical fourth order Runge–Kutta. The method is highly efficient. The main computation consists of the solution of two Poisson-like equations at each Runge–Kutta time stage for which standard FFT based fast Poisson solvers are used. An example of Lorenz flow is presented, in which the full fourth order accuracy is checked. The numerical simulation of a strong shear flow induced by a temperature jump, is resolved by two perfectly matching resolutions. Additionally, we present benchmark quality simulations of a differentially-heated cavity problem. This flow was the focus of a special session at the first MIT conference on Computational Fluid and Solid Mechanics in June 2001.
TL;DR: This paper proves the convergence of a numerical method for solving two-phase immiscible, incompressible flow in porous media that combines an upwind time implicit finite volume scheme for the saturation equation and a centered finite volume Scheme for the Chavent global pressure equation.
Abstract: In this paper, we prove the convergence of a numerical method for solving two-phase immiscible, incompressible flow in porous media. The method combines an upwind time implicit finite volume scheme for the saturation equation (hyperbolic-parabolic type) and a centered finite volume scheme for the Chavent global pressure equation (elliptic type). The capillary pressure is not neglected, and we study the case when the diffusion term in the saturation equation is weakly degenerated. Estimates on the approximate solution are proven; then by using compactness theorems we obtain a limit when the size of the discretization goes to zero, and we prove that this limit is the unique weak solution of the problem that we study.
TL;DR: In this article, the vorticity-stream function form of N-S equations is taken as the governing equations and the LRPIM method is adopted to simulate the two-dimensional natural convection problems within enclosed domain of different geometries.
Abstract: The LRPIM method is adopted to simulate the two-dimensional natural convection problems within enclosed domain of different geometries. In this paper, the vorticity-stream function form of N-S equations is taken as the governing equations. It was observed that the obtained results agreed very well with others available in the literatures, and with the same nodal density, the accuracy achieved by the LRPIM method is much higher than that of the finite difference (FD) method. The numerical examples show that the present LRPIM method can successfully deal with incompressible flow problems on randomly distributed nodes.