Multiscale Simulation of Rarefied Gas Flow for Engineering Design

Microprocessors chips are in most devices we interact with in our daily lives. From mobile devices, TVs, cars, fridges, petrol station pumps, servers that power the web and social media infrastructure --- the list is endless. Microprocessors have been doubling in power roughly every two years following Moore's law, which has been enabled by making the features of the chips smaller, fitting more transistors per unit area and driving the entire consumer electronics market worth more than £1 trillion per year. In order to continue to satisfy the industrial and societal demand that drives Moore's law, there are some fluid dynamics modelling challenges that we need to overcome.

The next-generation of photolithography machines that need to manufacture smaller, faster microprocessor chips and the new devices required to supercool the high-performance chips during operation can be enabled by understanding and predicting accurately how gases behave at the micro/nanoscales, or in vacuum-like conditions. In these multiscale flow problems, the fluid dynamics is often unintuitive and all equations we normally turn to for modelling and designing engineering flow problems, such as flow around aircraft and ships using Navier-Stokes equations, are no longer valid here, because the gas is no longer in local thermodynamic equilibrium, on which these classical equations are formulated.

The direct simulation Monte Carlo (DSMC), is the state-of-the-art software for modelling these non-equilibrium gas flows. It is a stochastic particle method with large numerical stability and can resolve the molecular nature of gases in three dimensional geometries. However, because it is a particle method, it requires a voracious computational cost to produce engineering solutions of scales that matter to industry. DSMC also performs poorly if those flows are at low speed, due to the inherent thermal noise in the particles blocking the measurable signals.

In this project, we propose developing a new multiscale method, one which combines DSMC with computationally cheaper models such as those used in Computational Fluid Dynamics (CFD). We will produce a step change in simulation efficiency and accuracy by connecting DSMC and CFD solvers using surrogate modelling and Bayesian inference.

With strong backing from our industrial partners, we will turn the outcome of this project into a free open-source computational solver released in the UK's OpenFOAM software that is validated with experimental data. The industrial focus of this project will be on processor-chip manufacturing, chip thermal management and electrospray technologies, but the underlying method is general to new directions in other research and industrial areas.