The investigator will develop improved numerical methods for simulating fluid flow, with emphasis on the vortex sheet model. The approach is based on the vortex method, in which Lagrangian points carry the vorticity. The working hypothesis is Prandtl's idea that the vortex sheet is an asymptotic model for a free shear layer in slightly viscous flow. The first task in this pro- posal is to develop a fast summation method to study spiral scal- ing properties in the Kelvin-Helmholtz problem. Other projects are a simulation of splitter plate flow with realistic boundary conditions, and a comparison of planar and axisymmetric vortex sheet roll-up. The investigator will compare vortex simulations with finite-difference solutions of the Navier-Stokes equations and with the available laboratory experiments. A key concern is to obtain accurate numerical solutions in order to make precise statements about the validity of the various modelling assump- tions. Fluid dynamics is concerned with the motion of gas (e.g. air) and liquid (e.g. water). A key goal is to understand the forces which act between the fluid and an immersed solid surface. For example, air flow past the wing is responsible for the lift force which supports an aircraft in flight. Fluid flow is important in many areas of science and technology, from internal combustion engines to weather prediction to blood flow. The mathematical equations which describe fluid motion are difficult to solve, and hence the investigator is developing numerical algorithms for use on high speed computers. The goal is to provide insight into the physics of fluid motion, and to create modelling tools to help engineers solve design problems.
