Implementation of Generalized Modes in a 3D Finite Difference Based Seakeeping Model

This work is an extension of the finite difference potential flow solver OceanWave3D-Seakeepingdeveloped by Afshar (2014) to include generalized modes. The continuity equation is solvedusing a fourth-order centered finite difference scheme which requires that the entire fluid domainis discretized as opposed to the more popular panel method where only the body surface - andsometimes the free surface and sea bottom - are discretized. The advantage for the finitedifference solver is thought to be found for complex or high-resolution problems where thecomputational time will scale better due to the sparse nature of the coefficient matrix. Thesolver is built using the open source framework Overture which consists of C++ libraries forsolving partial differential equations on overlapping grids and has a built-in overlapping gridgenerator Ogen.