%%%%%%%%title of contribution
\Atitle{High-Order Semi-Lagrangian Numerical Method for the Large-Eddy
Simulation of Reactive Flows
}
%%%%%%%%name of authors connected by "and"
\Aauthor{\underline{Rolf Jeltsch}$^1$, Julián T. Becerra Sagredo$^2$,
Wesley P. Petersen$^1$,
Jürg Gass$^3$}
%%%%%%%%abbreviation of authors names for running header
\renewcommand{\rauthor}{F. Author}
%%%%%%%affiliations and e-mail
\Aaddress{%
$^1$ Seminar for Applied Mathematics, ETH Zurich\\
$^2$ Center for Energy Research, National University of Mexico, Temixco, Mexico\\
$^3$ Laboratory of Thermodynamics in Emerging Technologies, ETH Zurich\\
 \quad{\tt jeltsch@math.ethz.ch}}
%%%%%%%abstract of contribution
\Aabstract{%
A high-order Semi-Lagrangian numerical method is developed for
the simulation of a subsonic methane/air flame. The fluid is described
by the Navier-Stokes equations for a mixture of ideal gases. Turbulence
is modeled using Large-Eddy simulation (LES) together with a transport
equation for the subgrid kinetic energy. For the chemical reactions
we use an unsteady flamelet model based on transport equations for the
mixture fraction and a reaction progress variable. This allows for
extinctions and re-ignitions by not assuming fast chemistry nor steady
flamelets.

To solve the resulting system of coupled transport equations a
Semi-Lagrangian (FSL) method, known from climate modeling, is used.
For the interpolations from the Lagrangian mesh points to a fix mesh
an interpolation based on piece wise polynomials of degree 2m which are
m-tmes differentiable are used. This interpolation is easy to implement,
computations are fast. It is conservative, conservative and creates
low or zero numerical diffusion and dispersion.

Finally the FSL method is used to simulate Sandia flame D.
For the 3-d simulations a mesh in cylindrical coordinates is
used where singular derivatives and high frequencies at the polar
axis are controlled.
}