Showing papers on "Incompressible flow published in 2002"

Level Set Methods and Dynamic Implicit Surfaces

Abstract: This book is an introduction to level set methods and dynamic implicit surfaces. These are powerful techniques for analyzing and computing moving fronts in a variety of different settings. While it gives many examples of the utility of the methods to a diverse set of applications, it also gives complete numerical analysis and recipes, which will enable users to quickly apply the techniques to real problems. The book begins with a description of implicit surfaces and their basic properties, then devises the level set geometry and calculus toolbox, including the construction of signed distance functions. Part II adds dynamics to this static calculus. Topics include the level set equation itself, Hamilton-Jacobi equations, motion of a surface normal to itself, re-initialization to a signed distance function, extrapolation in the normal direction, the particle level set method and the motion of co-dimension two (and higher) objects. Part III is concerned with topics taken from the fields of Image Processing and Computer Vision. These include the restoration of images degraded by noise and blur, image segmentation with active contours (snakes), and reconstruction of surfaces from unorganized data points. Part IV is dedicated to Computational Physics. It begins with one phase compressible fluid dynamics, then two-phase compressible flow involving possibly different equations of state, detonation and deflagration waves, and solid/fluid structure interaction. Next it discusses incompressible fluid dynamics, including a computer graphics simulation of smoke, free surface flows, including a computer graphics simulation of water, and fully two-phase incompressible flow. Additional related topics include incompressible flames with applications to computer graphics and coupling a compressible and incompressible fluid. Finally, heat flow and Stefan problems are discussed. A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change its topology or develop singularities, will find this book interesting and useful.

High-Order Methods for Incompressible Fluid Flow

Abstract: Preface 1. Fluid mechanics and computation: an introduction 2. Approximation methods for elliptic problems 3. Parabolic and hyperbolic problems 4. Mutidimensional problems 5. Steady Stokes and Navier-Stokes equations 6. Unsteady Stokes and Navier-Stokes equations 7. Domain decomposition 8. Vector and parallel implementations Appendix A. Preliminary mathematical concepts Appendix B. Orthogonal polynomials and discrete transforms.

Lattice Boltzmann model for incompressible flows through porous media.

Abstract: In this paper a lattice Boltzmann model is proposed for isothermal incompressible flow in porous media. The key point is to include the porosity into the equilibrium distribution, and add a force term to the evolution equation to account for the linear and nonlinear drag forces of the medium (the Darcy's term and the Forcheimer's term). Through the Chapman-Enskog procedure, the generalized Navier-Stokes equations for incompressible flow in porous media are derived from the present lattice Boltzmann model. The generalized two-dimensional Poiseuille flow, Couette flow, and lid-driven cavity flow are simulated using the present model. It is found the numerical results agree well with the analytical and/or the finite-difference solutions.

Vorticity and Incompressible Flow. Cambridge Texts in Applied Mathematics

Abstract: In this book, the theoretical and experimental analyses of the velocity fields with vorticity are applied to explain the physical phenomena of flow patterns of various types of vortex flows and of the flow structures in the boundary layer with high velocity gradient on a solid surface. Further, the vortex flow in nature is not always circular, but also elliptic rotational flows occur under stable and unstable conditions. Therefore, the fundamental mathematical and applied descriptions of vorticity...

A coupled lattice BGK model for the Boussinesq equations

Abstract: In this paper, a thermal lattice BGK model is developed for the Boussinesq incompressible fluids. The basic idea is to solve the velocity field and the temperature field using two independent lattice BGK equations, respectively, and then combine them into one coupled model for the whole system. The porous plate problem and the two-dimensional natural convection flow in a square cavity with Pr=0.71 and various of Rayleigh numbers are simulated using the model. The numerical results are found to be in good agreement with the analytical solutions or those of previous studies. Copyright © 2002 John Wiley & Sons, Ltd.

Global Weak Solutions for the Two-Dimensional Motion of Several Rigid Bodies in an Incompressible Viscous Fluid

Abstract: We consider the two-dimensional motion of several non-homogeneous rigid bodies immersed in an incompressible non-homogeneous viscous fluid. The fluid, and the rigid bodies are contained in a fixed open bounded set of R 2 . The motion of the fluid is governed by the Navier-Stokes equations for incompressible fluids and the standard conservation laws of linear and angular momentum rule the dynamics of the rigid bodies. The time variation of the fluid domain (due to the motion of the rigid bodies) is not known a priori, so we deal with a free boundary value problem. The main novelty here is the demonstration of the global existence of weak solutions for this problem. More precisely, the global character of the solutions we obtain is due to the fact that we do not need any assumption concerning the lack of collisions between several rigid bodies or between a rigid body and the boundary. We give estimates of the velocity of the bodies when their mutual distance or the distance to the boundary tends to zero.

Mixed hp -DGFEM for Incompressible Flows

Abstract: We consider several mixed discontinuous Galerkin approximations of the Stokes problem and propose an abstract framework for their analysis. Using this framework, we derive a priori error estimates for hp-approximations on tensor product meshes. We also prove a new stability estimate for the discrete divergence bilinear form.

