Multiphase adjoint optimization for efficient calculation of rigid body positions in Navier-Stokes flow
FacultiesFakultät für Mathematik und Wirtschaftswissenschaften
This thesis is concerned with the development of a new method for an efficient calculation of optimal rigid body positions in Navier-Stokes flow. The application that we consider is the calculation of ship running attitudes for different ship speeds and the corresponding resistance value. For this purpose the problem formulation and the so far commonly used calculation procedure based on the equations of motion are examined for possible savings in computational effort. As this approach suffers from inertial effects, the problem is mathematically reformulated as an optimization problem, which promises to reach the wanted equilibrium position significantly faster. In order to efficiently solve the optimization problem, we make use of gradient-based algorithms. The main idea here is to achieve an efficient gradient evaluation using adjoint calculus. This provides the benefit of a gradient evaluation for which the calculation effort is independent of the parameter space dimension. To this end a continuous adjoint formulation is derived for single-phase and multiphase Navier-Stokes flow and the optimization of arbitrary, weighted force and moment components with respect to rigid body positions. For the differentiation with respect to domain variations a transformation approach to a reference domain is used. This allows the setup of an exact analytical formula for the objective function gradient. This formula is derived for arbitrary, parametrized transformation functions. The analytical derivation is supplemented with the numerical implementation of the new method and its application to realistic test cases. Numerical examples show that the developed adjoint gradient evaluation is very accurate and considerably more efficient in comparison to finite differences gradients. Therefore the adjoint solution procedure is capable to speed up the calculation of ship running attitudes significantly without loss of accuracy in the results for resistance and rigid body positions.
Subject HeadingsNavier-Stokes-Gleichung [GND]
Multiphase flow [LCSH]
Navier-Stokes equations [LCSH]