Open AccessA node-numbering-invariant directional length scale for simplex elements
Author(s) -
Kenji Takizawa,
Yuki Ueda,
Tayfun E. Tezduyar
Publication year - 2019
Publication title -
mathematical models and methods in applied sciences/mathematical models and methods in applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.582
H-Index - 85
eISSN - 1793-4060
pISSN - 0218-2025
DOI - 10.1142/s0218202519500581
Subject(s) - numbering , simplex , computation , scale invariance , scale (ratio) , length scale , context (archaeology) , node (physics) , element (criminal law) , mathematics , computer science , algorithm , mathematical analysis , geometry , physics , mechanics , statistics , acoustics , quantum mechanics , paleontology , political science , law , biology
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.