At the intersection of computational fluid dynamics and abstract painting you find the grid.
I love these accidental alignments of perspective, when two things I enjoy come together in unforeseen ways.
Engineers Are Abstract Too
Let’s back up one step. A lot of engineers (you know who you are) are openly hostile (OK, maybe only casually “meh”) to abstract art, as though abstraction is a completely repugnant and insidiously unhelpful concept.
Thought experiment: If realism and representation are the true goals of art, why hasn’t photography killed painting?
Yet a lot of engineering, including CFD, is exactly that – an abstraction. Wikipedia tells us that abstraction is a process for creating concepts and ideas from real things, from first principles. A CAD model is an abstraction of a real, tangible object. CFD geometry is a further abstraction (simplification, defeaturing) of the CAD model. A mesh is a further abstraction (a discrete one) of the flow volume around the CAD model. RANS is an abstraction of the Navier-Stokes equations which are in turn an abstraction of a real flowing fluid.
In other words, as much as we may pretend that a CFD result is the real thing, it’s really just an abstract approximation. (And slow your roll, experimentalists. There’s not much real about a tiny airplane in a box with a fan blowing over it.)
Regardless of whether we’re delusional about the “realness” of CFD, many of you are thinking to yourself “But the purpose of a CFD abstraction is to approximate reality, to gain insight into reality, and there’s nothing real about blobs of paint on canvas.”
Yet, insight into reality is precisely what abstract painters are trying to achieve. They are distilling the human experience into a graphic language. They don’t paint a person or a forest or an ocean or a bowl of fruit – they paint the essence of the experience of seeing a person or being in a forest.
Next time you’re standing in front of an abstract painting don’t try to figure out what it is; ask how it makes you feel.
I mean, if Monet’s intent in painting Impression Sunrise was to faithfully represent the appearance of the harbor in the morning he did a pretty crappy job. The boats hardly look like boats, you can’t hardly see the shoreline at all, and the water – heck, waves don’t look like that.
“My kid could paint that.”
But if Monet’s intent was to capture the impression of being in the harbor at sunrise, being alone in a large, peaceful, open space where the new sun barely illuminates and the chill of the night remains, and there’s the promise of movement into the day ahead – his success is astounding.
Back to the Grid
So where was I? Right, the grid, CFD, and painting.
abstract critical is one of my must-read art blogs. (The other is Modern Art Notes.) abstract critical hosts an on-going discussion on the use of grids in painting. They propose the grid as a guidepost the non-art-expert public uses to identify one extreme of modern abstraction with gestural works at the opposite pole (think Martin vs. Pollock).
Allow me to quote directly: “Where many abstract artists have viewed the grid as signalling the promise of liberation, others have viewed it as restriction, one which reduces the spatial or expressive possibilities of painting; perhaps this tension is necessary if the grid is to continue to play an active role in abstract painting.”
Without stretching the language too grossly, you can imagine similar thoughts about structured versus unstructured grids. Certainly the generation of structured hex grids can be daunting relative to their more automated cousins, unstructured meshes.
However, I am also a believer that form is liberating. The form of a structured grid pays dividends on the solver side in terms of computational efficiency and accuracy. The tension between structured and unstructured approaches is indeed necessary as structured methods try to become more automated and unstructured methods try to become more accurate and efficient. Hybrid meshing may be classified as a result of that tension, as a means of getting the benefits of both structured and unstructured.
What’s the point?
Grids provide a framework for interpreting and structuring abstraction whether that’s in art or science.
Try reading The Viewer and The Grid and let me know what you think. In it you’ll read that the very rectilinearity of the grid is what marks it as abstract – opposite the representational – because those right angles don’t occur in nature. Yet it’s probably the rectilinearity which makes the grid that much more palatable to us engineers.
And yes, I wanted to write about this because of the coincidental timing with our latest step toward resolving the tension between structured and unstructured methods: the recent release of semi-structured hex layer generation in Pointwise’s T-Rex hybrid meshing technique.