Shape Optimization For Navier-Stokes Boundary and A Dimensional Splitting Method

The Drag Functional (Hydraulic Force acting on the Boundary) is chosen as the objective functional for shape optimization of the Navier-Stokes boundary. Since conjugate gradient methods to compute optimization must do numerical differential for the 3D Stress tensor and Gateaux derivative of solutions of the Navier-Stokes equation with respect to the shape of the boundary, this is a difficult and inefficient problem.

Our contributions are that all computations for the conjugate gradient method for this kind of optimization do not need numerical differentiation for stress tensor and Gateaux derivative of solutions of the Navier-Stokes equation with respect to the shape of the boundary; it is only necessary to solve two-dimensional boundary layer equations I,III,IV.

Event Topic

Stochastic & Multiscale Modeling and Computation