# hpfem/esco2012-boa

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 \title{Numerical Modeling of the Flow Structures around Thin Body in the Stratified Fluid} \tocauthor{L. Benes} \author{} \institute{} \maketitle \begin{center} {\large Lud\v{e}k Bene\v{s}}\\ Dept. of Technical Mathematics CTU Prague, Karlovo n\'{a}m. 13, CZ-121\,35 Prague 2\\ {\tt benes@marian.fsik.cvut.cz} \\ \vspace{4mm}{\large Tom\'{a}\v{s} Bodn\'{a}r}\\ Dept. of Technical Mathematics CTU Prague, Karlovo n\'{a}m. 13, CZ-121\,35 Prague 2, Czech Republic\\ {\tt bodnar@marian.fsik.cvut.cz} \\ \vspace{4mm}{\large Philippe Frauni\'{e}}\\ Universit\'{e} du Sud Toulon-Var, Laboratoire de Sondages Electromagn\'{e}tiques de l'Environnement Terrestre, B\^{a}timent F, BP 132, 83957 La Garde Cedex, France\\ {\tt Philippe.Fraunie@lseet.univ-tln.fr} \end{center} \section*{Abstract} Numerical simulation of an internal gravity waves past a moving body in a stably stratified flow is performed in comparison with laboratory experiments. The flow field in the towing tank with a moving thin horizontal strip is modeled using different computational ways and different numerical schemes. The mathematical model is based on the Boussinesq approximation of the averaged Navier--Stokes equations. The resulting set of partial differential equations is then solved by two different numerical schemes. The first method is the second-order finite volume AUSM MUSCL scheme combined with the artificial compressibility method in dual time . For the time integration the second order BDF method is used in physical time, while the third order Runge-Kutta method is used in artificial time. The second scheme is based on the high order compact finite-difference discretizations. The time integration is carried out by the Strong Stability Preserving Runge-Kutta scheme. The developing of the internal waves is studied by different ways. The obstacle is supposed either as the stationary in the incoming flow or as the moving body in the stratified fluid. In the simplest case, the thin body is modeled only by the appropriate boundary condition, then via penalization technique or by simple immersed boundary method. All computations are compared each other and also with the experiment. \bibliographystyle{plain} \begin{thebibliography}{10} \bibitem{ben1} {\sc L. Bene\v{s} and J. F\''{u}rst and Ph. Frauni\'{e}}. {Comparison of Two Numerical Methods for the Stratified Flow}. Computers \& Fluids Vol. 46, Issue 1, 2011, p.148-154. \bibitem{ben2} {\sc T. Bodn\'{a}r and L. Bene\v{s} and Ph. Frauni\'{e} and K. Kozel}. {Application of Compact Finite--Difference Schemes to Simulations of Stably Stratified Fluid Flows}. Applied Mathematics and Computations, doi:10.1016/j.amc.2011.08.058, in press. \end{thebibliography}