A finite element method for high Reynolds number viscous fluid flow using two step explicit scheme

1983 ◽  
Vol 3 (2) ◽  
pp. 137-163 ◽  
Author(s):  
Mutsuto Kawahara ◽  
Hirokazu Hirano
Keyword(s):  
Finite Element Method ◽  
Reynolds Number ◽  
Finite Element ◽  
Fluid Flow ◽  
Viscous Fluid ◽  
High Reynolds Number ◽  
Explicit Scheme ◽  
Viscous Fluid Flow ◽  
High Reynolds ◽  
Element Method

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

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 5 ◽  
Author(s):  
Bilen Emek Abali
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
General Procedure ◽  
Computational Cost ◽  
Viscous Fluid Flow ◽  
Closed Form Solutions ◽  
Element Method

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.

Immersed Methods for High Reynolds Number Fluid-Structure Interactions

2017 ◽  
Vol 14 (06) ◽  
pp. 1750068 ◽  
Author(s):  
Lucy T. Zhang
Keyword(s):  
Finite Element Method ◽  
Reynolds Number ◽  
Finite Element ◽  
High Reynolds Number ◽  
Fluid Structure Interactions ◽  
Immersed Finite Element Method ◽  
Immersed Finite Element ◽  
High Reynolds ◽  
Immersed Methods ◽  
Reynolds Number Flows

Immersed methods are considered as a class of nonboundary-fitted meshing technique for simulating fluid–structure interactions. However, the conventional approach of coupling the fluid and solid domains, as in the immersed boundary method and the immersed finite element method, often cannot handle high Reynolds number flows interacting with moving and deformable solids. As the solid dynamics is imposed by the fluid dynamics, it often leads to unrealistically large deformation of the solid in cases of high Reynolds number flows. The first attempt in resolving this issue was proposed in the modified immersed finite element method (mIFEM), however, some terms were determined heuristically. In this paper, we provide a full and rigorous derivation for the mIFEM with corrections to the previously proposed terms, which further extends the accuracy of the algorithm. In the “swapped” coupling logic, we solve for the dynamics of the solid, and then numerically impose it to the background fluid, which allows the solid to control its own dynamics and governing laws instead of following that of the fluid. A few examples including a biomedical engineering application are shown to demonstrate the capability in handling large Reynolds number flows using the derived mIFEM.

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