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Abstract
Fundamental solutions (Green’s functions) to Grad’s steady-state linearised 13-moment equations for non-equilibrium gas flows are derived. The creeping microscale gas flows, to which they pertain, are important to understanding the behaviour of atmospheric particulate and the performance of many potential micro/nano technologies. Fundamental solutions are also derived for the regularised form of the steady-state linearised 13-moment equations, due to Struchtrup & Torrilhon (Phys. Fluids, vol. 15 (9), 2003, pp. 2668–2680). The solutions are compared to their classical and ubiquitous counterpart: the Stokeslet. For an illustration of their utility, the fundamental solutions to Grad’s equations are implemented in a linear superposition approach to modelling external flows. Such schemes are mesh free, and benefit from not having to truncate and discretise an infinite three-dimensional domain. The high accuracy of the technique is demonstrated for creeping non-equilibrium gas flow around a sphere, for which an analytical solution exists for comparison. Finally, to demonstrate the method’s geometrical flexibility, the flow generated between adjacent spheres held at a fixed uniform temperature difference is explored.
Highlights
Simulating low-speed dilute gas flow around microscale particulates has a raft of potential applications: in health, in security and in atmospheric science
Flows falling in between these approximate limits (0.01 Kn 1) are described as being in the transition regime, and present a major simulation challenge: being beyond the physical model of classical fluid dynamics, but inaccessible to the accurate techniques developed from kinetic theory
In the most straightforward use, a flow field is represented by a superposition of Stokeslets that are given a combination of strengths chosen to satisfy the same number of conditions at nodes on the boundary. This approach is known as the method of fundamental solutions (MFS) or the superposition method, amongst other names
Summary
Simulating low-speed dilute gas flow around microscale particulates has a raft of potential applications: in health (e.g. modelling inhalation of fine particulate), in security (e.g. predicting the transport of bacteria-laden aerosolized droplets) and in atmospheric science (e.g. understanding the climatic impact of volcanic ash). In the most straightforward use, a flow field is represented by a superposition of Stokeslets (positioned, say, inside a particle) that are given a combination of strengths chosen to satisfy the same number of conditions at nodes on the boundary This approach is known as the method of fundamental solutions (MFS) or the superposition method, amongst other names This is a convenient feature of MFS for external flows
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