具有不确定性量化的非平衡流建模与仿真
Modeling and Simulation of Non-equilibrium Flows with Uncertainty Quantification
摘要：
在气体动力学的研究中，理论建模和数值模拟大多建立在确定性的设置上。考虑到流体理论中的粗粒度建模，流场解与真实世界物理之间可能存在相当大的不确定性。从分子水平到流体动力学水平研究不确定性的产生、传播和演化，为发展合理的理论和可靠的多尺度算法带来了巨大的机遇和挑战。本文研究了多尺度气体动力学系统的随机行为，特别是非平衡效应。基于动力学模型方程及其升尺度宏观系统，采用随机Galerkin方法进行了理论分析。采用一种新的随机动力学格式对均匀松弛、正激波结构、剪切层和盖驱动空腔问题进行了数值模拟。不同种类的不确定性与气体演化过程有关。新的物理观测，如平均场和不确定性之间的协同传播模式，不同阶数的不确定性的敏感性，以及从连续到稀薄区域的边界效应的影响，将被识别和理论分析。本文作为一个启发式的研究量化的不确定性在多尺度流动动力学。
英文摘要：
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.
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