PU-DWR Combustion

This software provides a space-time finite element solver to the low Mach number combustion equations with goal oriented adaptive mesh refinement.

• Note: This software is a modification of DTM++/dwr-diffusion.

Equations

The combustion equations describe the reaction between a dimensionless temperature $\theta$ and a combustable species concentration $Y$:

$$\displaylines{ \partial_t\theta -\Delta\theta = \omega(\theta,Y)\quad\text{ in }\Omega\times(0,T),\\\ \partial_t Y -\frac{1}{Le}\Delta Y = -\omega(\theta,Y)\text{ in }\Omega\times(0,T). }$$

The reaction itself is described by Arrhenius law

$$\omega(\theta,Y)\coloneqq\frac{\beta}{2Le}Y\exp(\frac{\beta(\theta-1)}{1+\alpha(\theta-1)}),$$

with parameters

• Lewis Number $Le>0$
• gas expansion rate $\alpha > 0$
• dimensionless activation energy $\beta >0$

Adaptivity

Goal oriented adaptivity is achieved by the dual-weighted residual method (DWR), with a space-time partition-of-unity as described in

Please cite this paper if you used the space-time PU-DWR method of this software.

@article{thiele2024numerical,
  title={Numerical modeling and open-source implementation of variational partition-of-unity localizations 
  of space-time dual-weighted residual estimators for parabolic problems},
  author={Thiele, Jan Philipp and Wick, Thomas},
  journal={Journal of Scientific Computing},
  volume={99},
  number={1},
  pages={25},
  year={2024},
  publisher={Springer}
}

Setup

Dependencies

This software has the following dependencies which can be installed together using candi:

• MUMPS
• Trilinos
• p4est
• HDF5
• deal.II v9.3.0 at least, linked to the previous packages

Configure and Build

The software is configured and build using CMake by calling the following commands in the root folder of the repository.

   cmake -S. -Bbuild --DEAL_II_DIR=<path_to_your_deal_installation
   cmake --build build

This sets up a build directory in which the executable will be located. It can be called as a single process or with MPI

    ./build/pu-dwr-combustion input/default.prm # single process
    mpirun -n <numprocs> build/pu-dwr-combustion input/default.prm # MPI parallel