Praveen Chandrashekar

Centre for Applicable Mathematics, TIFR, Bangalore

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The fitted mesh story

Philippe Caupennet
Theoretical Aerodynamic Department of DEA

On that Friday evening, the viewing room was almost full. As usual for the week-end, it was time for the “Team” to get into the most dangerous numerical practices.

But everybody could feel, on that particular evening, the charged intensity that always characterized a big premiere.

Gathered around two screens, three men stood: the Head of Meshing (wearing his signature colored glasses that allowed him to see in 3 dimensions), the Head of Adaptive Remeshing, and of course, the Chief himself who was quietly reading the Bible in a corner of the room, in order to calm down his anxiety…

Nevertheless, he was the one responsible for having started the whole dramatic process.

“Last night”, he said when he arrived, “I kept thinking while you were peacefully asleep, and I am now convinced that we have to modify the mesh without stopping the calculation process”.

Nobody could imagine the emotion that swept though the members of the “Team” at that moment, each face turned toward him and smiling in gratitude. They had been waiting for him for hours… and he was there… and he had thought!!

The session began shortly after, at the precise moment when the Chief defined on the screen the intervention area. Everyone felt the moment was special.

He took authoritatively the 3D mouse and started operating it with a sort of sensuality.

It was the same device which was used to color code the most incredible objects coming to life out of this man’s brain. The same man who was said to know better than air what it ought to do.

The “Team” gradually saw a red circle appear on the screen, probably the area where the terrifying negative tetrahedral was hiding.

The process was now in full swing. Three assistants stood close together around the main 3D screen and held separate mesh parts while the Head of Meshing dropped his hand through the tetrahedral, trying to reach the negative one.

The navy-blue entropy flow started slowly trickling along his arm. Blue: that was rather good… But a few weeks earlier, the liquid had turned more and more limpid and the process had stopped with yellowish tears.

At the same time, it was possible to see in the heart of the mesh the hesitating movement of a new shock wave, trying to find its right position. Nevertheless, several tetrahedral had to be cut and the Head of Adaptative Remeshing was working hard to create new connections around.

“Alert!” screamed an assistant who was looking intently at a curve on a smaller screen, “the convergence curve is diverging!”.

“OK. Drop the C.F.L. to 2”, the Head of Meshing answered quietly.

“C.F.L. = 2. It seems to be working.”

The Head of Meshing went on, with slow and precise movements, trying to reach the ultimate limits of his network. He had an assistant mop his brow, but he would not let anybody replace his 3D glasses.

Suddenly, it was full-alert status again.

“It’s diverging, my God, it’s diverging”, kept repeating the rather distraught assistant.

The Chief closed quietly his Bible and moved closer. “Proceed on implicit now…” he ordered.

“OK, Boss”, answered the assistant, clearly relieved.

Everybody stood still, intent on the movement of the convergence curve. But it was too late. The Head of Meshing managed to take his arm out just in time. The long moment of silence that followed was interrupted by the last message:

“OC4 OLD PSW IS 00098FF43FA11 … “

In the general consternation, the Chief could barely be heard:

“What was the Mach number?”

“And the incidence?”

“OK, it’s not so terrible then. By the way, I know the result. We should have found something like 12.475 dm2”

The “Team” members looked around smiling. Of course, that was it ! They had been hesitating between 11.650 and 12.580. Some people had even dared suggest such unthinkable figures like 10.001 and even 9.565 ! But the real answer was really 12.475 and looking around the everlasting drawings on the screens, they shared a similar thought: “Why do things the easy way when you can do it the hard way?”