Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 29, Issue 14, Pages 2719-2753Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202519500581
Keywords
Stabilization parameter; simplex element; directional element length; node-numbering; invariance
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Funding
- Rice-Waseda research agreement
- ARO [W911NF-17-1-0046]
- Top Global University Project of Waseda University
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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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