Stokes’ Flow Elements

Stokes’ Flow Elements

Stokes’ flow elements neglect acceleration, and thus requires no additional stabilization.

Tr21Stokes element

Standard 6 node triangular element for stokes flow, with quadratic geometry, velocity and linear pressure. Both compressible and incompressible material behavior is supported (and also the seamless transition between the two). The element features are summarized in Table 59.

Table 59 Tr121Stokes element summary

Keyword	Tr121Stokes
Description	Standard 6 node triangular element for stokes flow, with quadratic geometry, velocity and linear pressure
Parameters	NIP: allows to change the default number of integration point used, possible values are 8, 27 (default) and 64.
Unknowns	Unknown pressure in nodes 1–3 with unknown velocity (V_u and V_v) in all 6 nodes.
Approximation	Quadratic approximation of geometry and velocity, linear pressure approximation.
Integration
Features
Status	Reliable

Tet21Stokes element

Standard 10 node tetrahedral element for stokes flow, with quadratic geometry, velocity and linear pressure. The element features are summarized in Table Table 60.

Table 60 Tet21Stokes element summary

Keyword	Tet21Stokes
Description	Standard 10 node tetrahedral element for stokes flow, with quadratic geometry, velocity and linear pressure
Parameters	NIP: allows to change the default number of integration point used, possible values are 8, 27 (default) and 64.
Unknowns	Unknown pressure (P_f) in nodes 1–4, and unknown velocity (V_u, V_v, V_w) in all nodes.
Approximation	Quadratic approximation of geometry and velocity, linear pressure approximation.
Integration
Features
Status	Untested

Hexa21Stokes element

Standard 27 node hexahedral element for stokes flow, with quadratic geometry, velocity and linear pressure. The element features are summarized in Table Table 61.

Fig. 26 Hexa21Stokes element. Node numbering and face numbering.

Table 61 Hexa21Stokes element summary

Keyword	Hexa21Stokes
Description	Standard 10 node tetrahedral element for stokes flow, with quadratic geometry, velocity and linear pressure
Parameters	NIP: allows to change the default number of integration point used, possible values are 8, 27 (default) and 64.
Unknowns	Unknown pressure (P_f) in nodes 1–8, and unknown velocity (V_u, V_v, V_w) in all nodes.
Approximation	Quadratic approximation of geometry and velocity, linear pressure approximation.
Integration
Features
Status	Untested

Tr1BubbleStokes element

So called “Mini” element in 2D. A 3 node triangular element for stokes flow, with linear geometry and pressure. Velocity is enriched by a bubble function. Should not be used with materials that have memory (which is uncommon for flow problems). The element features are summarized in Table 62.

Table 62 Tr1BubbleStokes element summary

Keyword	Tr1BubbleStokes
Description	So called “Mini” 2D element
Parameters	NIP: allows to change the default number of integration point used, possible values are 8, 27 (default) and 64.
Unknowns	Unknown pressure (P_f) in all nodes, and unknown velocity (V_u, V_v) in all nodes and one internal dof manager.
Approximation	Linear geometry and pressure. Velocity is enriched by a bubble function.
Integration
Features
Status	Untested

Tet1BubbleStokes element

So called “Mini” element in 3D. A 4 node tetrahedral element for stokes flow, with linear geometry and pressure. Velocity is enriched by a bubble function. Should not be used with materials that have memory (which is uncommon for flow problems). The element features are summarized in Table 63.

Table 63 Tet1BubbleStokes element summary

Keyword	Tet1BubbleStokes
Description	So called “Mini” 3D element
Parameters	NIP: allows to change the default number of integration point used, possible values are 8, 27 (default) and 64.
Unknowns	Unknown pressure (P_f) in all nodes, and unknown velocity (V_u, V_v) in all nodes and one internal dof manager.
Approximation	Linear geometry and pressure. Velocity is enriched by a bubble function.
Integration
Features
Status	Untested