Computational methods for free surface flow

Introduction

Computation in flows with free and moving boundaries like the open-channel flow is a difficult task. The position of the boundary is known only at the initial time and its location at later times can be determined as using various methods like the Interface Tracking Method and the Interface Capturing Method.

Boundary conditions

Neglecting the phase change at the free surface, the following boundary conditions apply.

Interface capturing method

In computation of two-fluid flows, in some cases the interface might be too complex to track while keeping the frequency of re-meshing at an acceptable level. Not being able to reduce the frequency of re-meshing in 3D might introduce overwhelming mesh generation and projection costs, making the computations with the interface-tracking technique no longer feasible. In such cases, interface-capturing techniques, which do not normally require costly mesh update steps, could be used with the understanding that the interface will not be represented as accurately as we would have with an interface-tracking technique.
Methods which do not define the interface as sharp boundary. A fixed grid extends beyond the free surface over which the computation is performed. To determine the shape of the free surface, the fraction of each cell near the interface is computed that is partially filled.

Marker-and-cell or MAC Scheme

MAC scheme was proposed by Harlow and Welch in 1965. In this method, a massless particle is introduced at the initial time at the free surface. The motion of this massless particle is followed with the passage of time.
Benefit: This scheme can treat complex phenomena like wave breaking.
Drawback: In three dimensional flow solving the equations governing fluid flow and also following the motion of a large number of markers both simultaneously demands high computational power.

Modifications to MAC and VOF scheme

Marker and micro-cell method in which local grid refinement is done according to the following criteria:
only the cells having 0 < c < 1 are refined.
This method is more efficient than MAC scheme because only the cells at the boundary are refined. But in this method, the free surface profile is not sharply defined.

Hybrid methods

There are some fluid flows which do not come under either of the category, for example, bubbly flows. For the computation of such two-phase flows which do not come under any of the above discussed categories, elements are borrowed from both surface-capturing and surface-tracking methods. Such methods are called hybrid methods. In this method, fluid properties are smeared over a fixed number of grid points normal to the interface. Now, as in interface capturing method, both fluids are treated as single fluid with variable properties. Interface is also tracked as in interface-tracking method to prevent it from smearing by moving the marker particles using the velocity field generated by the flow solver. marker particles are added and removed to maintain the accuracy by keeping the approximate spacing between them equal.