Representation of Waves on a Discrete Mesh
Representation of Waves on a Mesh This demonstrates how waves of various wavelengths are represented on a mesh. In computer models it is impossible to store and process the property at the fluid at every point as there are an infinite number of points. Instead the properties of a fluid are stored at various discrete points, called a mesh. Here a propagating wave is shown in black. The mesh has a resolution of 5; that is the wave is sample at the points x= ..., -10, -5, 0, 5, 10, ... . The approximation of this wave on the mesh is shown by the red points. These points are joined by red lines to show how the wave is being approximated. When the wavelength is large (eg 40) compared to the resolution, the approximation is good. That is the red and black lines closely resemble each other. However, as the wavelength decreases the approximation becomes steadily worse. When the wavelength is twice the resolution of the mesh (ie 10) the approximate wave no longer propagates, it is a standing wave whose amplitude periodically decays and grows. Even worse when the wavelength is small (eg 6) the approximate wave is of an entirely different wavelength and travelling in the opposite direction. This is one of the reasons that fluid simulations need to filter out small wavelength phenomena (such as turbulence) that are poorly resolved, they are incorrectly represented in the model.
Explore what effects (if any) that changing the speed, amplitude and wavelength of the wave has on its representation on the mesh by using the sliders in the top left of the worksheet.