Spectral element methods for incompressible flow

The emphasis will be on developing discretization and solution algorithms for solving the unsteady, incompressible Navier-Stokes equations. The applications will be selected from the laminar to the transitional flow regime.

Einar M. Rønquist, Department of mathematical sciences, NTNU Trondheim, Norway:

• Governing equations
• Spatial discretization (the spectral element method)
  • Poisson
  • Stokes
  • Convection-diffusion
  • Navier-Stokes
• Temporal discretization
  • Multi-step methods
  • Operator splitting methods
  • Segregated algorithms

Paul F. Fisher, Mathematics and Computer Science Division, Argonne National Laboratory, USA:

• Solution methods
  • Iterative methods
  • Preconditioning
  • Domain decomposition methods
  • Fast diagonalization methods
• High Reynolds number flows (Re ~ O(1000))
  • Transitional flows
  • Filtering
  • Grid generation
  • Parallel processing
• Applications
  • Blood flow
  • Convection heat transfer
  • (Free surface flow)

The above list is tentative, and the actual lecture topics and lecture order will be chosen and mixed at a later stage.

Runge-Kutta discontinuous Galerkin methods for convection-dominated problems

Bernardo Cockburn, Mathematics, University of Minnesota, USA:

• An overview of the development of Discontinuous Galerkin methods
• The Runge-Kutta Discontinuous Galerkin method for nonlinear hyperbolic problems.
• The Local Discontinuous Galerkin method for convection-diffusion problems.
• A unified analysis of Discontinuous Galerkin methods for elliptic problems.
• Discontinuous Galerkin methods for incompressible flows.