\documentclass[10pt,ct]{poster}
\usepackage{epsfig}
\usepackage{amsmath}
\usepackage{amsmath}

\newcommand{\ux}{{\bf{x}}}
\newcommand{\uu}{{\bf{u}}}
\newcommand{\uv}{{\bf{v}}}

\begin{document}

\begin{poster}
%{\vspace{-1.9cm}12th Workshop on Two-Phase Flow Predictions 21-25 March 2010, Halle (Germany)}
{\vspace{-2.0cm}{\small{
\hspace{3.5cm} 12th Workshop on Two-Phase Flow Predictions, 21-25 March 2010, Halle (Germany)
\vspace{0.2cm}
}}\\
|~~~~~~~~~~~~~~~~~~~~~TEST CASE: LES of particle-laden turbulent channel flow}
%{\vspace{-1.9cm}TEST CASE: LES of particle-laden turbulent channel flow}
{\vspace{-0.4cm}{\small{
GROUP UUD-UPI: C. Marchioli, A. Soldati, Dept. Energy Technologies, University of Udine
$\&$ M.V. Salvetti, Dept. Aerospace Engineering, University of Pisa (Italy)\\
GROUP TUE: J.G.M. Kuerten, Dept. Mechanical Engineering, Technische Universiteit Eindhoven (Netherlands)\\
GROUP IMFT-ASU: A. Ndri Konan, P. Fede, O. Simonin, Universit\'{e} de Toulouse; INPT, UPS;
Institut de M\'{e}canique des Fluides de Toulouse;
CNRS (France)
$\&$ K.D. Squires, Mechanical and Aerospace Engineering Dept., Arizona State University (USA)\\
GROUP TUM: C. Gobert, M. Manhart, Dept. Civil Engineering, Munich University of Technology (Germany)\\
}}}
{mlu_logo.ps}

~\\
\vspace{-0.8cm}
\section{Equation of particle motion (with drag and inertia)}
\vspace{-0.4cm}
\begin{equation}
\nonumber
\begin{array}{l}
\frac{d\ux_i}{dt}=\uv_i~,~~~
\frac{d\uv_i}{dt}=\frac{{\hat{\uu}}(\ux_i,t)-\uv_i}{\tau_p}(1+0.15Re_p^{0.687}),
\end{array}
\label{eq:particle}
\end{equation}
{\small{
\noindent
$\ux_i$, $\uv_i$ and $\tau_p$: particle position, velocity and relaxation time.\\
${\hat{\uu}}(\ux,t)$: filtered fluid velocity (issued by LES).
}}

