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

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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.