Abstract
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.
Highlights
In this paper, we introduce a node-numbering-invariant directional length scale for simplex elements used in flow computations with the stabilized and variational multiscale (VMS) methods, discontinuity-capturing (DC) methods, and other special methods that require a directional element length.1.1
Stabilized and VMS methods are widely used in flow computations
We have introduced a directional element length expression meeting that requirement
Summary
We introduce a node-numbering-invariant directional length scale for simplex elements used in flow computations with the stabilized and variational multiscale (VMS) methods, discontinuity-capturing (DC) methods, and other special methods that require a directional element length
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More From: Mathematical Models and Methods in Applied Sciences
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