Saturday, September 23

MS33
Fitted Mesh Techniques for Flow Problems

10:30 AM-12:30 PM
Center City 2

Robust layer-resolving methods are important for flow problems having non-smooth solutions with singularities related to boundary layers. A numerical method is layer-resolving if it generates, at each point of the domain, numerical approximations of the exact solution and its derivatives, for all values of the singular perturbation parameter. These approximations must satisfy pointwise error bounds and be computable with an amount of work, all of which are independent of this parameter. It is robust if these approximations inherit the stability properties of the exact solution by preserving the monotonicity of the original problem. Robust layer-resolving methods are constructed using upwind finite difference operators on Shishkin meshes for four classical flow problems.

10:30-10:55 Direct Robust Layer-resolving Numerical Methods for Flow in a Converging Channel

John J. H. Miller, Organizer; Daniel Murphy, Trinity College, Ireland; and Grigorii I. Shishkin, Russian Academy of Sciences, Russia

11:00-11:25 Direct Robust Layer-resolving Methods for Flow Over a Flat Plate

Paul A. Farrell, Kent State University, USA; Alan F. Hegarty, University of Limerick, Ireland; John J. H. Miller, Organizer; Eugene O'Riordan, Dublin City University;; and Gregorii I. Shishkin, Russian Academy of Sciences, Russia

11:30-11:55 A Direct Robust Layer-resolving Method for the Solution of the Navier-Stokes Equations for Axisymmetric Stagnation Point Flow

John J. H. Miller, Organizer; Alison P. Musgrave, Trinity College, Ireland; and Grigorii I. Shishkin, Russian Academy of Sciences, Russia

12:00-12:25 Robust Layer-resolving Numerical Methods for the Falkner-Skan Problem

John Butler, Trinity College, Ireland; John J. H. Miller, Organizer; and Gregorii I. Shishkin, Russian Academy of Sciences, Russia