Finite scale theory: Predicting nature’s shocks

In this paper, we describe a continuum model that accurately reproduces the experimentally measured structure of physical shocks in a perfect gas. We begin by presenting a history of shock structure research, theoretical, experimental and numerical, to quantify the significant discrepancies between Navier–Stokes predictions and laboratory measurements. In our first main result, we discuss modifications that generalize the Chapman–Enskog approximation and lead to a new continuum model termed the Finite Scale Equations. In our second main result, we use this continuum model to calculate shock structure with results comparable in accuracy to numerical simulations based on the Boltzmann equation.