Laminar Channel Flow
Stationary and incompressible laminar Poiseuille flow in a two- dimensional rectangular channel. With a constant inflow profile u(0,y) = Umax and fixed no-slip walls, a fully developed laminar parabolic profile, u(y,L) = Umax4/h2y(h-y) is expected to develop at the outflow. This model is available as an automated …
Magnetic Field Around a Permanent Magnet
Example of simulation and visualization of the two-dimensional static magnetic potential field around a u-shaped permanent magnet. This model is available as an automated tutorial by selecting Model Examples and Tutorials… > from the File menu. Or alternatively, follow the linked step-by-step instructions. …
Poisson Equation
The classic Poisson equation is one of the most fundamental partial differential equations (PDEs). Although one of the simplest equations, it is a very good model for the process of diffusion and comes up in many applications (for example fluid flow, heat transfer, and chemical transport). It is therefore fundamental …
Poisson Equation with a Point Source
The classic Poisson equation is one of the most fundamental partial differential equations (PDEs). Although one of the simplest equations, it is a very good model for the process of diffusion and comes up again and again in many applications such as in fluid flow, heat transfer, and chemical transport. This example …
Potential Flow Over an Airfoil
This example models and simulates the flow field around the cross section of a NACA airfoil using the inviscid potential equation. The potential field is here modeled with the classic Laplace PDE equation with a correction for the discontinuity at the trailing edge (the Kutta condition). On the boundaries, there is …
Resistive Heating in a Tungsten Filament
This example models resistive Joule heating where the resulting current from an applied electric potential will heat a thin spiral shaped Tungsten wire, such as can be found in incandescent light bulbs. The filament reaches an equilibrium temperature where the internal heat generation is balanced by radiative heat loss …
Resonance Frequencies of a Room
This example studies the resonance frequencies of an empty room by using the Helmholtz equation for the time-harmonic pressure field Δp + k2 = 0 The resulting eigenmodes can be compared to and validated against the analytical solution for the resonance frequencies of a boxed enclosure, that is f = c/2*√( (i/lx)2 …
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 …
Shrink Fitting of an Assembly
This example models shrink fitting of a two part assembly. A chilled tungsten rod is inserted into a slot in a heated steel frame. The rod can be fitted due to thermal expansion of the frame, and when the assembly reaches equilibrium temperature the two parts will be joined due to the ensuing pressure fit. The model …
Spherical Capacitor
Model of an electrostatic spherical capacitor. The example makes use of a 2D axisymmetric approximation with three subdomains, where an electric charge is applied between the middle insulating layer. For this configuration the analytic capacitance can be calculated as 4*πεrε0/dr, where dr is the thickness of the …