Modeling and Simulation of Non-equilibrium Flows with Uncertainty Quantification

TL;DR

This paper investigates the stochastic behavior of non-equilibrium gas flows across multiple scales, introducing a new kinetic scheme to analyze how uncertainties propagate and influence flow dynamics from molecular to continuum levels.

Contribution

It develops a stochastic kinetic scheme and theoretical framework for analyzing uncertainty propagation in non-equilibrium gas flows across multiple scales.

Findings

Uncertainty propagation patterns between mean fields and fluctuations.

Sensitivity of flow features to different uncertainty orders.

Boundary effects influence from continuum to rarefied regimes.

Abstract

In the study of gas dynamics, theoretical modeling and numerical simulation are mostly set up with deterministic settings. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between flow-field solutions and real-world physics. To study the emergence, propagation and evolution of uncertainties from molecular to hydrodynamic level poses great opportunities and challenges to develop both sound theories and reliable multi-scale algorithms. In this paper, we study the stochastic behavior of multi-scale gas dynamic systems, especially focusing on the non-equilibrium effects. The theoretical analysis is presented on the basis of kinetic model equation and its upscaling macroscopic system, with the reformulation from the stochastic Galerkin method. A newly developed stochastic kinetic scheme is employed to conduct numerical simulation of homogeneous relaxation, normal shock structure, shear layer and lid-driven cavity problems. Different kinds of uncertainties are involved in conjunction with the gas evolutionary processes. New physical observations, such as the synergistic propagation pattern between mean fields and uncertainties, sensitivity of different orders of uncertainties, and the influence of boundary effects from continuum to rarefied regimes, will be identified and analyzed theoretically. The paper serves as a heuristic study of quantifying the uncertainties within multi-scale flow dynamics.