Lectureurs and Topics

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.

Published October 20, 2010