A. Saalehi

Doctor of Philosophy, St. Edmund Hall, University of Oxford, Michaelmas Term 1995

Quadtree-based Finite Element Modelling of Laminar Separated Flow Past a Cylinder

Summary

Wave loading on maritime structures occurs as the result of complex fluid-structure processes for which analytical solutions of the governing conservation equations cannot be obtained. This thesis is concerned with the numerical modelling low Reynolds number flow past single and multiple cylinders. The main objectives of the work are to present a novel finite element mesh generation method and details of Galerkin and streamline upwind Petrov-Galerkin (SUPG) finite element schemes for laminar flow simulation. It should be noted that the present work is essentially a precursor to the modelling of the flows at high Reynolds numbers including turbulence and free surface effects which have to be included in typical maritime flow situations.

The finite element mesh is generated in tow stages. First, an underlying quadtree-based grid is obtained by recursive subdivision of the computational domain about boundary and flow seeding points. The decomposition process is controlled by an integer numbering system which leads to the grid information being stored efficiently in an offered form and completed quickly. The hierarchical grid has a fractal-like quality which allows grid cells to be concentrated locally in areas of interest. Special care is paid to obtaining 2:1 aspect rations between adjacent cells and overall grid uniformity. Second, the resulting rectangular hierarchical grid is triangularised to give the finite element mesh. Curved boundaries of the domain are accurately discretised using a technique to ensure smooth boundaries.

Galerkin and streamline upwind Petrof-Galerkin (SUPG) finite element methods are used to discretise the governing Navier-Stokes and continuity equations written in primitive variables form. Neumann velocity boundary conditions, suitable for the divergence form of the governing equations, are used at the outlet boundaries. The discretised equations are solved by Newton iteration with the aid of re-ordering and frontal solver algorithms from the Harwell subroutine library. Results are presented for separated laminar flow past a single cylinder at Reynolds numbers equal to 0.01, 10, 30 40, 100 and 200. Steady flow past multiple cylinders at Reynolds numbers 0.01, 0.011 and 40 are also considered. Comparisons are made with present experimental and alternative numerical data.

(no thesis available)