Shape optimization for some wave resistance problems
We consider an immersed object moving at constant speed in calm water.
The water is seen as an incompressible inviscid fluid and the flow is
irrotationnal. The wave resistance is the drag force exerted by the
fluid on the object. This force is due to the presence of the
water/air interface (indeed, if there were only water, then
d’Alembert’s paradox would imply that this drag force is zero).
In this talk, we will consider two shape optimization problems related
to the wave resistance, from a theoretical and numerical point of
view. The first problem is the optimization of ship hulls in the
context of thin ships. In this case, Michell’s wave resistance formula
avoids to use the state equation. The second problem is a fully
immerged infinite cylinder. In this case, the state equation is the