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 …
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 + k2p = 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 …
Stress Analysis of a Thick Plate
This is a benchmark and validation model for linear elasticity where an elliptical thick plate with a hole is subjected to a uniform pressure load of 106 MPa [1]. The outer surface is assumed to be constrained from expansion, in addition to the center line which is fixed in the z-direction. Symmetry is also utilized so …
Supersonic Flow Over an Obstacle
Steady inviscid flow over a cylindrical bump using the compressible Euler equations. The flow at the inlet is supersonic with Ma = 1.4 resulting in a series of reflected shock waves as the flow hits the obstacle]. The obstacle could represent anything from a protrusion on an aircraft wing to a structural feature in a …
Transient Heat Diffusion in a Rod
This example is a classic one-dimensional transient heat diffusion problem where a solid rod of unit length is kept at fixed temperature at the right end, T = 25, and losing heat from a constant outward heat flux qn = 1 at the other end. After the simulation the computed results can be compared with the analytic …
Vibration Modes of a Hollow Cylinder
This model studies the vibration modes of a free and hollow cylinder using an axisymmetric approximation. No loads or constrains are applied as the free modes are sought. The cylinder is 10 m long, has a center diameter of 2 m, and is 0.4 m thick. Moreover, the material of the cylinder is considered to be steel with E …
Vibrations of a Circular Membrane
This example computes the the vibration modes, eigenvalues, and frequencies for a circular drum or membrane. The membrane is modeled by the unit circle and assumed to be attached to a rigid frame. The Poisson PDE equation is used with the Eigenvalue solver to compute the solution. This model is available as an …
Vortex Flow
This example studies the time dependent decay from introducing standing vortices in a periodic domain. Due to the even spacing and counter rotation, the vortices will stay in place and simply loose intensity with time, and eventually the flow will return to a perfectly steady state. This is in fact one of the few model …