Laminar Flow (spf)

Incompressible laminar Navier-Stokes flow (P1-P1 stabilized). Elmer FlowSolve.

Interface settings

Setting	Default	Choices / type
Discretization
Element order	Linear	Linear, Quadratic
Physical Model
Neglect inertial term (Stokes flow)	Off	Check box
Elmer Solver
Additional Elmer solver keywords Lines appended verbatim to this interface’s Solver section in the .sif file		Text (multi-line)

Setting

Symbol

Unit

Default

Choices / type

Discretization

Element order

Linear

Linear, Quadratic

Physical Model

Neglect inertial term (Stokes flow)

Off

Check box

Elmer Solver

Additional Elmer solver keywords
Lines appended verbatim to this interface’s Solver section in the .sif file

Text (multi-line)

Domain features

Fluid Properties

Selection: Domains (all by default) · Physics ribbon › Domains, or right-click the interface in the Model Builder

\(\rho(\mathbf{u}\cdot\nabla)\mathbf{u} = \nabla\cdot[-p\mathbf{I}\mu(\nabla\mathbf{u}\nabla\mathbf{u}^T)] + \mathbf{F},\ \nabla\cdot\mathbf{u}=0\)

Setting Symbol Unit Default Choices / type

Setting	Symbol	Unit	Default	Choices / type
Fluid Properties
Density	ρ		From material	From material, User defined
rho	ρ	`kg/m^3`	`0`	Expression
Dynamic viscosity	μ		From material	From material, User defined
mu	μ	`Pa*s`	`0`	Expression

Fluid Properties

Density

From material

From material, User defined

rho

kg/m^3

0

Expression

Dynamic viscosity

From material

From material, User defined

Pa*s

0

Expression

Volume Force

Selection: Domains · Physics ribbon › Domains, or right-click the interface in the Model Builder

\(\mathbf{F}\)

Setting Symbol Unit Default Choices / type

Setting	Unit	Default	Choices / type
Volume Force
F x	`N/m^3`	`0`	Expression
F y	`N/m^3`	`0`	Expression
F z	`N/m^3`	`0`	Expression

Volume Force

F x

N/m^3

0

Expression

F y

N/m^3

0

Expression

F z

N/m^3

0

Expression

Gravity

Selection: Domains · Physics ribbon › Domains, or right-click the interface in the Model Builder

\(\mathbf{F} = \rho\mathbf{g}\)

Setting Symbol Unit Default Choices / type

Setting	Symbol	Unit	Default	Choices / type
Gravity
g x		`m/s^2`	`0`	Expression
g y		`m/s^2`	`-g_const`	Expression
g z		`m/s^2`	`0`	Expression
Density
Density	ρ		From material	From material, User defined
rho	ρ	`kg/m^3`	`0`	Expression

Gravity

g x

m/s^2

0

Expression

g y

m/s^2

-g_const

Expression

g z

m/s^2

0

Expression

Density

From material

From material, User defined

rho

kg/m^3

0

Expression

Initial Values

Selection: Domains (all by default) · Physics ribbon › Domains, or right-click the interface in the Model Builder

Setting Symbol Unit Default Choices / type

Setting	Symbol	Unit	Default	Choices / type
Initial Values
Velocity field x		`m/s`	`0`	Expression
Velocity field y		`m/s`	`0`	Expression
Velocity field z		`m/s`	`0`	Expression
Pressure	p	`Pa`	`0`	Expression

Initial Values

Velocity field x

m/s

0

Expression

Velocity field y

m/s

0

Expression

Velocity field z

m/s

0

Expression

Pressure

Pa

0

Expression

Boundary features

Wall

Selection: Boundaries (all by default) · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\(\mathbf{u} = \mathbf{0}\)

Setting	Symbol	Unit	Default	Choices / type
Boundary Condition
Wall condition			No slip	No slip, Slip

Setting

Symbol

Unit

Default

Choices / type

Boundary Condition

Wall condition

No slip

No slip, Slip

Inlet

Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\(\mathbf{u} = -U_0\mathbf{n}\)

Setting Symbol Unit Default Choices / type

Setting	Symbol	Unit	Default	Choices / type
Boundary Condition
Boundary condition			Velocity	Velocity, Pressure
Velocity
Specification			Normal inflow velocity	Normal inflow velocity, Velocity field
Normal inflow velocity	U₀	`m/s`	`0.1`	Expression
u0 x		`m/s`	`0`	Expression
u0 y		`m/s`	`0`	Expression
u0 z		`m/s`	`0`	Expression
Pressure Conditions
Pressure	p₀	`Pa`	`0`	Expression

Boundary Condition

Boundary condition

Velocity

Velocity, Pressure

Velocity

Specification

Normal inflow velocity

Normal inflow velocity, Velocity field

Normal inflow velocity

U₀

m/s

0.1

Expression

u0 x

m/s

0

Expression

u0 y

m/s

0

Expression

u0 z

m/s

0

Expression

Pressure Conditions

Pressure

p₀

Pa

0

Expression

Outlet

Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\([-p\mathbf{I}+\mathbf{K}]\mathbf{n} = -p_0\mathbf{n}\)

Setting Symbol Unit Default Choices / type

Setting	Symbol	Unit	Default	Choices / type
Pressure Conditions
Pressure	p₀	`Pa`	`0`	Expression
Normal flow The tangential velocity is zero at the outlet: a parallel outflow, which keeps a fully developed profile undisturbed up to the outlet			Off	Check box

Pressure Conditions

Pressure

p₀

Pa

0

Expression

Normal flow
The tangential velocity is zero at the outlet: a parallel outflow, which keeps a fully developed profile undisturbed up to the outlet

Off

Check box

Symmetry

Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\(\mathbf{u}\cdot\mathbf{n} = 0\)

No settings.

Open Boundary

Selection: Boundaries · Physics ribbon › Boundaries, or right-click the interface in the Model Builder

\([-p\mathbf{I}+\mathbf{K}]\mathbf{n} = \mathbf{0}\)

No settings.

Result variables

Name Description Unit

Name	Description	Unit
`u`	Displacement field, x component	`m`
`v`	Displacement field, y component	`m`
`w`	Displacement field, z component	`m`
`spf.u_vec`	Velocity field	`m/s`
`spf.U`	Velocity magnitude	`m/s`
`spf.u`	Velocity field, x component	`m/s`
`spf.v`	Velocity field, y component	`m/s`
`spf.w`	Velocity field, z component	`m/s`
`p`	Pressure	`Pa`

u

Displacement field, x component

m

v

Displacement field, y component

m

w

Displacement field, z component

m

spf.u_vec

Velocity field

m/s

spf.U

Velocity magnitude

m/s

spf.u

Velocity field, x component

m/s

spf.v

Velocity field, y component

m/s

spf.w

Velocity field, z component

m/s

p

Pressure

Pa