## Multiphysics

Multiphysics is the process of simulation and study of coupled physical phenomena such as heat transfer, fluid dynamics, and structural mechanics. Multiphysics modeling typically involves first formulating systems of coupled partial differential equations (PDE) with appropriate boundary and initial conditions. The involved PDEs can be discretized with numerical solution method such as the finite element method (FEM) after which the arising discrete matrix system can be solved with a suitable solver.

FEATool Multiphysics enables Matlab and Octave users to easily define multiphysics couplings directly through the graphical user interface and the Matlab command line by simply typing in the coupling as it would be written on paper. FEATool then discretizes and solves the equation systems in a true monolithic and fully coupled manner. In addition to easily defined custom equations, the following predefined multiphysics modes are available which can be combined to create complex multiphysics models

- Heat Transfer

- Convection and Diffusion

- Navier-Stokes Equations

- Linear Elasticity

- Plane Stress

- Plane Strain

- Conduction Media DC

- Poisson Equation

## Heat Transfer

Heat transport through conduction in solids and convection in fluids can be modeled with the heat transfer physics mode in FEATool. The temperature field can be coupled to other physics modes such as structural mechanics applications for thermal stresses, fluid flow to account for buoyancy effects, or convection, diffusion, and reaction equations to account for thermal chemical reactions. Moreover, two way couplings can easily be made to account for the fluid flows convection of the temperature field. The following heat transfer model examples are available in FEATool

- Resistive heating of a Tungsten filament

- Free and forced convection in a heat exchanger

- Natural convection in a square cavity

- 2D heat conduction with natural convection and radiation

- One dimensional stationary heat transfer with radiation

- One dimensional transient heat conduction

- Two dimensional heat transfer with convective cooling

- Two dimensional transient cooling shrink fitting example

- Axisymmetric steady state heat conduction of a cylinder

## Structural Mechanics

FEATool features three predefined physics modes for structural mechanics applications and can solve 3D static solid problems with a linear elasticity assumption, and 2D plane stress and strain approximations. In addition thermal strain effects are also pre-defined and can thus quickly be coupled to a heat transfer application. Parametric studies of both geometry and input variables such as load forces are also easily set up through the use of the m-script file functionality. The following benchmark and solid mechanics test models are available

- Heat induced stress in a brake disk

- Stress computation for a hole in a thin plate

- Three dimensional example of stress on a bracket

- Parametric study of the bracket deformation model

- Stress of loaded I-beam supported by two brackets

- Linear elasticity benchmark test case

- Bending of a beam due to piezoelectric effects

- NAFEMS plane stress benchmark example

- NAFEMS plane stress benchmark of a tapered plate

- NAFEMS thermal stress plate deformation benchmark

- NAFEMS benchmark for plane stress in an elliptic membrane

## Fluid Mechanics

Performing Octave and Matlab CFD simulations have never been so easy. Both stationary and time-dependent computational fluid dynamics (CFD) simulation problems can be set up directly in the GUI. And by using multiphysics, the flow field and pressure can be coupled to other physics modes such as heat transfer and chemical transport models. This allows for complex CFD simulations such as reactive and multiphase flows to be set up with ease. Also, by using higher order finite elements complex quantities such as drag and lift forces for aerodynamics simulations can also evaluated very accurately. FEATool has been thoroughly validated for many computational fluid dynamics CFD benchmarks and simulation models

- Flow around a cylinder in a channel

- Incompressible driven cavity flow

- Fluid flow over a backwards facing step

- Two dimensional decay of a standing vortex

- Instationary flow around a cylinder in a channel

- Laminar flow in a curved three dimensional pipe

- Axisymmetric flow in a narrowing pipe

- Axisymmetric impinging jet

- Free and forced convection in a heat exchanger

- Natural convection in a square cavity

- Multiphase flow example of a static bubble

- Multiphase flow example of a rising bubble

- Multiphase flow example of a breaking dam

## Classic PDE Equations

Implementations for classic PDE equations such as Poisson, Laplace, Wave and Convection and Diffusion Equations are readily available. In addition FEATool allows users to define their own equations with any number of dependent variables, both in the GUI and on the command line. Furthermore, the finite element FEM problem definitions are fully accessible and can be modified users though the command line interface.

- Poisson equation on a line

- Poisson equation on a circle

- Poisson equation on a unit square

- Poisson equation on a rectangle with complex solution

- Poisson equation on a sphere

- Poisson equation on a unit cube

- Poisson equation on a unit circle with a point constraint

- Laplace equation on a unit square

- Wave equation on a unit circle

- Diffusion equation on a unit square with different solutions

- Diffusion equation on a line with exact solutions

- Convection and diffusion on a unit square

- Periodic convection and diffusion on a line with exact solution

- Infinite time dependent convection and diffusion on a line

- One dimensional Burgers equation with steady solution

- Dominating convection example requiring artificial stabilization

- Time dependent one dimensional convection and reaction model

- Black-Scholes model equation implemented as a custom equation