Towards Accurate Numerical Methods for Ship Flows on Composite Overlapping Grids

Doktorsavhandling, 2002

Numerical methods are presented that are designed to make accurate ship-flow computations more feasible. One method concerns the automatic generation of high-quality computational grids. It treats the grids as competing individuals in a population, where an individual's fitness is based on a measure of grid quality. The fitness of the population is improved by a genetic algorithm.The method works well in standard parallel environments. Two other methods, one line-implicit and the other alternating-direction implicit, are designed to advance solutions in time on composite overlapping grids. Both have a computational cost which is of the same order as for a corresponding explicit method. The line-implicit method is conditionally stable and is used to solve the incompressible Navier-Stokes equations in boundary layers. The time step is independent of the grid step size in the direction normal to a no-slip boundary. The alternating-direction implicit method is unconditionally stable and it is applied to a convection-diffusion equation. This equation is used to model the Navier-Stokes equations and the method is intended for solutions in wake regions. The stability properties and accuracy are supported by numerical experiments. Both methods and an explicit method can be applied on different component grids to minimize the computational time for a numerical simulation. The emphasis of the work has been on the basic numerical algorithms and all verification has been carried out using generic test cases. Although the primary objective has been to enable more accurate ship-flow predictions, all methods are of general interest in computational fluid dynamics.