Computational methods for finding exact solutions of shear flows
Seminar Room 1, Newton Institute
Direct numerical solution begins with an initial velocity field and uses the incompressible Navier-Stokes equation to evolve that field forward in time. It has been a huge success and has provided theoretical support for a large number of experiments and natural phenomena. To find steady solutions and traveling waves, one must solve for velocity fields that satisfy certain nonlinear requirements. To find periodic or relative periodic solutions, one must solve for an initial velocity field that evolves in time over a single period to reach a final state that is equal to the initial state modulo certain symmetries. This talk will describe the use of direct numerical solution, Krylov subspace methods, and the hookstep technique from nonlinear optimization to find such solutions.