Model Adaptation for Hyperbolic Systems with Relaxation

In numerous applications, a hierarchy of models is available to describe the phenomenon under consideration. We focus in this work on general hyperbolic systems with stiff relaxation source terms together with the corresponding hyperbolic equilibrium systems. The goal is to determine the regions of the computational domain where the relaxation model (so-called fine model) can be replaced by the equilibrium model (so-called coarse model), in order to simplify the computation while keeping the global numerical accuracy. With this goal in mind, a numerical indicator which measures the difference between the solutions of both models is developed, using a numerical Chapman-Enskog expansion. The reliability of the adaptation procedure is assessed on various test cases coming from two-phase flow modeling. Key-words. Hyperbolic system, finite volume methods, relaxation, model adaptation, Chapman-Enskog expansion, two-phase flows. Mathematics Subject Classification. 35L45, 65M08, 65M55, 35C20, 76T10