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An Accurate Finite Element Method for the Numerical Solution of Isothermal and Incompressible Flow of Viscous Fluid

Institute of Mechanics, Technische Universität Berlin, 10587 Berlin, Germany
Received: 24 October 2018 / Revised: 18 December 2018 / Accepted: 3 January 2019 / Published: 8 January 2019
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Abstract

Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms—allowing a robust and accurate simulation for any process—are still missing. Either a very high computational cost is necessary for a direct numerical solution (DNS) or some limiting procedure is used by adding artificial dissipation to the system. These stabilization methods are useful; however, they are often applied relative to the element size such that a local monotonous convergence is challenging to acquire. We need a computational strategy for solving viscous fluid flow using solely the balance equations. In this work, we present a general procedure solving fluid mechanics problems without use of any stabilization or splitting schemes. Hence, its generalization to multiphysics applications is straightforward. We discuss emerging numerical problems and present the methodology rigorously. Implementation is achieved by using open-source packages and the accuracy as well as the robustness is demonstrated by comparing results to the closed-form solutions and also by solving well-known benchmarking problems. View Full-Text
Keywords: finite element method; fluid dynamics; computation; viscous fluid flow finite element method; fluid dynamics; computation; viscous fluid flow
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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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Abali, B.E. An Accurate Finite Element Method for the Numerical Solution of Isothermal and Incompressible Flow of Viscous Fluid. Fluids 2019, 4, 5.

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