Showing papers on "Incompressible flow published in 1997"

On pressure and velocity boundary conditions for the lattice Boltzmann BGK model

Abstract: Pressure ~density! and velocity boundary conditions are studied for 2-D and 3-D lattice Boltzmann BGK models ~LBGK! and a new method to specify these conditions is proposed. These conditions are constructed in consistency with the wall boundary condition, based on the idea of bounceback of the non-equilibrium distribution. When these conditions are used together with the incompressible LBGK model @J. Stat. Phys. 81 ,3 5 ~1995!# the simulation results recover the analytical solution of the plane Poiseuille flow driven by a pressure ~density! difference. The half-way wall bounceback boundary condition is also used with the pressure ~density! inlet/outlet conditions proposed in this paper and in Phys. Fluids 8, 2527 ~1996! to study 2-D Poiseuille flow and 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback boundary condition is comparable with that of other published boundary conditions and it has better stability behavior. © 1997 American Institute of Physics. @S1070-6631~97!03406-5#

Lattice boltzmann model for the incompressible navier-stokes equation

Abstract: In this paper a lattice Boltzmann (LB) model to simulate incompressible flow is developed. The main idea is to explicitly eliminate the terms of o(M 2), where M is the Mach number, due to the density fluctuation in the existing LB models. In the proposed incompressible LB model, the pressure p instead of the mass density ρ is the independent dynamic variable. The incompressible Navier–Stokes equations are derived from the incompressible LB model via Chapman–Enskog procedure. Numerical results of simulations of the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2D Womersley flow are presented. The numerical results are found to be in excellent agreement with theory.

Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension

Abstract: A second-order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented. The interface may consist of an elastic boundary immersed in the fluid or an interface between two different fluids. The interface is represented by a cubic spline along which the singularly supported elastic or surface tension force can be computed. The Stokes equations are then discretized using the second-order accurate finite difference methods for elliptic equations with singular sources developed in our previous paper [SIAM J. Numer. Anal., 31(1994), pp. 1019--1044]. The resulting velocities are interpolated to the interface to determine the motion of the interface. An implicit quasi-Newton method is developed that allows reasonable time steps to be used.

An adaptive level set approach for incompressible two-phase flows

Abstract: In Sussman, Smereka and Osher, a numerical method using the level set approach was formulated for solving incompressible two-phase flow with surface tension. In the level set approach, the interface is represented as the zero level set of a smooth function; this has the effect of replacing the advection of density, which has steep gradients at the interface, with the advection of the level set function, which is smooth. In addition, the interface can merge or break up with no special treatment. The authors maintain the level set function as the signed distance from the interface in order to robustly compute flows with high density ratios and stiff surface tension effects. In this work, they couple the level set scheme to an adaptive projection method for the incompressible Navier-Stokes equations, in order to achieve higher resolution of the interface with a minimum of additional expense. They present two-dimensional axisymmetric and fully three-dimensional results of air bubble and water drop computations.

Nonlinear theory of unstable fluid mixing driven by shock wave

Abstract: A shock driven material interface between two fluids of different density is unstable. This instability is known as Richtmyer–Meshkov (RM) instability. In this paper, we present a quantitative nonlinear theory of compressible Richtmyer–Meshkov instability in two dimensions. Our nonlinear theory contains no free parameter and provides analytical predictions for the overall growth rate, as well as the growth rates of the bubble and spike, from early to later times for fluids of all density ratios. The theory also includes a general formulation of perturbative nonlinear solutions for incompressible fluids (evaluated explicitly through the fourth order). Our theory shows that the RM unstable system goes through a transition from a compressible and linear one at early times to a nonlinear and incompressible one at later times. Our theoretical predictions are in excellent agreement with the results of full numerical simulations from linear to nonlinear regimes.

A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries

Abstract: Many problems in fluid dynamics require the representation of complicated internal or external boundaries of the flow. Here we present a method for calculating time-dependent incompressible inviscid flow which combines a projection method with a "Cartesian grid" approach for representing geometry. In this approach, the body is represented as an interface embedded in a regular Cartesian mesh. The advection step is based on a Cartesian grid algorithm for compressible flow, in which the discretization of the body near the flow uses a volume-of-fluid representation. A redistribution procedure is used to eliminate time-step restrictions due to small cells where the boundary intersects the mesh. The projection step uses an approximate projection based on a Cartesian grid method for potential flow. The method incorporates knowledge of the body through volume and area fractions along with certain other integrals over the mixed cells. Convergence results are given for the projection itself and for the time-dependent algorithm in two dimensions. The method is also demonstrated on flow past a half-cylinder with vortex shedding.

