Volume of fluid (VOF) method for the dynamics of free boundaries

A continuum method for modeling surface tension

http://dns2.asia.edu.tw/~ysho/YSHO-English/2000%20Engineering/PDF/Int%20J%20Hea%20Mas%20Tra15,%201787.pdf

A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows

A new technique is described for the numerical investigation of the time‐dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free The full Navier‐Stokes equations are written in finite‐difference form, and the solution is accomplished by finite‐time‐step advancement The primary dependent variables are the pressure and the velocity components Also used is a set of marker particles which move with the fluid The technique is called the marker and cell method Some examples of the application of this method are presented All non‐linear effects are completely included, and the transient aspects can be computed for as much elapsed time as desired

Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface

This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics. The IB formulation of such problems, derived here from the principle of least action, involves both Eulerian and Lagrangian variables, linked by the Dirac delta function. Spatial discretization of the IB equations is based on a fixed Cartesian mesh for the Eulerian variables, and a moving curvilinear mesh for the Lagrangian variables. The two types of variables are linked by interaction equations that involve a smoothed approximation to the Dirac delta function. Eulerian/Lagrangian identities govern the transfer of data from one mesh to the other. Temporal discretization is by a second-order Runge–Kutta method. Current and future research directions are pointed out, and applications of the IB method are briefly discussed. Introduction The immersed boundary (IB) method was introduced to study flow patterns around heart valves and has evolved into a generally useful method for problems of fluid–structure interaction. The IB method is both a mathematical formulation and a numerical scheme. The mathematical formulation employs a mixture of Eulerian and Lagrangian variables. These are related by interaction equations in which the Dirac delta function plays a prominent role. In the numerical scheme motivated by the IB formulation, the Eulerian variables are defined on a fixed Cartesian mesh, and the Lagrangian variables are defined on a curvilinear mesh that moves freely through the fixed Cartesian mesh without being constrained to adapt to it in any way at all.

/pdf/the-immersed-boundary-method-xfkx3wd291.pdf

The immersed boundary method

The marker and cell method for high‐speed computer was used to investigate the motion of a fluid whose free surface has been perturbed by an impulsive sinusoidal pressure. For gravity pointing out of the fluid, the resulting motion exhibits Rayleigh‐Taylor instability, whose progress is followed from low amplitude to the asymptotic bubble and spike stage. The effects of small and large viscosity are contrasted. For gravity pointing into the fluid, the large‐amplitude oscillatory motion exhibits a shift of resonance frequency and other effects of nonlinearity. Comparisons of results are presented wherever previous analytical or experimental work was available, and many new aspects of these types of flow are discussed. The calculations are based upon the full, time‐dependent, nonlinear Navier‐Stokes equations for an incompressible fluid.

Numerical Study of Large‐Amplitude Free‐Surface Motions

A numerical, fluid-dynamics technique for high-speed computers is described and illustrated. It applies to the solution of problems dealing with incompressible viscous fluids and involving nonsteady motions in several dimensions in space. The ability to handle free-surface boundary conditions allows waves to be studied through all phases of breaking and splashing, as well as a number of related phenomena.

https://science.sciencemag.org/content/sci/149/3688/1092.full.pdf

J. Eddie Welch

Papers

Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface

Numerical Study of Large‐Amplitude Free‐Surface Motions

Liquid Waves by Computer.