Computational Cardiovascular Analysis with the Variational Multiscale Methods and Isogeometric Discretization

2020 ◽  
pp. 151-193 ◽  
Author(s):  
Thomas J. R. Hughes ◽  
Kenji Takizawa ◽  
Yuri Bazilevs ◽  
Tayfun E. Tezduyar ◽  
Ming-Chen Hsu
Keyword(s):  
Multiscale Methods ◽  
Variational Multiscale ◽  
Isogeometric Discretization ◽  
Variational Multiscale Methods

scholarly journals A node-numbering-invariant directional length scale for simplex elements

2019 ◽  
Vol 29 (14) ◽  
pp. 2719-2753 ◽  
Author(s):  
Kenji Takizawa ◽  
Yuki Ueda ◽  
Tayfun E. Tezduyar
Keyword(s):  
Significant Role ◽  
Multiscale Methods ◽  
Length Scale ◽  
Length Scales ◽  
Variational Multiscale ◽  
The Past ◽  
Stabilized Methods ◽  
Variational Multiscale Methods ◽  
Solution Gradient

Variational multiscale methods, and their precursors, stabilized methods, have been very popular in flow computations in the past several decades. Stabilization parameters embedded in most of these methods play a significant role. The parameters almost always involve element length scales, most of the time in specific directions, such as the direction of the flow or solution gradient. We require the length scales, including the directional length scales, to have node-numbering invariance for all element types, including simplex elements. We propose a length scale expression meeting that requirement. We analytically evaluate the expression in the context of simplex elements and compared to one of the most widely used length scale expressions and show the levels of noninvariance avoided.

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