An Investigation of Uncertainty Propagation in Non-equilibrium Flows

Abstract

ABSTRACT Considerable uncertainties can exist between the field solutions of coarse-grained fluid models and the real-world flow physics. To study the emergence, propagation, and evolution of uncertainties poses great opportunities and challenges to develop both sound theories and reliable numerical methods. In this paper, we study the stochastic behaviour of multi-scale gaseous flows from molecular to hydrodynamic level, especially focussing on the non-equilibrium effects. The theoretical analysis is presented based on the gas kinetic model and its upscaling macroscopic system with random inputs. A newly developed stochastic kinetic scheme is employed to conduct numerical simulation of multi-scale and non-equilibrium flows. Different kinds of uncertainties are involved in the gas evolutionary processes. New physical observations, such as the synchronous travel pattern between mean fields and uncertainties, sensitivity of different orders of uncertainties and the influence of boundary effects from continuum to rarefied regimes, are identified and analysed.