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 Models
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
Nonlinear Heat Transfer
Heat Transfer with Events
Heat Transfer in Porous Media
Heat Transfer with Mixed Dimensions
Heat Transfer with Phase Change
Heat Transfer with Model Order Reduction
Appendix
Nomenclature
References
Mass Transport
Mass Transport
Introduction
Mass Balance Equation
Boundary Conditions in Mass Transport
Nomenclature
References
Mass Transport Models
Multiphysics
Physics
Physics Models
Physics Examples
Structural Mechanics
Solid Mechanics
Equations
Linear elastic material models
Isotropic linear elastic materials
Orthotropic linear elastic materials
Anisotropic linear elastic materials
Generalization of the linear elastic constitutive equation
Initial Strains
Thermoelasticity
Initial Stresses
Plane Strain and Stress
Limits of linear elasticity
The equation form of SolidMechanicsPDEComponent
Nonlinear Elastic Material Models - Hypoelastic Models
Hyperelasticity
Failure Theory
Multiple materials
Nomenclature
References
Structural Mechanics Models
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.