Efficient Wildland Fire Simulation via Nonlinear Model Order Reduction

TL;DR

This paper introduces a nonlinear hyper-reduction method tailored for advection-dominated systems, significantly improving the efficiency and accuracy of wildland fire simulations with traveling combustion waves.

Contribution

A novel hyper-reduction technique based on dynamic basis functions that enhances reduced-order modeling for complex, advection-driven phenomena like wildland fires.

Findings

Outperforms classical methods in run time and accuracy

Effective for advection-dominated, traveling wave systems

Enables efficient offline/online parameter-dependent modeling

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.