Efficient Wildland Fire Simulation via Nonlinear Model Order Reduction

Abstract: We propose a new hyper-reduction method for a recently introduced nonlinear model reduction framework based on dynamically transformed basis functions and especially well-suited for advection-dominated systems. Furthermore, we discuss applying this new method to a wildland fire model whose dynamics feature traveling combustion waves and local ignition and is thus challenging for classical model reduction schemes based on linear subspaces. The new hyper-reduction framework allows us to construct parameter-dependent reduced-order models (ROMs) with efficient offline/online decomposition. The numerical experiments demonstrate that the ROMs obtained by the novel method outperform those obtained by a classical approach using the proper orthogonal decomposition and the discrete empirical interpolation method in terms of run time and accuracy.