Model Order Reduction of Combustion Processes with Complex Front Dynamics

In this work we present a data driven method, used to improve mode-based model order reduction of transport fields with sharp fronts. We assume that the original flow field $q(\mathbf{x},t)=f(\phi(\mathbf{x},t))$ can be reconstructed by a front shape function $f$ and a level set function $\phi$. The level set function is used to generate a local coordinate, which parametrizes the distance to the front. In this way, we are able to embed the local 1D description of the front for complex 2D front dynamics with merging or splitting fronts, while seeking a low rank description of $\phi$. Here, the freedom of choosing $\phi$ far away from the front can be used to find a low rank description of $\phi$ which accelerates the convergence of $\Vert q- f(\phi_n)\Vert$, when truncating $\phi$ after the $n$th mode. We demonstrate the ability of this new ansatz for a 2D propagating flame with a moving front.