Pierre-Simon Laplace was born 23 March 1749 in Normandy, France. He was a prolific mathematician and scientist, and his name shows up in numerous mathematical terms: Laplace equation, Laplace transform, and Laplacian operator.
The Laplace equation is an elliptic partial differential equation that describes the behavior of a potential function in space. It has a couple of uses in CFD. First, in the olden days of CFD, that is the 1970’s, solving Laplace’s equation for velocity potential was the state of the art. It describes flow of a non-viscous fluid, and that is still good enough for a lot of applications.
Second, Laplace’s equation is the basis for the elliptic solvers used in Gridgen and Pointwise to smooth structured surface and volume grids. In Pointwise, go to the Grid, Solve panel, look at Interior Control Functions in the Attributes tab, and you will see that “Laplace” is one of the choices. Laplace’s equation is good to use for grid generation because its solutions are naturally smooth and regular, which are good properties for a computational mesh.
Laplace also made fundamental contributions to celestial mechanics, including early speculation on the existence of black holes, and the theory of probability and statistics. When Napoleon commented that Laplace’s works made no mention of God, Laplace famously replied, “I had no need of that hypothesis.”
Maybe grid generation is not one of Laplace’s major legacies, but his contributions are important to us none the less.
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