In my first blog I promised reflections based on my 40 years in CFD. How best to start?
What was the advice that the King of Hearts gave to the White Rabbit? – “Begin at the beginning, go on to the end, and then stop.” While not specifically intended in the context of blogs – it seems like good advice to me. So – starting at the beginning …
I must confess that I got into fluid dynamics rather by accident. Following my BSc, I was initially intending to do a PhD at Imperial College in Lubrication (or Tribology, as it now seems to be known). At the last minute I decided that this wasn’t for me – so, rather than get a “real job”, I desperately started looking for alternative post-graduate opportunities. I recall in the summer of 1968 going around Mech Eng at Imperial College talking to course organisers and possible research supervisors – among them Brian Launder, then a relatively junior lecturer, responsible for the Heat Transfer Section’s MSc course. I was impressed by his enthusiasm (I guess he did a good selling job on me!), and I enrolled on the course, with the promise of a likely PhD project to follow.
At this time Professor Spalding’s Heat Transfer Section (HTS) was just getting started in CFD. Suhas Patankar’s ground-breaking PhD (with Spalding) completed in 1965 had resulted in a computational method for 2D boundary layers, which has been widely used over the years under the name of GENMIX. Then the PhDs of Akshai Runchal and Mika Wolfstein led, in about 1968, to a 2D method for elliptic recirculating flows (documented in Gosman, Pun, Runchal, Spalding & Wolfstein, “Heat & Mass Transfer in Recirculating Flows”, Academic Press, London, 1969). My introduction to CFD was the use of this software in my MSc project, on “Flow and Heat Transfer in a Laminar Axisymmetric Thermosyphon”.
Following this, a research group, funded by an SRC contract, was set up, to develop computational methods for 3D parabolic, boundary-layer flows – the first step for the HTS group (and pretty much for anyone) into 3D fluid dynamic computations. This started in 1969. The members were (initially) Professor Spalding, David Gosman (then a newly-appointed Lecturer, and my PhD supervisor), Larry Caretto (on sabbatical from Berkeley University I believe), Bob Curr (a Research Fellow in the HTS), Devraj Sharma (a fellow PhD student), and myself.
As with any new research project, we started with a literature survey. Other than the prior work in the HTS, pretty much all there was available was the work by Francis Harlow’s group at Los Alamos, which had been developing methods for 2D transient flows. I recall particularly a paper by Harlow and Welch on 2D transient flow with a free surface, which I studied avidly.
Unlike the prior HTS work, the Harlow methods solved directly for the “primitive variables” pressure and velocities. The HTS 2D elliptic method, by contrast, solved for the derived variables stream function and vorticity (from which pressure and velocities were then deduced). The advantage of this approach was that it avoided the troublesome coupling of pressure and velocities encountered when solving for the primitive variables. This disadvantage was that it was difficult to extend it to 3D flows. So, for our 3D parabolic work we decided early on, like Harlow’s group, to solve directly for pressure and velocities.
I forget the exact work allocation within the research group – but I was the lucky one, who created the first software and applied it to a simple 3D parabolic flow – the inlet region of a rectangular passage. And I immediately encountered a problem which is now familiar to generations of CFD practitioners. Initially we naturally used what is now called a co-located grid – with pressure and velocities solved for at the same locations. This seemed like the obvious approach – it was what was done in prior HTS methods. Though, interestingly, Harlow and Welch used a staggered grid – but we didn’t initially realise why!
In my first calculations I immediately encountered the classic problem of “decoupled pressure fields” (sometimes described as “oscillations in pressure”). Essentially, for an incompressible flow of the kind that we were considering, it turns out that the central-difference approximation in evaluating the pressure term in the momentum equations, means that the finite volume equations can be satisfied by (completely unphysical) solutions with a number (in 2D, four) of decoupled pressure fields, on a sort of “chequerboard” arrangement. Having identified the problem, I recommended the obvious solution – the use of a staggered grid, with velocities solved for at locations midway between the pressure nodes (like Harlow and Welch!). This is what we did from then on in the HTS computational work – and was the approach used by pretty much all of the CFD community until the early 1980s, when the method of Rhie and Chow provided a way around the “decoupled pressure fields” problem.
Then at around this time (mid 1970) Suhas Patankar returned to the HTS after a short period back at IIT Kanpur – and joined our research group. CFD history was about to be written!
To be continued …