The Numerical Stability of Nonlinear Floating Body Calculations

Abstract

Chairperson: Armin W. Troesch &&The numerical stability of nonlinear interaction problems is investigated by applying potential flow assumptions to oscillating, non-wallsided two-dimensional and three-dimensional axisymmetric bodies. This interaction problem is solved using a mixed two-step Eulerian_-Lagrangian method. In the first step, Laplace's equation is solved to determine the unknown potential values on the body and the unknown derivatives of the potentials on the free surface. In the second step, free surface boundary conditions are applied using the results of the first step to find the evolved free surface location and new potential values on the new location. Each step has particular mathematical characteristics (elliptic or parabolic_like), so that each step requires different numerical schemes. Consequently, the numerical stability of this body-wave interaction problem contains the characteristics of both of these two steps.