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的一种新的建模技术，我最近提出的实际气体流量预测。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解决。它允许准确和负担得起的预测的气体流动行为的制度，以前是不可能的，并承诺更有效的数值解决方案，许多传统的工程情况。气体流动的精确建模是许多工程领域的一个组成部分，包括运输和发电技术的设计。它对于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使用当前方法描述。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流应用中的实际气流预测提供改进的技术和软件。传统上，工程气流应用已使用Navier-Stokes方程建模。该模型忽略了关于气体的基于颗粒的结构的细节，假设它们存在于非常小的物理尺度上，并且不需要描述宏观流动行为。在许多传统的情况下，它是一个精确的模型，然而，有实际应用中的Navier-Stokes方程是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，这些情况下，必须使用计算昂贵的粒子为基础的方法建模。最近，我提出了一个新的模型，可以用来作为一个替代的Navier-Stokes方程在传统的情况下，气体流量预测，同时保持准确和有效的解决方案的气体流量问题，其中一些知识的颗粒的行为是必要的。而不是试图模拟单个粒子，只有气体粒子的重要统计特性的演变建模。我的模型也被设计成具有数学特征，使得更容易获得精确和鲁棒的数值解。这对于复杂的流动几何形状尤其如此，因为在实际工程应用中经常需要。第一个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，如微机电系统的微管道中的流动和高马赫数冲击波的内部结构中的流动预测有显着的改善，仍然有必要对模型进行最后的改进。物理上的改进包括开发更精确的气固界面边界处理和改进气粒碰撞过程的建模。该项目的第二个主要目标是在现代开源高性能流场求解器中实现我的新模型。为了证明我的新技术的优势，为现实世界的实际工程问题，它必须实现在这样一个大规模的流动求解器。控制我的模型的方程的数学结构是这样一种形式，标准的强大和准确的数值方法可以很容易地应用。该求解器将允许以前不可能的流动问题的有效和准确的解决方案。

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.