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{\large Adrian Sandu \\
{\bf Non-Conventional Time Stepping Methods for Solving the Flow Equations}}

Computational Science Lab \\ Department of Computer Science \\ Virginia Tech \\ Blacksburg \\ VA 24061-0106
\\
{\tt sandu@cs.vt.edu}\\
Amik St-Cyr\end{center}

(for the Special Session on Environmental and Energy Science)


This talk discusses recent results on a time stepping methodology for
solving flow equations. We currently investigate an extrapolation-based
family of integrators. The base method is linearly implicit Euler, paired
with a matrix-free approach for the solution of the linear system. The
extrapolation technique allows to construct high order Rosenbrock-type
integrators, allows to combine implicit and explicit methods, and allows
to use different time steps on different parts of the domain. Results are
shown for high order spatial discretizations working on adaptive meshes.


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