# Equation Syntax Articles and Tutorials

## Space-Time Transformation of 1D Time-Dependent to a 2D Stationary Simulation Model

## Space-Time Transformation of 1D Time-Dependent to a 2D Stationary Simulation Model

Space-Time Finite Element (FEM) Simulation FEATool Multiphysics is a very flexible CAE physics and continuum mechanics simulation toolbox, allowing users to customize, easily define, and solve their own systems of partial differential equations (PDE). In the following it is shown how the custom equation feature can be …

## Custom Implementation of an Algebraic Turbulence Model

## Custom Implementation of an Algebraic Turbulence Model

Performing accurate simulation of turbulent flows is still a challenging topic today, especially with limited computational resources. Although the Navier-Stokes equations are perfectly valid in the turbulent flow regime, one typically have to resort to some form of turbulence modeling in order to reduce computational …

## Modeling with Non-constant Coefficients in FEATool Multiphysics

## Modeling with Non-constant Coefficients in FEATool Multiphysics

FEATool Multiphysics has been designed to be as easy to use as possible, and conveniently features built-in parsing and evaluation of non-constant variables and coefficients. This allows users to quickly and easily enter modeling expressions formulated much as one would write on paper, all without having to develop, …

## Euler-Bernoulli Beam - FEATool Modeling and Implementation Example

## Euler-Bernoulli Beam - FEATool Modeling and Implementation Example

This post will discuss how to implement and model elastic deformations of simple beams with FEATool Multiphysics. Although also available as a pre-defined physics mode and GUI option, beams and truss structures can also be implemented and accurately simulated with slight extension of the available FEM MATLAB functions …

## Multiphysics Modeling of Heat Induced Stress in a Brake Disk

## Multiphysics Modeling of Heat Induced Stress in a Brake Disk

This tutorial illustrates how to couple a heat transfer model with linear elasticity by manually defining the multiphysics equations with the FEATool PDE syntax. The custom model examines how temperature rise in a brake disk under braking results in heat induced displacements with resulting increased stresses and …

## Custom Equations and the Weak PDE Formulation Equation Syntax

## Custom Equations and the Weak PDE Formulation Equation Syntax

The following post further examines PDE equation parsing and specifying custom equations in FEATool. Furthermore, a simple parametric heat transfer model will be shown and set up as a custom PDE equation, suitable for both the MATLAB command line and m-script file modeling. Stationary heat transfer by conduction and …

## Axisymmetric Modeling Using the Custom Equation Syntax

## Axisymmetric Modeling Using the Custom Equation Syntax

FEATool has been designed to be able to perform MATLAB multiphysics simulations in all spatial dimensions (1D, 2D, and 3D). However, running full 3D simulations often requires a significant amount of computational resources, that is memory and simulation time. It is therefore desirable to find simplifications to reduce …

## Modeling with Custom Equations in the FEATool GUI

## Modeling with Custom Equations in the FEATool GUI

FEATool Multiphysics features an equation parser which allows users to very easily implement and simulate custom systems of equations. The goal as always with FEATool is to make it as easy as possible, the parser can therefore interpret equations written almost as one would on paper. For example a two dimensional …

## Adding Multiphysics Equations and Using Complex Expressions

## Adding Multiphysics Equations and Using Complex Expressions

The FEATool GUI makes it easy to add and coupled multiphysics equations and complex expressions to your models. This post illustrates how to do this. After starting to work with a physics mode it is easy to add one or more other modes by going to the + tab in the Equation Settings dialog box. There you can simply …