@conference {364,
	title = {Operator splitting versus source linearization for the reaction-(advection)-diffusion equation in OpenFOAM{\textregistered}},
	booktitle = {31. Deutscher Flammentag Manuskripte },
	year = {2023},
	month = {09/2023},
	abstract = {<p>Novel combustion technologies like MILD or (ultra-)lean combustion aim to reduce pollutant emissions and increase process efficiency. Pollutants are reduced by distributing the reaction zone over large regions and keeping the combustion temperature low. Lower temperatures also reduce heat loss and increase combustion efficiency. These combustion conditions can come at the cost of unstable operation caused by frequent near-extinction or near-ignition states in the flame. These unstable states must be captured when modeling MILD or (ultra-)lean flames. Solving the reaction-advection-diffusion fully coupled is often prohibitive because of the numerical effort and the memory requirements. Common Computational Fluid Dynamics (CFD) codes use operator splitting (OS) schemes to overcome this issue. OS divides the reaction-diffusion problem into sub-problems and provides an algorithm to recover the original problem{\textquoteright}s solution by combining the sub-problems. The advantage of OS is that the individual sub-problems, e.g., transport and chemistry, can be solved with specialized solvers. The main drawback of using OS schemes is a loss of accuracy when recovering the original problem. Near-ignition or near-extinction states pose a peculiar problem for OS schemes, and the predicted results can deviate significantly from the actual one; furthermore, they can introduce a time step size dependence of the steady-state solution. OpenFOAM{\textregistered} uses a particular OS; the chemistry sub-problem is linearized and added as an explicit source to the transport problem. Technically speaking, this approach is not an OS but a source term linearization. As the open-source CFD toolbox OpenFOAM{\textregistered} is increasingly used for combustion simulations, understanding the accuracy, the steady-state consistency and the temporal evolution of the linearization approach is essential. In this work, the performance of the OpenFOAM{\textregistered} source linearization is evaluated and compared to OS schemes. The accuracy and steady-state consistency are evaluated by scalar linear stability analysis, while the temporal evolution is evaluated using near-ignition and near-extinction perfectly-stirred reactor test cases.</p>
},
	keywords = {Linear stability analysis, OpenFOAM{\textregistered}, operator splitting, Perfectly stirred reactor (PSR), Reaction-diffusion(-advection) equation, Reactive flow},
	author = {Markus B{\"o}senhofer}
}
@inbook {215,
	title = {Computational Improvements for the Eddy Dissipation Concept by Operator Splitting and Tabulation},
	booktitle = {Proceedings of the 28th European Symposium on Computer Aided Process Engineering},
	volume = {43},
	number = {2010},
	year = {2018},
	pages = {1687{\textendash}1692},
	abstract = {<p>The Eddy Dissipation Concept (EDC) is a well working concept for turbulent reacting flows, which depicts the influence of chemical reactions as well as turbulence. The problem when using detailed chemical mechanisms - necessary for more information about radical species and pollutants - is the vastly increased computational demand. Operator splitting and in situ adaptive tabulation (ISAT) can be a way to reduce the computational effort and improve the application of detailed chemical mechanisms with the EDC. Two operator splitting mechanisms are presented and used for the simulation of Sandia Flame D. The computational time can be decreased and the results fit well to the experimental results.</p>
},
	keywords = {Eddy Dissipation Concept (EDC), in situ adaptive tabulation (ISAT), OpenFOAM, operator splitting, turbulent combustion},
	isbn = {9780444642356},
	issn = {15707946},
	doi = {10.1016/B978-0-444-64235-6.50294-1},
	author = {Wartha, Eva-Maria and B{\"o}senhofer, Markus and Harasek, Michael}
}
