PDEModels Overview
This tutorial, 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 cannot 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 and 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
Contents
Helmholtz Equation
Acoustic Boundary Conditions
Nomenclature
References
Acoustics Examples
Electromagnetics
Electric Currents
Magnetostatics for Permanent Magnets
Introduction
Equations
Convergence of Magnetostatics Models
Conditions at Material Interfaces
Nomenclature
References
Quasistatic Magnetic Fields
Introduction
Equations
Convergence of Magnetic Models
Conditions at Material Interfaces
Edge/Vector Elements
Nomenclature
References
Electromagnetics Examples
Fluid Dynamics
Fluid Dynamics Models
Fluid Dynamics Examples
Heat Transfer
Heat Transfer
Contents
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
Contents
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
Contents
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
Non-axes-aligned material
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
Solid Mechanics in a Nutshell
Nonlinear Elastic Material Models—Hypoelastic Models
Hyperelasticity
Failure Theory
Multiple Materials
Nomenclature
References
Hyperelasticity
Contents
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.