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