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Aerospace 2018, 5(1), 16; https://doi.org/10.3390/aerospace5010016

Discontinuous Galerkin Finite Element Investigation on the Fully-Compressible Navier–Stokes Equations for Microscale Shock-Channels

Centre for Computational Engineering Sciences, Cranfield University, Cranfield, Bedfordshire MK43 0AL, UK
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Received: 24 November 2017 / Revised: 10 January 2018 / Accepted: 30 January 2018 / Published: 3 February 2018
(This article belongs to the Special Issue Computational Aerodynamic Modeling of Aerospace Vehicles)
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Abstract

Microfluidics is a multidisciplinary area founding applications in several fields such as the aerospace industry. Microelectromechanical systems (MEMS) are mainly adopted for flow control, micropower generation and for life support and environmental control for space applications. Microflows are modeled relying on both a continuum and molecular approach. In this paper, the compressible Navier–Stokes (CNS) equations have been adopted to solve a two-dimensional unsteady flow for a viscous micro shock-channel problem. In microflows context, as for the most gas dynamics applications, the CNS equations are usually discretized in space using finite volume method (FVM). In the present paper, the PDEs are discretized with the nodal discontinuous Galerkin finite element method (DG–FEM) in order to understand how the method performs at microscale level for compressible flows. Validation is performed through a benchmark test problem for microscale applications. The error norms, order of accuracy and computational cost are investigated in a grid refinement study, showing a good agreement and increasing accuracy with reference data as the mesh is refined. The effects of different explicit Runge–Kutta schemes and of different time step sizes have also been studied. We found that the choice of the temporal scheme does not really affect the accuracy of the numerical results. View Full-Text
Keywords: computational fluid dynamics (CFD); microfluidics; numerical methods; gasdynamics; shock-channel; microelectromechanical systems (MEMS); discontinuous Galerkin finite element method (DG–FEM); fluid mechanics computational fluid dynamics (CFD); microfluidics; numerical methods; gasdynamics; shock-channel; microelectromechanical systems (MEMS); discontinuous Galerkin finite element method (DG–FEM); fluid mechanics
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Zingaro, A.; Könözsy, L. Discontinuous Galerkin Finite Element Investigation on the Fully-Compressible Navier–Stokes Equations for Microscale Shock-Channels. Aerospace 2018, 5, 16.

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