Regularity Results for Two-Dimensional Flows of Multiphase Viscous Fluids

Abstract: Global regularity results for weak solutions of the Navier-Stokes equations for two-dimensional multiphase incompressible fluids are proved under suitable conditions on the viscosity without assuming positive lower bounds on the initial density. As an application, we deduce regularity properties for the integral curves of the corresponding velocity field. Finally, we prove regularity results “in the small” for strong solutions.

Coupled Fluid-Structural Characteristics of Actuators for Flow Control

Abstract: The characteristics of a typical flow control actuator design are discussed. The device is based on a resonating structure that interacts with a closed volume of fluid to create a concentrated jet through an exit orifice. The resulting unsteady flow through the orifice introduces viscous effects that are characterized by the Stokes parameter based on the orifice diameter. An optimum operating Stokes parameter is then computed by matching this viscous dominated solution to an ideal, inviscid result. The actuator is modeled with a system of coupled equations that describe its fluid-structural behavior.

Parallel computation of incompressible flows with complex geometries

Abstract: SUMMARY We present our numerical methods for the solution of large-scale incompressible flow applications with complex geometries. These methods include a stabilized finite element formulation of the Navier‐Stokes equations, implementation of this formulation on parallel architectures such as the Thinking Machines CM-5 and the CRAY

Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation

Abstract: In this paper the simulation of incompressible flow in two dimensions by the least-squares finite element method (LSFEM) in the vorticity-velocity-pressure version is studied. In the LSFEM, the equations for continuity of mass and momentum and a vorticity equation are minimized on a discretization of the domain of interest. A problem is these equations are minimized in a global sense. Thus this method may not enforce that div$\underline{u} = 0$ at every point of the discretization. In this paper a modified LSFEM is developed which enforces near zero residual of mass conservation, i.e., div$\underline{u}$ is nearly zero at every point of the discretization. This is accomplished by adding an extra restriction in the divergence-free equation through the Lagrange multiplier strategy. In this numerical method the inf-sup or say LBB condition is not necessary, and the matrix resulting from applying the method on a discretization is symmetric; the uniqueness of the solution and the application of the conjugate gradient method are also valid. Numerical experience is given in simulating the flow of a cylinder with diameter 1 moving in a narrow channel of width 1.5. Results obtained by the LSFEM show that mass is created or destroyed at different points in the interior of discretization. The results obtained by the modified LSFEM show the mass is nearly conserved everywhere.

Three-dimensional coupled fluid-structure simulation of pericardial bioprosthetic aortic valve function

Abstract: A computational, three-dimensional coupled fluid-structure dynamics model was developed for a generic pericardial aortic valve in a rigid aortic root graft with physiologic sinuses. Valve geometry was based on that of the natural valve. Blood flow was modeled as pulsatile, laminar, Newtonian, incompressible flow. The structural model accounted for material and geometric nonlinearities and also simulated leaflet coaptation. A body fitted grid was used to subdivide the flow domain into computational finite volume cells. Shell finite elements were used to discretize the leaflet volume. A finite volume computational fluid dynamics code and finite element structure dynamics code were used to solve the flow and structure equations, respectively. The fluid flow and structural equations were coupled using an implicit "influence coefficient" technique. Physiologic ventricular and aortic pressure waveforms were prescribed as the flow boundary conditions. The aortic flow field, valve structural configuration, and leaflet stresses were computed at 2 msec intervals. Model predictions on aortic flow and transient variation in valve orifice area were in close agreement with corresponding experimental in vitro data. These findings suggest that the computer model has potential for being a powerful design tool for bioprosthetic aortic valves.

A Lagrange multiplier/fictitious domain method for the numerical simulation of incompressible viscous flow around moving rigid bodies: (I) case where the rigid body motions are known a priori

Abstract: We describe in this Note a method for the numerical simulation of incompressible viscous flow around moving rigid bodies; we suppose the rigid body motions a priori known. The computational technique takes advantage of a time discretization by operator splitting a la Marchuk-Yanenko and of a finite element space discretization on a fixed mesh, to combine a Lagrange multiplier/fictitious domain treatment of the rigid body motions with an L2-projection technique, to force the incompressibility condition. The results of numerical experiments concerning flow around moving disks at Reynolds number of the order of 100 are presented.

An Adaptive Mesh Projection Method for Viscous Incompressible Flow

Abstract: Many fluid flow problems of practical interest---particularly at high Reynolds number---are characterized by small regions of complex and rapidly varying fluid motion surrounded by larger regions of relatively smooth flow. Efficient solution of such problems requires an adaptive mesh refinement capability to concentrate computational effort where it is most needed. We present in this paper a fractional step version of Chorin's projection method for incompressible flow, with adaptive mesh refinement, which is second-order accurate in both space and time. Convection terms are handled by a high-resolution upwind method which provides excellent resolution of small-scale features of the flow, while a multilevel iterative scheme efficiently solves the parabolic and elliptic equations associated with viscosity and the projection. Numerical examples demonstrate the performance of the method on two-dimensional problems involving vortex spindown with viscosity and inviscid vortex merger.

