Heterogeneous Multiscale Methods for Interface Tracking of Combustion Fronts

Abstract. In this paper we investigate the heterogeneous multiscale methods (HMM) for interface tracking and apply the technique to the simulation of combustion fronts. Our goal is to overcome the numerical difficulties, which are caused by different time scales between the transport part and the reactive part in the model equations of some interface tracking problems, such as combustion processes. HMM relies on an efficient coupling between the macroscale and microscale models. When the macroscale model is not fully known explicitly or not valid in localized regions, HMM provides a procedure for supplementing the missing data from a microscale model. Here we design and analyze a multiscale scheme in which a localized microscale model resolves the details in the model and a phase field or a front tracking method defines the interface on the macroscale. This multiscale technique overcomes the difficulty of stiffness of common problems in combustion processes. Numerical results for Majda’s model and reactive Euler equations in one and two dimensions show substantially improved efficiency over traditional methods.