Efficient Simulation of Nonlinear Flows in Rarefied Gases

稀薄气体中非线性流动的有效模拟

• 批准号: 248330224
• 负责人: Professor Dr. Manuel Torrilhon
• 金额: --
• 依托单位: Center for Computational Engineering Science - Mathematics Division (MathCCES)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/248330224?language=en
• 关键词: Efficient; Simulation; Nonlinear; Flows; Rarefied

The computation of gas flows is typically based on the Navier-Stokes equations for the velocity field combined with the energy balance and Fourier's law if the temperature field is of interest. However, these classical models are valid only for flows close to thermal equilibrium. For situations in rarefied gases or in microscopic settings the Navier-Stokes-Fourier system (NSF) is known to produce physically wrong results, so that they can not be used in these cases. Over the past years new continuum models have been developed on the bases of moment equations of the Boltzmann equation which extend the range of applicability of conventional fluid dynamics. One of these models is the Regularized 13-Moment system (R13) which forms a set of partial differential equations for density, velocity and temperature, as well as stress tensor and heat flux. In an earlier DFG project the R13 system has been successfully developed to a mature simulation tool for slow rarefied gas systems, like in microscopic settings.However, one of the main drawbacks of classical moment equations like the R13 system is the restriction to small perturbation like in slow, low Mach number processes. The mathematical reason can be found in the expansion technique used to approximate the velocity distribution function of the gas particles. The current project explores new ways to extend the use of moment equations to strongly nonlinear processes, exhibiting strong variations in velocity and temperature, like shock waves in hypersonics. During the project we will combine two modern approaches to reconstruct a distribution from moments: maximum likelihood/entropy estimation from statistics and the quadrature method of moments, introduced in multi-phase/multi-disperse flows. A successful and efficient reconstruction will allow to handle boundary conditions and to implement a numerical method easily. One application-inspired test case will consider flow impingement of satellite thrusters.

气流的计算通常基于速度场的Navier-Stokes方程，如果对温度场感兴趣，则结合能量平衡和傅立叶定律。然而，这些经典模型仅对接近热平衡的流动有效。对于稀薄气体或微观环境中的情况，已知Navier-Stokes-Fourier系统（NSF）会产生物理错误的结果，因此它们不能用于这些情况。在过去的几年中，新的连续介质模型已经发展的基础上的矩方程的玻尔兹曼方程，扩大了适用范围的传统流体动力学。这些模型之一是正则13矩系统（R13），它形成了一组密度，速度和温度的偏微分方程，以及应力张量和热通量。在早期的DFG项目中，R13系统已经成功地发展成为一个成熟的模拟工具，用于缓慢稀薄气体系统，如在微观环境中，然而，经典的矩方程，如R13系统的主要缺点之一是限制小扰动，如在缓慢，低马赫数过程。数学上的原因可以在用于近似气体粒子的速度分布函数的展开技术中找到。目前的项目探索了新的方法，将力矩方程的使用扩展到强非线性过程，表现出速度和温度的强烈变化，如高超音速中的冲击波。在项目过程中，我们将联合收割机结合两种现代方法来重建矩分布：统计学中的最大似然/熵估计和多相/多分散流中引入的矩量法。一个成功的和有效的重建将允许处理边界条件，并容易实现的数值方法。一个应用启发的测试案例将考虑卫星推进器的气流冲击。