\section{Method (LES of particle-laden flow)}
\vspace{-0.5cm}
\begin{itemize}
%
\item COMMON BASE-SIMULATION PARAMETERS
%
\vspace{-0.2cm}
{\small{
%
%-------------------------------------------------------------------
\begin{itemize}
\item
Shear Reynolds number
(based on half channel height)
: $Re_{\tau}=150$
\item
\vspace{-0.1cm}
Particle Stokes number: $St=1$, $5$ and $25$
\item
\vspace{-0.1cm}
Size of the computational domain
(streamwise, wall-normal, spanwise):
$L_x \times L_z \times L_y = 4 \pi h \times 2 h \times 2 \pi h $
\item
\vspace{-0.1cm}
Grid resolution: $N_x \times N_z \times N_y = 64\times65\times64$
\item
\vspace{-0.1cm}
Tracked particles: $N_p=10^5$ particles for each $St$
\end{itemize}
%-------------------------------------------------------------------
%
}}
%
\item GROUP UUD-UPI (Marchioli, Soldati, Salvetti)
%
\vspace{-0.2cm}
{\small{
%
%-------------------------------------------------------------------
\begin{itemize}
\item Flow solver: Fourier-Galerkin (streamwise-spanwise) and Chebyshev collocation method (wall-normal)
\item
\vspace{-0.1cm}
SGS model: dynamic eddy-viscosity model
\item
\vspace{-0.1cm}
Time integration of fluid: $2^{nd}$-order Adams-Bashforth (nonlinear terms),
implicit Crank-Nicolson (linear terms)
\item
\vspace{-0.1cm}
Time integration of particles: $4^{th}$-order Runge-Kutta
\item
\vspace{-0.1cm}
Fluid velocity interpolation: $6^{th}$-order Lagrange polyn.
\end{itemize}
%-------------------------------------------------------------------
%
}}
%
\item GROUP TUE (Kuerten)
%
\vspace{-0.2cm}
{\small{
%
%-------------------------------------------------------------------
\begin{itemize}
\item Flow solver: Fourier-Galerkin (streamwise-spanwise) and Chebyshev collocation method (wall-normal)
\item
\vspace{-0.1cm}
SGS model: dynamic eddy-viscosity model
\item
\vspace{-0.1cm}
Time integration of fluid: $3^{rd}$-order Runge-Kutta (nonlinear terms) and implicit Crank-Nicolson (linear terms)
\item
\vspace{-0.1cm}
Time integration of particles: $2^{nd}$-order Heun method
\item
\vspace{-0.1cm}
Fluid velocity interpolation: $4^{th}$-order Lagrange-Hermite
\end{itemize}
%-------------------------------------------------------------------
%
}}
%
\item GROUP IMFT-ASU (Konan, Fede, Simonin, Squires)
%
\vspace{-0.2cm}
{\small{
%
%-------------------------------------------------------------------
\begin{itemize}
\item Flow solver: fractional-step method for the NS equations. Spatial derivatives evaluated using $2^{nd}$-order centered differences
\item
\vspace{-0.1cm}
SGS model: eddy-viscosity model with wall damping
\item
\vspace{-0.1cm}
Time integration of fluid: $2^{nd}$-order Adams-Bashforth (nonlinear terms) and Crank-Nicolson (linear terms)
\item
\vspace{-0.1cm}
Time integration of particles: $2^{nd}$-order Adams-Bashforth
\item
\vspace{-0.1cm}
Fluid velocity interpolation: $4^{th}$-order Lagrange polyn.
\end{itemize}
%-------------------------------------------------------------------
%
}}
%
\item GROUP TUM (Gobert, Manhart)
%
\vspace{-0.2cm}
{\small{
%
%-------------------------------------------------------------------
\begin{itemize}
\item Flow solver: finite-volume method for the NS equations. Spatial derivatives evaluated using $2^{nd}$-order centered differences
\item
\vspace{-0.1cm}
SGS model: dynamic Lagrange Smagorinsky eddy-viscosity model
\item
\vspace{-0.1cm}
Time integration of fluid: $3^{rd}$-order Runge-Kutta
\item
\vspace{-0.1cm}
Time integration of particles: $4^{th}$-order adaptive linear-implicit Runge-Kutta (Rosenbrock-Wanner scheme)
\item
\vspace{-0.1cm}
Fluid velocity interpolation: $4^{th}$-order Lagrange polyn.
\end{itemize}
%-------------------------------------------------------------------
%
}}
\end{itemize}

~\\
\vspace{-0.79cm}

\section{Results}
Mean and RMS Fluid Velocities:

\vspace{-0.3cm}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/mean-fluid-strmw-vel.ps,height=5.0cm,angle=270}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/fluid-rms.ps,height=5.0cm,angle=270}
\vspace{0.3cm}

\noindent
Mean and RMS Particle Velocities:

\vspace{-0.3cm}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/mean-St1-particle-strmw-vel.ps,height=5.0cm,angle=270}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/particle-St1-rms.ps,height=5.0cm,angle=270}

\vspace{-0.2cm}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/mean-St5-particle-strmw-vel.ps,height=5.0cm,angle=270}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/particle-St5-rms.ps,height=5.0cm,angle=270}

\vspace{-0.2cm}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/mean-St25-particle-strmw-vel.ps,height=5.0cm,angle=270}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/particle-St25-rms.ps,height=5.0cm,angle=270}

\vspace{0.3cm}

\noindent
Particle Concentrations:

\vspace{-0.2cm}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/conc-St1.ps,height=5.0cm,angle=270}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/conc-St5.ps,height=5.0cm,angle=270}
\vspace{0.3cm}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/conc-St25.ps,height=5.0cm,angle=270}
\hspace{-0.5cm}\epsfig{file=../database/FIGURE/conc-interp.ps,height=5.0cm,angle=270}

\end{poster}

\end{document}