Water Bioengineering Techniques: for Watercourse Bank and Shoreline Protection

Abstract: Preface to Fourth Edition.Chapter 1 Properties of Fluids.Chapter 2 Fluid Statics.Chapter 3 Fluid Flow Concepts and Measurements.Chapter 4 Flow of Incompressible Fluids in Pipelines.Chapter 5 Pipe Network Analysis.Chapter 6 Pump-pipeline System Analysis and DesignChapter 7 Boundary Layers on Flat Plates and in Ducts.Chapter 8 Steady Flow in Open Channels.Chapter 9 Dimensional Analysis, Similitude and Hydraulic Models.Chapter 10 Ideal Fluid Flow and Curvilinear Flow.Chapter 11 Gradually Varied Unsteady Flow from Reservoirs.Chapter 12 Mass Oscillations and Pressure Transients in Pipelines.Chapter 13 Unsteady Flow in Channels.Chapter 14 Uniform in Loose-boundary Channels.Chapter 15 Hydraulic Structures.Answers.Index.Conversion Table.

Analysis of Some Quadrilateral Nonconforming Elements for Incompressible Elasticity

Abstract: In this work, some nonconforming elements on arbitrary quadrilateral meshes in solving incompressible elastic equations are analyzed. A uniform optimal convergence rate is established at the incompressible limit $ u = 0.5$ for both displacement and stresses (or pressure in the case of incompressible flow).

Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method

Abstract: A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

Delayed singularity formation in 2D compressible flow

Abstract: The initial value problem for the compressible Euler equations in two space dimensions is studied. Of interest is the lifespan of classical solutions with initial data that is a small perturbation from a constant state. The approach taken is to regard the compressible solution as a nonlinear superposition of an underlying incompressible flow and an irrotational compressible flow. This viewpoint yields an improvement for the lifespan over that given by standard existence theory. The estimate for the lifespan is further improved when the initial data possesses certain symmetry. In the case of rotational symmetry, a result of S. Alinhac is reconsidered. The approach is also applied to the study of the incompressible limit. The analysis combines energy and decay estimates based on vector fields related to the natural invariance of the equations. 0. Introduction. The compressible Euler equations comprise a nonlinear symmetric hyperbolic system of PDE's that model ideal fluid flow. The charac teristic wave speeds of this system are given by the fluid velocity and the local sound speed. The two wave families associated to these speeds may be con sidered separately. Hydrodynamical waves are described by the incompressible Euler equations, while acoustical waves are approximated by the linear wave equation, or more precisely, by the compressible Euler equations with irrotational fluid velocity. This paper attempts to use the nonlinear superposition of these two flows to study the long time behavior of small amplitude disturbances in two dimensional compressible fluid flow. Consider the initial value problem for the compressible Euler equations in two or three space dimensions with smooth initial data which is a small perturbation of amplitude e from a constant state. The life span is defined as the largest time interval on which there exists a classical solution to the initial value problem. From the theory of symmetric hyperbolic systems (6), (8), the life span is at least 0(\/e). Results on formation of singularities show that the life span of a classical solution is no better than 0(\/e2) in 2D, (16), and O (exp(l/^2)) in 3D, (17). In this paper, we extend the length of the life span under various assumptions on the initial data, in two space dimensions. The simplest case is the one in which the initial fluid velocity is irrotational, that is, its curl is zero. The compressible Euler equations then behave much the same as scalar nonlinear wave equations. (This can readily be guessed by writing the velocity as the gradient of a potential, although we will not use this approach here.) We shall see in Theorem 2 that the life span of 2D irrotational

A wave equation approach to the numerical solution of the Navier-Stokes equations for incompressible viscous flow

Abstract: In this Note we describe a novel method for the solution of the Navier-Stokes equations for incompressible viscous fluids. This method, which can be viewed as an alternative to the methods of characteristics, takes advantage of a time discretization by operator splitting to decouple incompressibility-diffusion from advection. The incompressibility-diffusion steps can be treated by classical Stokes solvers. Concerning the advection steps, thanks to the incompressibility of the advecting field, we can replace the corresponding transport equations by second order in time wave equations, which are much easier to solve numerically despite the fact that they are associated to degenerate elliptic operators. Numerical experiments confirm the good computational properties of the new method.