## Orthotropic Heat Conduction

## Orthotropic Heat Conduction

This is an example of modeling anisotropic heat conduction in an orthotropic material where a heated solid bar suddenly is cooled by submerging it in a cool fluid. The material features different thermal conductivities in the x and y-directions which is accounted for by modifying the diffusion term in the heat transfer …

## Axisymmetric Fluid Flow

## Axisymmetric Fluid Flow

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

## Black-Scholes Equation

## Black-Scholes Equation

This is an example showing how to define a custom parital differential equation (PDE) equation model in the FEATool Multiphysics. In this case the Black-Scholes model equation, which is used in financial analytics to model derivatives and options pricing. The non-linear partial differential equation to be solved reads …

## Shallow Water Equations

## Shallow Water Equations

This example models a moving wave in a pool of shallow water. Although these types of fluid flows are governed by the full three-dimensional Navier-Stokes equations, they can be simplified with a two dimensional approximation, where the z-dimension is replaced with a variable h for the unknown free surface height …

## Two Material Wave Guide Interface

## Two Material Wave Guide Interface

This example studies the interface between two different materials in a section of a wave guide. The change in material causes the waves to travel at different speeds. This changing diffraction pattern of the planar time harmonic waves can be investigated by using the Helmholtz equation for the amplitude of the waves A …

## Wave Equation on a Circle

## Wave Equation on a Circle

This tutorial explains how to set up and solve a generalized wave equation model on a circle, like for example for a drum or membrane, and then tracks how the initial parabolic deformed state will affect the resulting shape. The wave equation is one of the classic hyperbolic partial differential equations (PDE) of the …

## Interference and Diffraction

## Interference and Diffraction

The classic double-slit experiment considers a planar and periodic oscillating wave which hits and passes two narrow slits. Assuming the slits are narrow enough, the passing waves will bend and cause an interference pattern, while diffraction will attenuate the off axis resulting amplitude. In the example the Helmholtz …