zcwang6
(Zcwang6)
June 19, 2024, 8:34pm
1

Dear freefem team, I am currently trying to implement the following method in freefem. In the section 2.1 of the paper, it includes 3 pdes for solving. The last one is the elasticity equation which is clear to me, however I am not sure if it possible to solve the first 2 PDEs in Freefem [N-S with boby force and engery equation]. Thank you for the help.

Three-dimensional topology optimization of thermal-fluid-structural problems for cooling system design.pdf (7.5 MB)

fb77
(François Bouchut)
June 20, 2024, 11:21am
2
You can apply Newton’s method as described in

p.73
The source is available at

```
/****************************************************************************/
/* This file is part of FreeFEM. */
/* */
/* FreeFEM is free software: you can redistribute it and/or modify */
/* it under the terms of the GNU Lesser General Public License as */
/* published by the Free Software Foundation, either version 3 of */
/* the License, or (at your option) any later version. */
/* */
/* FreeFEM is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the */
/* GNU Lesser General Public License for more details. */
/* */
/* You should have received a copy of the GNU Lesser General Public License */
/* along with FreeFEM. If not, see <http://www.gnu.org/licenses/>. */
/****************************************************************************/
// Author: F. Hecht
// Stationnary imcompressible Navier Stokes Equation with Newton method (jan. 2012)
verbosity=0;
```

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You have to adapt the method to include temperature (this should not lead to serious difficulties).

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