Conservative and Accurate Solution Transfer Between High-Order and Low-Order Refined Finite Element Spaces

Abstract One-dimensional fully developed channel flow was solved using a modified k–ω turbulence model that was recently proposed for use with high-order finite element schemes. In order to study this new turbulence model’s behavior, determine its dependence on boundary conditions and model constants, and find efficient methods for obtaining solutions, the model was first examined using a linear finite element discretization in 1D. The results showed that an accurate estimate of the parameter εk which is used to define k in terms of the working variable k~ is essential to get an accurate solution. Also, the turbulence model depended sensitively on an accurate estimate of the distance of the first grid point from the wall, which can be difficult to estimate in unstructured grids. This is used for the boundary condition of specific dissipation rate on the wall. This model was then implemented in a high-order finite element code that uses an unstructured mesh of triangles to verify that the 1D results were predictive of the behavior of the full 2D discretization. High-order 2D results were obtained on triangular meshes with element aspect ratios up to 250000.

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Hybrid Reduced Model of Rotor

Archive of Mechanical Engineering ◽

10.2478/meceng-2013-0021 ◽

2013 ◽

Vol 60 (3) ◽

pp. 319-333

Author(s):

Rafał Hein ◽

Cezary Orlikowski

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Hybrid Model ◽

Rotor System ◽

Reduced Model ◽

Order Model ◽

Gyroscopic Effect ◽

Reduced Models ◽

Rigid Finite Element Method ◽

Low Order

Abstract In the paper, the authors describe the method of reduction of a model of rotor system. The proposed approach makes it possible to obtain a low order model including e.g. non-proportional damping or the gyroscopic effect. This method is illustrated using an example of a rotor system. First, a model of the system is built without gyroscopic and damping effects by using the rigid finite element method. Next, this model is reduced. Finally, two identical, low order, reduced models in two perpendicular planes are coupled together by means of gyroscopic and damping interaction to form one model of the system. Thus a hybrid model is obtained. The advantage of the presented method is that the number of gyroscopic and damping interactions does not affect the model range

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High-Order Finite Element Methods for Singularly-Perturbed Elliptic and Parabolic Problems.

10.21236/ada290410 ◽

1993 ◽

Author(s):

Slimane Adjerid ◽

Mohammed Aiffa ◽

Joseph E. Flaherty

Keyword(s):

Finite Element ◽

Finite Element Methods ◽

High Order ◽

Singularly Perturbed ◽

Parabolic Problems

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A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

Computational Methods in Applied Mathematics ◽

10.1515/cmam-2019-0089 ◽

2020 ◽

Vol 20 (4) ◽

pp. 799-813

Author(s):

Joël Chaskalovic ◽

Franck Assous

Keyword(s):

Finite Element ◽

Finite Elements ◽

Asymptotic Relation ◽

Probabilistic Approach ◽

Random Variable ◽

High Order ◽

Relative Accuracy ◽

The Difference ◽

New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

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