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

TLDR

The marker and cell method is a numerical technique for simulating incompressible fluid flows with free surfaces. A new technique is described for the numerical investigation of the time‑dependent flow of an incompressible fluid whose boundary is partially confined and partially free. The method solves the full Navier–Stokes equations in finite‑difference form using time‑step advancement, tracking pressure and velocity fields while advecting marker particles that follow the fluid. The method accurately captures all nonlinear effects and can compute transient behavior for any desired duration, as demonstrated by several example applications.

Abstract

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.