Coefficient Form PDE (pde)

Scalar second-order PDE in coefficient form. Elmer ModelPDE.

Category

Mathematics › PDE Interfaces

Name (tag)

pde

Space dimensions

3D, 2D, 2D axisymmetric

Studies

Stationary, Time Dependent

Dependent variables

u Dependent variable u (1)

Default features

Coefficient Form PDE, Initial Values, Zero Flux

\(d_a\frac{\partial u}{\partial t} + \nabla\cdot(-c\nabla u) + \boldsymbol{\beta}\cdot\nabla u + a u = f\)

Interface settings

Setting Symbol Unit Default Choices / type

Discretization

Element order

Quadratic

Linear, Quadratic

Dependent Variables

Dependent variable name

u

Text

Elmer Solver

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

Text (multi-line)

Domain features

Coefficient Form PDE

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

\(d_a\frac{\partial u}{\partial t} + \nabla\cdot(-c\nabla u) + \boldsymbol{\beta}\cdot\nabla u + a u = f\)

Setting Symbol Unit Default Choices / type

Diffusion Coefficient

Diffusion coefficient c

1

Expression

Absorption Coefficient

Absorption coefficient a

0

Expression

Source Term

Source term f

1

Expression

Damping or Mass Coefficient

Damping or mass coefficient dₐ

1

Expression

Convection Coefficient

β x

0

Expression

β y

0

Expression

β z

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

Initial Values

Initial value for u

0

Expression

Boundary features

Dirichlet Boundary Condition

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

\(u = r\)

Setting Symbol Unit Default Choices / type

Dirichlet Boundary Condition

Prescribed value of u

r

0

Expression

Flux/Source

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

\(-\mathbf{n}\cdot(-c\nabla u) = g - q u\)

Setting Symbol Unit Default Choices / type

Boundary Flux/Source

Boundary flux/source g

0

Expression

Boundary Absorption/Impedance Term

Boundary absorption/impedance q

0

Expression

Zero Flux

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

\(-\mathbf{n}\cdot(-c\nabla u) = 0\)

No settings.

Result variables

Name Description Unit

u

Displacement field, x component

m