Finite Volume Methods for Incompressible Navier-Stokes Equations on Collocated Grids with Nonconformal Interfaces

Direct numerical solutions of the Navier-Stokes equations using Computational Fluid Dynamics methods are recognized as some the most advanced and accurate methods for prediction of flows around wind turbines. The ability of these methods to capture the dynamics of the complex flow properties appearing in the immediate vicinity of a wind turbine rotor makes them invaluable tools in the field of wind energy. Since direct computations of a fully resolved flow around a wind turbine are computationally expensive, a typical requirement for a good CFD method is that it is able to predict the flow field efficiently without jeopardizing the accuracy. In this thesis, some fundamental developments of direct CFD methods are presented to provide a platform for the development of sliding grid method for wind turbine computations. As one of the most prospective CFD methods for incompressible wind turbine computations, collocated grid-based SIMPLE-like algorithms are developed for computations on block-structured grids with nonconformal interfaces. A technique to enhance both the convergence speed and the solution accuracy of the SIMPLE-like algorithms is presented. The erroneous behavior, which is typical for some commonly used mass flux interpolations, is estimated, and a new interpolation technique, which eliminates these errors, is developed together with fully consistent SIMPLE-like algorithms. For the algorithms, both the accuracy and the convergence rate are shown to be higher than standard versions of the SIMPLE algorithm. The new technique is implemented in an existing conservative 2nd order finite-volume scheme flow solver (EllipSys), which is extended to cope with grids with nonconformal interfaces. The behavior of the discrete Navier-Stokes equations is discussed in detail and the developed technique, which exhibits both low implementation costs and high efficiency of the numerical scheme, is presented. A Geometric Multigrid method of the EllipSys flow solver is fully extended to block-structured grids with nonmatching blocks. An Optimized Schwarz method employed for the Incomplete Block LU relaxation scheme is shown to possess several optimal conditions, which enables to preserve high efficiency of the multigrid solver on both conformal and nonconformal grids. The developments are done using a parallel MPI algorithm, which can handle multiple numbers of interfaces with multiple block-to-block connectivity.