Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Fluid mechanics with interfaces
- 3 Numerical solutions of the Navier–Stokes equations
- 4 Advecting a fluid interface
- 5 The volume-of-fluid method
- 6 Advecting marker points: front tracking
- 7 Surface tension
- 8 Disperse bubbly flows
- 9 Atomization and breakup
- 10 Droplet collision, impact, and splashing
- 11 Extensions
- Appendix A Interfaces: description and definitions
- Appendix B Distributions concentrated on the interface
- Appendix C Cube-chopping algorithm
- Appendix D The dynamics of liquid sheets: linearized theory
- References
- Index
5 - The volume-of-fluid method
Published online by Cambridge University Press: 07 October 2011
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Fluid mechanics with interfaces
- 3 Numerical solutions of the Navier–Stokes equations
- 4 Advecting a fluid interface
- 5 The volume-of-fluid method
- 6 Advecting marker points: front tracking
- 7 Surface tension
- 8 Disperse bubbly flows
- 9 Atomization and breakup
- 10 Droplet collision, impact, and splashing
- 11 Extensions
- Appendix A Interfaces: description and definitions
- Appendix B Distributions concentrated on the interface
- Appendix C Cube-chopping algorithm
- Appendix D The dynamics of liquid sheets: linearized theory
- References
- Index
Summary
In Chapter 4 we saw several families of methods for locating and advecting the interface. Here, we focus on one of them: the VOF method. Historically, it was used for free surface flows with only one “fluid,” although it is now routinely used for two-fluid flows. In the VOF method the marker function is represented by the fraction of a computational grid cell which is occupied by the fluid assumed to be the reference phase.
A very large number (probably dozens) of VOF methods have been proposed. When we choose the method we try to strike a balance between several qualities: accuracy, simplicity and volume conservation.
Basic properties
The volume fraction or color function C is the discrete version of the characteristic function H; see Equation (4.3). We will be considering only two-phase or free-surface flows, so that the C data represent the fraction of each grid cell occupied by the reference phase. Furthermore, we restrict our analysis to Cartesian grids with square cells of side h = Δx = Δy.
The function C varies between the constant value one in full cells to zero in empty cells, while mixed cells with an intermediate value of C define the transition region where the interface is localized.
Low-order VOF methods do not need to specify the location of the interface in the transition region, but a geometrical interpretation of these methods shows that in two dimensions the interface line in each mixed cell is represented by a segment parallel to one of the two coordinate axes.
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- Direct Numerical Simulations of Gas–Liquid Multiphase Flows , pp. 95 - 132Publisher: Cambridge University PressPrint publication year: 2011
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