Solving non-linear PDEs on Gocad models using escript

Pablo Mejia-Herrera and Côme Le Breton and Arnaud Botella. ( 2014 )
in: Proc. 34th Gocad Meeting, ASGA

Abstract

This paper proposes a workflow to solve on Gocad 3D models mathematical systems, coupled, non-linear and time-dependent partial differential equations. Using escript, a Python-based environment for applying and then obtaining the PDEs solutions, a large variety of problems such as heat transfer, elastic deformation or wave propagation simulations can be solved directly in Gocad. Assisted by the GoPy plugin, the 3D model defines the space where the PDEs solver is computed. The finite-element-method mesh volume required for the simulations is provided by a Tsolid, where a python script reads the Tsolid ASCII file and then creates the 3D domain adapted to apply escript. The solution can be stored in the initial 3D model or exported for generic visualization platforms. The proposed workflow is demonstrated on a highly curved 3D model from the Furfooz region. There, we simulated a stationary darcy flux that evidences the utility and simplicity of the method.

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BibTeX Reference

@INPROCEEDINGS{,
    author = { Mejia-Herrera, Pablo and Le Breton, Côme and Botella, Arnaud },
     title = { Solving non-linear PDEs on Gocad models using escript },
     month = { "sep" },
 booktitle = { Proc. 34th Gocad Meeting },
      year = { 2014 },
 publisher = { ASGA },
  abstract = { This paper proposes a workflow to solve on Gocad 3D models mathematical systems, coupled, non-linear and time-dependent partial differential equations. Using escript, a Python-based environment for applying and then obtaining the PDEs solutions, a large variety of problems such as heat transfer, elastic deformation or wave propagation simulations can be solved directly in Gocad. Assisted by the GoPy plugin, the 3D model defines the space where the PDEs solver is computed. The finite-element-method mesh volume required for the simulations is provided by a Tsolid, where a python script reads the Tsolid ASCII file and then creates the 3D domain adapted to apply escript. The solution can be stored in the initial 3D model or exported for generic visualization platforms. The proposed workflow is demonstrated on a highly curved 3D model from the Furfooz region. There, we simulated a stationary darcy flux that evidences the utility and simplicity of the method. }
}