Deborah Mary Greaves

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

Numerical Modelling of Laminar Separated Flows and Inviscid Steep Waves using Adaptive Hierarchical Meshes

Summary

Adaptive hierarchical grid generation and its application to the simulation of viscous separated flow past a small diameter cylinder and of irrotational wave flows in tanks are considered in this thesis. The hierarchical grid generator is based on recursive subdivision of the domain of interest using quadtrees in two-dimension and octrees in three-dimensions. Two alternative schemes for efficient storage of the quadtree grid information are examined, tree traversal techniques are devised for neighbour finding, and accurate boundary representation is considered. It is found that hierarchical grids are straightforward to generate from sets of boundary adaptive seeding points.

The quadtree grids are first utilised in predicting laminar separated flow past a cylinder by solving the Navier-Stokes equations with a pressure correction method after discretisation using finite volumes. Vorticity levels in the evolving flow field are used to adapt the mesh at regular intervals, thus ensuring the grids are economical in array size. Results are obtained and compared with published data for unidirectional sub-critical flows past circular and square cylinders at Reynolds numbers up to Re = 5000.

In the second application, quadtree grids are triangularised to provide adaptive finite element meshes for irrotational free surface flows. The grid generator is coupled wit a potential flow theory finite element solver, developed by Wu and Eatock Taylor (1994a, b), and used to solve the two-dimensional non-linear time domain free surface problem. A time marching method is employed, and the mesh is adapted at each time step to flow the moving free surface. Numerical results are obtained for the following cases: standing waves in a rectangular tank; standing wave interaction with a fixed surface piercing rectangular body; and wave interaction with a fixed submerged horizontal circular cylinder in a rectangular container. Comparison is made with analytical and alternative numerical schemes.

It is concluded that hierarchical grids offer great promise for simulating maritime flows, but that efficient prediction of separated flow using such a mesh relies on a fast numerical solver. The advantages of the adaptive finite element method for irrotational free surface flows are most compelling for simulations involving complicated boundaries.

(No thesis available)