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施我最近提出的一种新的模拟技术，用于实际的气体流动预测。与经典的流体力学处理方法相比，我的新模型在物理上更准确，在计算上也更容易求解。它允许准确和负担得起的气体流动行为的预测，这是以前不可能的，并承诺为许多传统的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，包括运输和发电技术的设计。这对许多新兴技术领域也很重要，例如，微型传感器和其他微型机电系统等微型设备内的流动很难用目前的方法来描述。作为该项目的一部分开发的技术将增加关于气体基本行为的科学知识，并将为预测传统和新兴气体流动应用中的真实世界气体流动提供改进的技术和软件。**传统上，工程气体流动应用是使用纳维尔-斯托克斯方程建模的。该模型忽略了气体基于颗粒的结构的细节，因为它假设气体存在于非常小的物理尺度上，并且不是描述宏观流动行为所必需的。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方程并不是物理上准确的描述。这些包括微尺度气流、稀薄气流、高速气流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来建模。**最近，我提出了一个新的气体流量预测模型，该模型可以用来取代传统情况下的Navier-Stokes方程，同时对于需要了解颗粒行为的气体流动问题的解决既准确又有效。不是试图模拟单个粒子，而是只对气体粒子的重要统计特性的演化进行建模。我的模型也被设计成具有数学特征，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尤其如此，因为在现实世界的工程应用中经常需要这样做。**本项目由两个主要推力组成。首先是对我的模型的进一步发展和完善。尽管我已经证明，我的模型在非传统流动情况下的流动预测方面有了显著的改进，例如微型机电系统微管道中的流动和高马赫数冲击波的内部结构，但仍有必要对该模型进行最后的改进。物理改进包括开发更精确的气固界面边界处理和改进的气固碰撞过程模型。**该项目的第二个主要推力是在现代开源高性能流动解算器中实施我的新模型。为了展示我的新技术在现实世界实际工程问题中的优势，它必须在如此大规模的流动解算器中实现。控制我的模型的方程的数学结构是这样一种形式，标准的、强大的和精确的数值方法可以很容易地应用。该解算器将允许高效和准确地解决流动问题，这是以前不可能的。

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.