# Spatial model

## Definition

A spatial model is a model that spatially defines the material properties, i.e. in any point of space (at the nodes of problem).

The property is then defined using a formula, which allows the handling of spatial quantities.

## List of models

The spatial model is provided for B(H), J(E), D(E) behavior laws and

k(T), ρCp(T) thermal properties.

Property Name of model
B(H) / Magnetic property

Spatial linear isotropic

Spatial linear magnet

J(E) / Electric property Spatial isotropic
D(E) / Dielectric property Spatial linear isotropic
k(T) / Thermal conductivity Spatial isotropic
ρCp(T) / Volumetric heat capacity Spatial

## Example

An example of use of the spatial model is presented in the document “Multiphysics use case” for the J(E) property.

Data exchanges between a problem of electric conduction and a thermal problem are carried out in the studied case.

The electric resistivity (in the electric conduction problem) depends on the temperature (computed in the thermal problem).

The spatial formula used to define the resistivity depending on the temperature is as follows:

ρ(T)=(1+3,85.103 *Temp)*107

where:

• Temp is a spatial quantity (created in the problem of electric conduction) to store the temperature imported from the thermal problem.