Modeling Techniques

Anyone who has used CFD extensively will have his or her own preferences for what the best numerical methods are to use. The articles in this section explain some of the modeling techniques the author has used and why he believes they are good choices with respect to other methods.

CFD Modeling Techniques
Structured FAVOR™ grid in cylindrical coordinates

These articles center on the FAVOR™ (Fractional-Area-Volume-Obstacle-Representation) method and the VOF (Volume-of-Fluid) method.  When modeling fluid flow around complex obstacles many practitioners prefer to use computational grids that are deformed to the shape of the obstacles, these are generally referred to as body-fitted grids.  The FAVOR method, in contrast, employees easy to generate rectangular grids whose elements are assigned fractional areas and volumes.  The connection between these approaches is discussed in the articles FAVOR vs. Body-Fitted Coordinates and No Loss with FAVOR.

The tracking of fluid surfaces or interfaces using VOF has become quite popular; however, the idea behind this technique has been used or modified in numerous ways by different groups.  The article VOF – What’s in a Name? explains why the original method is superior to its many derivatives.

Structured FAVOR™ Grids

Both VOF and FAVORare volume-based, as opposed to surface based, computational methods. Even though it seems logical to directly describe fluid and obstacle surfaces on which boundary conditions are to be prescribed, a better method is to use the volumes of fluid and solid regions. Volumes have many advantages. Consider fluid surfaces that move and evolve in time-dependent computational simulations. These are referred to as free surfaces and their determination becomes an integral part of a fluid dynamic solution. Fluid surfaces can not only be created and destroyed over time, but may or may not completely enclose fluid masses.

A simple example is water exiting a hose. The surface area of the water is growing as it flows outward. If it breaks up into drops there are then multiple surfaces that are not connected to one another. Should two or more drops collide and coalesce their individual surfaces no longer exist being replaced by a single surface surrounding the combined drops. Or a simple fluid drop can arbitrarily deform resulting in a changing surface area, but its volume is unchanged when the fluid is incompressible. This sort of behavior makes the specification of individual surfaces problematic. On the other hand, defining volumes of fluids or solids makes sense because conservation of mass (and incompressibility in the form of unchanging volumes) is easier to maintain. Fluid volumes may coalesce and breakup as they will, allowing easy evaluation of their resulting surfaces. In volume methods the location of a surface is wherever the volume region ends. 

Volume methods are powerful numerical tools. How they are implemented in the VOF and FAVORtechniques is described in detail in the accompanying articles.