Topic

# Incompressible flow

About: Incompressible flow is a(n) research topic. Over the lifetime, 10646 publication(s) have been published within this topic receiving 323234 citation(s).

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31 Oct 2002TL;DR: 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.

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.

5,249 citations

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AeroVironment

^{1}Abstract: A new finite element formulation for convection dominated flows is developed. The basis of the formulation is the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes. When implemented as a consistent Petrov-Galerkin weighted residual method, it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods. The accuracy of the streamline upwind/Petrov-Galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples. The formulation is extended to the incompressible Navier-Stokes equations. An efficient implicit pressure/explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step. The effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a Reynolds number of 100.

4,827 citations

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TL;DR: A level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of two-phase flow where the interface can merge/break and the flow can have a high Reynolds number.

Abstract: A level set approach for computing solutions to incompressible two-phase flow is presented. The interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function. A new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface. We never have to explicitly reconstruct or find the zero level set. Consequently, we are able to handle arbitrarily complex topologies, large density and viscosity ratios, and surface tension, on relatively coarse grids. We use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations. We consider the motion of air bubbles and water drops. We also compute flows with multiple fluids such as air, oil, and water.

3,815 citations

01 Jun 1995

Abstract: A level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of two-phase flow where the interface can merge/break and the flow can have a high Reynolds number. A distance function formulation of the level set method enables one to compute flows with large density ratios (1000/1) and flows that are surface tension driven; with no emotional involvement. Recent work has improved the accuracy of the distance function formulation and the accuracy of the advection scheme. We compute flows involving air bubbles and water drops, to name a few. We validate our code against experiments and theory.

3,556 citations

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TL;DR: The performances of SIMPLE, SIMPLER, and SIMPLEC are compared for two recirculating flow problems and several modifications to the method are shown which both simplify its implementation and reduce solution costs.

Abstract: Variations of the SIMPLE method of Patankar and Spalding have been widely used over the past decade to obtain numerical solutions to problems involving incompressible flows. The present paper shows several modifications to the method which both simplify its implementation and reduce solution costs. The performances of SIMPLE, SIMPLER, and SIMPLEC (the present method) are compared for two recirculating flow problems. The paper is addressed to readers who already have experience with SIMPLE or its variants.

3,110 citations