Abstract
The optimal design of wave energy converters requires coupling of many different disciplines such as hydrodynamics, controls and geometry. Joint sensitivity calculation of all the disciplines is required for the gradient based optimization of the system objective. The adjoint method is the only viable method for calculating sensitivities with respect to a large number of input parameters at once as required in system design optimization problems. To this end, a discrete adjoint method is formulated, and the sensitivity of hydrodynamic coefficients is calculated for a point absorber system modeled as a sphere. The sensitivity are separated into real and imaginary sensitivities which one could interpret as the sensitivity for added mass and damping respectively. First, a differentiable boundary element method (BEM) based hydrodynamics code for fluid-structure interaction is developed in the Julia programming language. Automatic differentiation capabilities in Julia are then used to calculate the required partial derivatives for the adjoint equations. The accuracy of the automatic differentiation of Green's function and the resulting coefficients are compared with analytical derivation and the finite differences. The resulting sensitivities can be used in a large-scale gradient-based design optimization. The main contribution of this work is to formulate the discrete adjoint equations for the integral equations and modernize hydrodynamics BEM software to be able to provide necessary gradients. Thus, the method and formulation to get the sensitivities are discussed while the verification of the obtained gradients is an ongoing work.
The presentation for this paper at UMERC+METS 2024 can be found here.