Acoustic streaming induced by ultrasonic flexural vibrations and associated enhancement of convective heat transfer

Abstract: Acoustic streaming induced by ultrasonic flexural vibrations and the associated convection enhancement are investigated. Acoustic streaming pattern, streaming velocity, and associated heat transfer characteristics are experimentally observed. Moreover, analytical analysis based on Nyborg’s formulation is performed along with computational fluid dynamics (CFD) simulation using a numerical solver CFX 4.3. Two distinctive acoustic streaming patterns in half-wavelength of the flexural vibrations are observed, which agree well with the theory. However, acoustic streaming velocities obtained from CFD simulation, based on the incompressible flow assumption, exceed the theoretically estimated velocity by a factor ranging from 10 to 100, depending upon the location along the beam. Both CFD simulation and analytical analysis reveal that the acoustic streaming velocity is proportional to the square of the vibration amplitude and the wavelength of the vibrating beam that decreases with the excitation frequency. It is...

Numerical flow computation around aeroelastic 3D square cylinder using inflow turbulence

Abstract: Numerical flow computations around an aeroelastic 3D square cylinder immersed in the turbulent boundary layer are shown. Present computational code can be characterized by three numerical aspects which are 1) the method of artificial compressibility is adopted for the incompressible flow computations, 2) the domain decomposition technique is used to get better grid point distributions, and 3) to achieve the conservation law both in time and space when the flow is computed a with moving and transformed grid, the time derivatives of metrics are evaluated using the time-and-space volume. To provide time-dependant inflow boundary conditions satisfying prescribed time-averaged velocity profiles, a convenient way for generating inflow turbulence is proposed. The square cylinder is modeled as a 4-lumped-mass system and it vibrates with two-degree of freedom of heaving motion. Those blocks which surround the cylinder are deformed according to the cylinder`s motion. Vigorous oscillations occur as the vortex shedding frequency approaches cylinder`s natural frequencies.

An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: Part I. Theory and implementation

Abstract: A robust, artificial compressibility scheme has been developed for modelling laminar steady state and transient, incompressible flows over a wide range of Reynolds and Rayleigh numbers. Artificial compressibility is applied in a consistant manner resulting in a system of preconditioned governing equations. A locally generalized preconditioner is introduced, designed to be robust and offer good convergence rates. Free artificial compressibility parameters in the equations are automated to allow ease of use while facilitating improved or comparable convergence rates as compared with the standard artificial compressibility scheme. Memory efficiency is achieved through a multistage, pseudo-time-explicit time-marching solution procedure. A node-centred dual-cell edge-based finite volume discretization technique, suitable for unstructured grids, is used due to its computational efficiency and high-resolution spatial accuracy. In the interest of computational efficiency and ease of implementation, stabilization is achieved via a scalar-valued artificial dissipation scheme. Temporal accuracy is facilitated by employing a second-order accurate, dual-time-stepping method. In this part of the paper the theory and implementation details are discussed. In Part 11, the scheme will be applied to a number of example problems to solve flows over a wide range of Reynolds and Rayleigh numbers.

Zero Mach number limit for compressible flows with periodic boundary conditions

Abstract: We address the question of convergence to the incompressible Navier-Stokes equations for slightly compressible viscous flows with ill-prepared initial data and periodic boundary conditions (the case of the whole space has been studied in an earlier paper by the author). The functional setting is very close to the one used by H. Fujita and T. Kato for incompressible flows. For arbitrarily large initial data, we show that the compressible flow with small Mach number exists as long as the incompressible one does. In particular, it exists globally if the corresponding incompressible solution exists for all time. We further state a convergence result for the slightly compressible solution filtered by the group of acoustics. Introduction. An engineer would hardly make a distinction between incom- pressible flows and slightly compressible flows. Indeed, incompressible Navier- Stokes equations are usually regarded as an appropriate model for describing water. In the present paper, we study whether such an approximation is relevant from a mathematical viewpoint in the case of periodic boundary conditions. The case of the whole space has been treated in (8). After some convenient rescaling (see for instance the appendix of (16) or the introduction of (21)), the equations for a slightly compressible fluid read:

A lattice kinetic scheme for incompressible viscous flows with heat transfer.

Abstract: A lattice kinetic scheme for incompressible viscous flows with heat transfer is devel- oped based on the lattice Boltzmann method. In the new scheme, macroscopic vari- ables are calculated without velocity distribution functions. Thus, the scheme can save computer memory because there is no need to store the velocity distribution functions. Governing equations for the macroscopic variables are obtained by apply- ing the asymptotic theory. The continuity equation, the Navier-Stokes equations, and the convection-diffusion equation for fluid temperature are obtained with rel- ative errors of O(e 2 ), where e is a small parameter that is of the same order as a lattice spacing and is related to a relaxation parameter. In order to verify the accu- racy of the scheme, natural convection flows in a square cavity are simulated, and the calculated results are in good agreement with available standard results.

