A new finite-volume-based finite-element method using the quadratic elements is developed in the present study, to analyze the flow in micro and nano sizes with higher-order slip boundary conditions. The method is applied to gaseous flow in micro and nanoscale-channels. The developed method is carried out over a wide range of Knudsen numbers, which cover not only the continuum slip flow regime with 0≤Kn≤0.1 but also it entire the range of transient regime with 0.1<Kn≤10. To make the present computational model capable of simulating micro and nano sizes with the help of the Navier-Stokes equations, the modified high-order slip boundary conditions are applied which need utilizing the advantages of general quadratic second order elements in the computational domain. In other words, this paper introduces a new developed method, which is applied on higher-order elements, and employing reliable boundary conditions that all of these issues are used for the first time in the Micro/Nano study as well. The results reveal excellent agreement with those represented by analytical, DSMC, and Boltzmann calculations. The proposed method (using finite-volume-element strategy which benefits from the advantages of general quadratic second-order elements) is proved to be an efficient, practical, and accurate tool, which robustly extends the capability of our primitive large scale Navier-Stokes solver to micro and nano-scale flow predictions in slip and transient regimes. It can be regarded as a super alternative to classical molecular dynamics-based methods.
- Nanotechnology Institute
Computation of Rarefied Gaseous Flows in Micro to Nano Scale Channels With Slip to Transient Regimes Using General Second-Order Quadratic Elements
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Darbandi, M, & Daghighi, Y. "Computation of Rarefied Gaseous Flows in Micro to Nano Scale Channels With Slip to Transient Regimes Using General Second-Order Quadratic Elements." Proceedings of the ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. Darmstadt, Germany. June 23–25, 2008. pp. 55-64. ASME. https://doi.org/10.1115/ICNMM2008-62155
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