SFEMaNS  version 4.1 (work in progress)
Reference documentation for SFEMaNS
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1 // ---------------------------------------------------------------------
2 // $Id$
3 //
4 // This file is part of SFEMaNS.
5 //
6 // SFEMaNS is free software: you can redistribute it and/or modify
7 // it under the terms of the GNU General Public License as published by
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11 // SFEMaNS is distributed in the hope that it will be useful,
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125 <tr valign=top>
126  <td width="30%" align="left">
127  in construction
128  </td>
129  <td align="left">
130  This section follows the structure/tree of the code and proposes a description of the fortran files
131  involved in the initialization process and in the approximation of an equation
132  (temperature, mass, Navier-Stokes and Maxwell).
133  </td>
134 </tr>
135 </table>
136 */
section doc_intro_frame_work_num_app Numerical approximation subsection doc_intro_fram_work_num_app_Fourier_FEM Fourier Finite element representation The SFEMaNS code uses a hybrid Fourier Finite element formulation The Fourier decomposition allows to approximate the problem’s solutions for each Fourier mode modulo nonlinear terms that are made explicit The variables are then approximated on a meridian section of the domain with a finite element method The numerical approximation of a function f $f f is written in the following generic f with f $t f the time and f $M f the number of Fourier modes considered The unknown f f f f f f f f Omega_v f and f Omega f We also consider f a penalty method of the divergence of the velocity field is also implemented The method proceeds as follows
Definition: doc_intro.h:218