# PDEModels Overview

This notebook, in contrast, provides an overview over which fields of physics have a high level representation in the Wolfram Language. The various fields presented here have a varying degree of completeness. Again, if a specific equation is not presented here it does not mean that it can not be solved, it just means there is no high level representation yet. Future versions of the Wolfram language will continue to expand in this area.

Typically, a field of physics that is considered complete consists of a guide page specific to that area, one or more monographs explaining the theory behind the functions provided. In some cases verification notebooks are provided. A collection on models provides extended examples that showcase a specific application. The application models are typically more extensive then what one would normally find in the reference documentation. The example collection points to examples from the reference documentation that show a feature of particular interest.

The PDEs and boundary conditions guide page of a specific field of physics will link to a guide page that provides a listing of all available PDE functions and boundary conditions that are useful for creating PDE models in that area. A short description of the various PDE models can also be found on the guide page and a more detailed overview of which model makes use of which functionality is provided last.

## Acoustics

## Acoustics in the Frequency Domain

### Helmholtz Equation

### Acoustic Boundary Conditions

### Nomenclature

### References

## Acoustics Examples

## Electromagnetics

## Electromagnetics Examples

## Fluid Dynamics

## Fluid Dynamics Models

## Fluid Dynamics Examples

## Heat Transfer

## Heat Transfer

### Introduction

### Heat Equation

#### Introduction to Heat Equation

#### Heat Equation Derivation

#### Heat Transfer Model Setup

#### Model Parameter Setup

#### Basic Heat Transfer Example

#### Anisotropic and Orthotropic Heat Transfer

#### Heat Transfer with Events

#### Heat Transfer in Porous Media

#### Heat Transfer Model with Mixed Dimensions

#### Heat Transfer in Multi-Material Media

#### Heat Transfer with Model Order Reduction

#### Multiphysics Heat Transfer

### Appendix

### Nomenclature

### References

## Mass Transport

## Mass Transport

### Introduction

### Mass Balance Equation

#### Mass Balance Equation Introduction

#### Mass Balance Equation Derivation

#### Mass Transport Model Setup

#### Initial Mass Transport Example

#### Mass Transport with a Chemical Reaction

#### Anisotropic and Orthotropic Mass Diffusion

#### Interphase Mass Transfer

#### Mass Source Types

#### Multiphysics Mass Transport

### Boundary Conditions in Mass Transport

### Nomenclature

### References

## Multiphysics

## Physics

## Physics Examples

## SystemPhysics

## SystemPhysics Models

## Structural Mechanics

## Solid Mechanics

### Introduction

### Overview example and analysis types

### Equations

#### Linear elastic material models

##### Isotropic linear elastic materials

##### Orthotropic linear elastic materials

##### Transversely isotropic linear elastic materials

##### Anisotropic linear elastic materials

##### Material with variable orientation

##### Linear elastic materials

##### Generalization of the linear elastic constitutive equation

##### Initial strains

##### Thermoelasticity

##### Initial stresses

##### Plane strain, plane stress and axisymmetric models

##### Limits of linear elasticity

##### The equation form of SolidMechanicsPDEComponent

#### Nonlinear elastic material models - Hypoelastic models

#### Hyperelasticity

#### Failure theory

#### Multiple materials

### Nomenclature

### References

## Hyperelasticity

### Introduction

### St. Venant-Kirchhoff model

### Adding a new Material model

### Neo-Hookean model

### Strain invariants

### Compressibility

### Multiple material constitutive models

### Transversely isotropic hyperelastic materials

### Materials with two families of fibers

### References

## Structural Mechanics Examples

## The Finite Element Method

The finite element method is a solution method for partial differential equations and the main method to solve the PDE models presented here. More information on the finite element method is found in the following guide and overview page.