A Quasi-Monte Carlo Volume Integration and Chebyshev Picard Iteration Method for Time-Parallel Nonlinear Seakeeping Computations

Abstract

. The design and analysis of vessels and wave energy converters requires an under-standing of the nonlinear loads and responses in stochastic waves. A novel mesh-free potential flow methodology is introduced for simulating the response of a floating body with nonlinear Froude-Krylov and hydrostatic e ff ects. The nonlinear fluid forces are cast as volume integrals using Fluid Impulse Theory (FIT). These volume integrals are robustly evaluated using Quasi-Monte Carlo (QMC) integration over an implicit geometry without the need to discretize the hull or free surfaces. The resulting nonlinear equation of motion is solved with an impulse-adapted Chebyshev Picard iteration scheme (I-MCPI). By approximating the nonlinear momentum impulse with a Chebyshev series, the time derivative can be analytically computed, circumventing the numerical sensitivity of finite-di ff erencing. The solution is shown to converge over short parallelized subintervals, and sequentially concatenated to form long time records.