Tr21SUPG element

Implementation of P2P1 Taylor Hood element for transient incompressible flow analysis using SUPG and LSIC stabilization. It consists of globally continuous, piecewise quadratic functions for approximation in velocity space and globally continuous, piecewise linear functions for approximation in pressure space. LBB condition is satisfied. There are 3 degrees of freedom in vertices (two components of velocity and pressure), and 2 degrees of freedom in edge nodes (two components of velocity only). The node numbering is anti-clockwise, vertices are numbered first.

**Figure 21:** Tr21SUPG element - node and side numbering.
$\includegraphics[width=0.7\textwidth]{qtrplanstrss.eps}$ elemnode = [draw,circle,inner sep=1,fill=white] $\begin{tikzpicture}[scale=6,>=stealth] \draw[->] (-0.05,0) - (0.8,0) node[abov... ...ode[elemnode,midway] {} node[above left,midway] {6} (0.2,0.1); \end{tikzpicture}$

Keyword: Tr21SUPG
Parameters:

Unknowns: Two velocity components (V_u and V_v) and pressure (P_f) in vertices and two velocity components (V_u and V_v) in edge nodes are required.

Approximation: Quadratic approximation of velocity and linear approximation of pressure fields.

Integration: Integration is exact, each submatrix of element stiffness matrix is evaluated in proper number of Gauss points. Submatrices connected with velocity are evaluated in 7 or 13 points, mixed velocity-pressure submatrices in 3 or 7 points, submatrices connected with pressure in 3 points.

Loads: Constant boundary tractions are supported. Body loads representing the self-weight load are supported.

Multi-fluid analysis: The element has no support for solving problems with two immiscible fluids in a fixed spatial domain.

Borek Patzak 2011-12-29