2D SUPG/PSGP Elements

2D SUPG/PSGP Elements

Tr1SUPG element

Represents the linear triangular finite element for transient incompressible flow analysis using SUPG/PSPG stabilization with equal order approximation of velocity and pressure fields. Each node has 3 degrees of freedoms (two components of velocity and pressure). The node numbering is anti-clockwise. The element features are summarized in Table 65.

Fig. 28 Tr1SUPG element. Node numbering, Side numbering and definition of local edge c.s.(a).

Table 65 Tr1SUPG element summary

Keyword	Tr1SUPG
Description	linear triangular finite element for transient incompressible flow analysis using SUPG/PSPG algorithm
Specific parameters	[vof (rn)] [pvof (rn)]
Unknowns	Two velocity components (V_u and V_v) and pressure (P_f) are required in each node.
Approximation	Linear approximation of velocity and pressure fields.
Integration	exact
Loads	Constant boundary tractions are supported. Body loads representing the self-weight load are supported.
Multi-fluid analysis	The element has support for solving problems with two immiscible fluids in a fixed spatial domain. In the present implementation, a VOF and LevelSet tracking algorithms are used to track the position of interface. In case of VOF tracking, an initial VOF fraction (volume fraction of reference fluid) can be specified using vof (default is zero). Element can also be marked as allways filled with reference fluid (some form of source) using parameter pvof which specifies the permanent VOF value. In case of LevelSet tracking, the initial levelset is specified using reference polygon (see corresponding levelset record in oofem input manual). The material model should be of type Keyword: twofluidmat, that supports modelling of two immiscible fluids.
Status	Reliable
Tests/Examples	fm/scctest01.in

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. The element features are summarized in Table 66.

Fig. 29 Tr21SUPG element - node and side numbering.

Table 66 Tr21SUPG element summary

Keyword	Tr21SUPG
Description	P2P1 Taylor Hood element
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.
Status	Reliable

Tr1SUPGAxi element

Represents the linear triangular finite element for transient incompressible flow analysis using SUPG/PSPG stabilization with equal order approximation of velocity and pressure fields in 2d-axisymmetric setting. Each node has 3 degrees of freedoms (two components of velocity and pressure). The y-axis is axis of ratational symmetry. The node numbering is anti-clockwise. The element features are summarized in Table Table 67.

Fig. 30 Tr1SUPGAxi element. Node numbering, Side numbering and definition of local edge c.s.(a).

Table 67 Tr1SUPGAxi element summary

Keyword	Tr1SUPGAxi
Description	linear equal order approximation axisymmetric element
Specific parameters	[vof (rn)][pvof (rn)]
Unknowns	Two velocity components (V_u and V_v) and pressure (P_f) are required in each node.
Approximation	Linear approximation of velocity and pressure fields.
Integration	Gauss integration in seven point employed.
Loads	Constant boundary tractions are supported. Body loads representing the self-weight load are supported.
Multi-fluid analysis	The element has support for solving problems with two immiscible fluids in a fixed spatial domain. In the present implementation, a VOF tracking algorithm is used to track the position of interface. An initial VOF fraction (volume fraction of reference fluid) can be specified using vof (default is zero). Element can also be marked as always filled with reference fluid (some form of source) using parameter pvof which specifies the permanent VOF value. In this case, the material model should be of type Keyword: twofluidmat, that supports modelling of two immiscible fluids.
Status
Tests/Examples	benchmark/fm/axi04.oofem.in (and 2 more)