Discussion on momentum interpolation method for collocated grids of incompressible flow

Abstract: Discussions are given of the different momentum interpolation methods to evaluate the interface velocity in the collocated grid system. It is pointed out that the interface velocity is used in three cases in the overall numerical procedure of the solution of Navier-Stokes equations by utilizing a collocated grid: in the continuity equation; in the interface flow rate computation for the determination of the coefficients in discretization equation; and in the mass residual in the coefficient Ap. Analysis shows that it is better to adopt the momentum interpolation method in the three cases. Two new momentum interpolation methods, called MMIM1 and MMIM2, are proposed. Analysis shows that the two new methods can achieve numerical solutions that are independent of both the underrelaxation factor and the time step size. Taking lid-driven cavity flow as an example, numerical computations are conducted for several Reynolds numbers and different mesh sizes using the SIMPLE algorithm, and the results are compared w...

An improved unsteady, unstructured, artificial compressibility, finite volume scheme for viscous incompressible flows: Part II. Application

Abstract: In Part I of this paper, a preconditioned artificial compressibility scheme was developed for modelling laminar steady-state and transient, incompressible flows for a wide range of Reynolds and Rayleigh numbers. In this part, several examples of laminar incompressible problems are solved and discussed. The influence of various AC parameters on robustness and convergence rates are assessed for a complex category of problems. It is shown that the scheme developed in Part I is an accurate, robust and easy to use method for solving incompressible laminar flow problems over a wide range of flow regimes. Copyright © 2002 John Wiley & Sons, Ltd.

Modelling of vapour flow in deep penetration laser welding

Abstract: The pressure induced by vapour flow during keyhole wall evaporation in deep penetration laser welding could have a more significant role in stabilizing keyhole walls, compared to that due to ablation pressure induced by local wall evaporation. In this paper, vapour flow modelling in a blind keyhole is presented by considering both simple geometries such as straight or inclined cylinders and more realistic profiles deduced from a self-consistent equilibrium calculation. The numerical approach used in the discretization is based on the finite element method that allows us to solve a two-dimensional Navier-Stokes set of equations assuming incompressible flow. In our model, the laser beam aperture and multiple reflections effects are taken into account. A ray-tracing procedure allows one to obtain absorbed intensities and thus the local surface temperature on the keyhole walls. The deduced local gas ejection velocities on the edge of the Knudsen layer are thus the boundary conditions of the Navier-Stokes problem.

Optimal control of unsteady compressible viscous flows

Abstract: The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two-dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter-rotating viscous vortices above an infinite wall which, due to the self-induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall-normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.

Transition Prediction for Three-Dimensional Boundary Layers in Computational Fluid Dynamics Applications

Abstract: A method is presented for estimating the laminar/turbulent transition location in three-dimensional boundary layers for computational fluid dynamics (CFD) applications requiring numerous transition estimates with no user intervention. Given the Reynolds number and the Cp distribution, the location of transition is estimated based on the attachment-line state, the potential for relaminarization, the occurrence of laminar separation, and the growth of instabilities. Transition caused by instability is estimated based on N factors calculated for Tollmien-Schlichting waves and for stationary crossflow instabilities. A neural network is used (in place of solving the Orr-Sommerfeld stability equation) for determining the instability growth rates. The current version of the method assumes incompressible flow. The boundary-layer flow and instabilities are calculated based on an infinite-sweep (strip boundary layer) approximation; the instability calculations also employ the parallel-flow approximation

Convective heat transport in compressible fluids.

Abstract: We present hydrodynamic equations of compressible fluids in gravity as a generalization of those in the Boussinesq approximation used for nearly incompressible fluids. They account for adiabatic processes taking place throughout the cell (the piston effect) and those taking place within plumes (the adiabatic temperature gradient effect). Performing two-dimensional numerical analysis, we reveal some unique features of plume generation and convection in transient and steady states of compressible fluids. As the critical point is approached, the overall temperature changes induced by plume arrivals at the boundary walls are amplified, giving rise to overshoot behavior in transient states and significant noise in the temperature in steady states. The velocity field is suggested to assume a logarithmic profile within boundary layers. Random reversal of macroscopic shear flow is examined in a cell with unit aspect ratio. We also present a simple scaling theory for moderate Rayleigh numbers.

Flow simulations in rotary volumetric pumps and compressors with the fictitious domain method

Abstract: The fictitious domain (FD) method is an interesting method of flow calculation for domains where mesh generation is not straightforward. This method has been reported in literature to be able to simulate flow in relatively open domains with incompressible fluids. In this paper a FD technique is tested for flow calculations inside closed geometries and for compressible flow. The computational fluid dynamics code FLUENT, versions 5.4 and 6.0, has been extended with user-defined functions and has been used for the analysis of incompressible flow in a lobe pump and the analysis of compressible flow in a tooth compressor. The results show that the FD method can be made to work for incompressible flow, although further development is necessary for compressible flow.