Abstract
The optimization of an obstacle shape immersed in an Eulerian flow is investigated. In order to construct a descent method, we consider the differentiation of the flow solution with respect to the shape. In the continous case, the Hadamard variational formula yields the formal derivatives. In the discrete case, we choose an upwind method with flux splitting, and proved that an exact gradient can be derived using the adjoint state. The behavior of a gradient method is studied for a family of nozzle flows.
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