MrsDrPoe: What in the WORLD is CFD?

Well good afternoon again! What another glorious day that the Lord hath made! Today is Thesis Tuesday, so we'll be discussing one of the many things that I love - fluid mechanics. (Note: please recall that I'm currently working on my dissertation but I love alliteration.)

My research is in the area of Computational Fluid Dynamics (CFD), which is simply employing computers to simulate fluid flow. While that sounds simple enough, it is actually quite complicated. There are 4-5 rather large partial differential equations that govern the flow of a fluid; for the majority of the "real life" scenarios that we are interested in, these equations cannot be solved exactly. So we must utilize computers to obtain numerical approximations to derivatives in these equations in order to achieve a solution. WHEW!

I have decided, since most of my readers (as far as I know) aren't really familiar with these concepts to dedicate the first several of these Tuesday posts to an undergraduate level discourse on fluid mechanics, in hopes that you can gain a better understanding (and perhaps a love) for the subject. So here goes nothing!

A fluid is any substance which continuously deforms (or flows) when a shear stress is applied. Engineers typically think of forces as coming in two flavors: normal and shear. Here is the difference:

a normal force is one perpendicular (at a 90 degree angle) to the notebook (here "into"), while a shear force is one parallel to the notebook (here "across" or "along"). Both liquids and gases possess this trait of flowing when a shear force is applied, so both are considered fluids.

If you've ever taken a chemistry class, you know that everything is made up of atoms. Groups of atoms are called molecules. If we look at a glass of water:

we don't see all the tiny molecules that make up this liquid. But if we zoom in reeeeeally far:

we can see that the liquid is made up of molecules with some space in between (approximately 0.00001 mm). (Recall that for gasses, the space in between these molecules is larger - close to 0.0001 mm.)

If we say that the water is 10 degrees Celsius, we're really saying that each molecule is that temperature NOT the space. So when we know properties or characteristics of a fluid, we actually only know those properties or characteristics at certain points (where molecules are located). This is known as a discrete field. The opposite of a discrete field is a continuous field. Like the name suggestions, for this type of field, we know all the properties/information about this field at every single infinitesimally small location in the field. The difference looks something like this:

Typically, we make what is called the continuum assumption. This assumption means that we will be treating fluids as continuous fields, even though we know that they are discrete fields. This assumption is valid when the spacing between the molecules is very small. For most situations of interest, we are looking at fluids at full scale (water in a cup), so the spacing is very tiny, and the assumption is valid. For nanoscale situations (really zoomed in view of water), the spacing is considered relatively large, and this assumption breaks down.

Well, I think that's enough for one day. I hope that you've found this somewhat interesting and that you'll tune in next Tuesday for the second installment!