FINITE ELEMENT SOLUTION OF A MODEL FREE SURFACE PROBLEM BY THE OPTIMAL SHAPE DESIGN APPROACH

Optimal shape design approach is applied to numerical computation of a model potential free boundary value problem. The problem is discretized using the nite element method. To test the approach the problem is formulated in both velocity potential and stream function formulation and four di erent nite element discretizations are used. Associated minimization problem is solved using the quasi-Newton method. Gradient of the cost function is computed by solving the algebraic adjoint equation. Gravity and surface tension forces are included in the model. Viability of the method is showed by solving problems with important e ects of gravity and surface tension forces.