First-order models for viscous heat-conducting gas-flow predictions both in and out of local equilibrium

这项研究计划的目标是进一步发展和数值实现一种新的建模技术，我最近提出了实际的气体流动预测。我的新模型在物理上更精确，在计算上比经典的流体动力学处理更容易求解。它允许在以前不可能实现的情况下准确和负担得起的气体流动行为预测，并为许多传统工程情况提供更有效的数值解决方案。气体流动的精确建模是许多工程领域不可或缺的一部分，包括交通和发电技术的设计。这对许多新兴技术领域也很重要，例如，微传感器和其他微机电系统等微尺度设备内的流动难以用现有方法描述。作为该项目的一部分，开发的技术将增加有关气体基本行为的科学知识，并将为传统和新兴气体流动应用中的实际气体流动预测提供改进的技术和软件。**传统上，工程气体流动应用已使用Navier-Stokes方程建模。该模型忽略了有关气体颗粒结构的细节，假设它们存在于非常小的物理尺度上，并且没有必要描述宏观流动行为。在许多传统情况下，它是一个精确的模型，然而，在实际应用中，Navier-Stokes方程并不是一个物理上准确的描述。这些包括微尺度气体流动、稀薄流动、高速流动和非平衡电离等离子体。目前，这些情况必须使用计算昂贵的基于粒子的方法进行建模。**最近，我提出了一种新的气体流动预测模型，可以用来替代传统情况下的Navier-Stokes方程，同时在解决需要一些粒子行为知识的气体流动问题时保持准确和有效。而不是试图模拟单个粒子，只模拟气体粒子的重要统计特性的演变。我的模型也被设计成这样，它具有数学特征，使准确和健壮的数值解更容易获得。这对于复杂的流动几何形状来说尤其如此，因为在现实世界的工程应用中经常需要这样做。这个项目由两个主要部分组成。首先是我的模型的进一步发展和完善。虽然我已经表明，我的模型在非常规流动情况下的流动预测方面有了显著的改进，例如微机电系统的微管道中的流动和高马赫数激波的内部结构，但仍有必要对模型进行最后的改进。物理上的改进包括对气固界面进行更精确的边界处理和改进气-颗粒碰撞过程的建模。**这个项目的第二个主要推力是在现代开源高性能流求解器中实现我的新模型。为了证明我的新技术在现实世界实际工程问题中的优势，必须在这样一个大规模的流动求解器中实现。控制我的模型的方程的数学结构是这样一种形式，可以很容易地应用标准的、强大的和精确的数值方法。这个求解器将允许有效和准确地解决以前不可能的流动问题。

The goal of this research program is the further development and numerical implementation of a new modelling technique that I have recently proposed for practical gas-flow predictions. My novel model is more physically accurate and computationally easier to solve than classical fluid-dynamic treatments. It allows for the accurate and affordable prediction of gas-flow behaviour in regimes that were not possible previously and promises more efficient numerical solution for many traditional engineering situations. Accurate modelling of gas flows is an integral part of many engineering fields, including the design of transportation and power-generation technologies. It is also important for many emerging areas of technology, for example, flows within micro-scale devices such as micro sensors and other micro-electromechanical systems are difficult to describe using current methods. The techniques developed as part of this project will increase scientific knowledge regarding the fundamental behaviour of gases and will provide improved techniques and software for the prediction of real-world gas flows in both traditional and emerging gas-flow applications.**Traditionally, engineering gas-flow applications have been modelled using the Navier-Stokes equations. This model ignores the details regarding the particle-based structure of gases by assuming that they exist at very small physical scales and are not necessary to describe macroscopic flow behaviour. It is an accurate model in many traditional situations, however, there are practical applications for which the Navier-Stokes equations are not a physically accurate description. These include micro-scale gas flows, rarefied flows, high-speed flows, and non-equilibrium ionized plasmas. Currently, these situations must be modelled using computationally expensive particle-based methods.**Recently I proposed a new model for gas-flow prediction that can be used as a replacement for the Navier-Stokes equations in traditional situations, while remaining both accurate and efficient for the solution of gas-flow problems in which some knowledge of the particle behaviour is necessary. Rather than attempting to simulate individual particles, only the evolution of important statistical properties of the gas particles are modelled. My model has also been designed such that it has mathematical features that make accurate and robust numerical solutions easier to obtain. This is especially true for complicated flow geometries, as are often needed in real-world engineering applications.**This project consists of two main thrusts. The first is the further development and refinement of my model. Though I have shown that my model gives a marked improvement in flow predictions in unconventional flow situations, such as flows in the micro conduits of micro-electromechanical systems and the internal structure of high-mach-number shock waves, there remains final refinements to the model that are necessary. Physical refinements include the development of a more accurate boundary treatment for gas-solid interfaces and improved modelling of gas-particle collisional processes.**The second major thrust of this project is the implementation of my new model in a modern open-source high-performance flow solver. In order to demonstrate my new technique's advantages for real-world practical engineering problems, it must be implemented in such a large-scale flow solver. The mathematical structure of the equations governing my model are of such a form that standard powerful and accurate numerical methods can be easily applied. This solver will allow for the efficient and accurate solution of flow problems that were not previously possible.