The use of numerical simulations in fluid dynamics has exploded over the past half century with new computational techniques being developed constantly. Most methods involve solving the equations of motion (or an approximation thereof) on a grid of points known as a mesh. To accurately capture the physics, meshes must often be quite closely packed in areas where detail is needed, but they can be more widely spaced in areas where the flow is not changing quickly. An increasingly common technique is adaptive meshing in which the mesh of grid points shifts between time steps; this places more grid points where the flow requires them and removes them from less important areas in order to reduce computational time.
An example of adaptive meshing is shown above. On the left particles are falling into salt water. The colors show the concentration of particles. The right side shows the solid particles and the fluid mesh around them. Notice how the grid shifts as the particles fall. (Image credit: C. Jacobs et al., source)