Title: High-resolution finite element schemes for coupled problems

Speaker: Matthias Moller, Techncial University of Dortmunc

Date/Time: October 14, 2009          

Location: CSRI/Room 90

Brief Abstract: Algebraic criteria for the design of non-oscillatory methods are reviewed in a general framework. For a given discretization (e.g., standard Galerkin finite elements) these mathematical constraints can be readily enforced by means of conservative matrix manipulations. A family of high-resolution finite element schemes for convection- dominated flow problems is constructed based on the so-called algebraic flux correction (AFC) approach. Implicit time integration methods are employed to permit the use of moderately large time steps even on locally refined meshes.

A linearized version of the flux corrected transport (FCT) algorithm is presented which allows for an accurate cost-effective treatment of highly time-dependent flow problems. In each time step, an implicit non-oscillatory low-order method is used to predict a provisional solution. Flux limiting is applied as post-processing step to remove excessive numerical diffusion without generating spurious undershoots and overshoots. The basic concepts are first described for scalar conservation laws and extended to hyperbolic system of equations.

Numerical examples are presented for the compressible Euler equations which are equipped with a thin-shell Lorentz force model and coupled with a scalar tracer equation. All simulations are performed using the in-house code Featflow2. Some implementation details and advanced features such as dynamic grid adaptation are briefly addressed.

CSRI POC: John Shadid, 505-845-7876