Meshfree Least Square-based Finite Difference method in CFD applications

Most commercial computational fluid dynamics (CFD) packages available today are based on the finite volume- or finite element method. Both of these methods have been proven robust, efficient and appropriate for complex geometries. However, due to their crucial dependence on a well constructed grid, extensive preliminary work have to be invested in order to obtain satisfying results. During the last decades, several so-called meshfree methods have been proposed with the intension of entirely eliminating the grid dependence. Instead of a grid, meshfree methods use the nodal coordinates directly in order to calculate the spatial derivatives. In this master thesis, the meshfree least square-based finite difference (LSFD) method has been considered. The method has initially been thoroughly derived and tested for a simple Poisson equation. With its promising numerical performance, it has further been applied to the full Navier- Stokes equations, describing fluid motions in a continuum media. Several numerical methods used to solve the incompressible Navier-Stokes equations have been proposed, and some of them have also been presented in this thesis. However, the temporal discretization has finally been done using a 1st order semi-implicit projection method, for which the primitive variables (velocity and pressure) are solved directly. In order to verify the developed meshfree LSFD code, in total four flow problems have been considered. All of these cases are well known due to their benchmarking relevance, and LSFD performs well compared to both earlier observations and theory. Even though the developed program in this thesis only supports two dimensional, incompressible and laminar flow regimes, the idea of meshfree LSFD is quite general and may very well be applied to more complex flows, including turbulenc