These html pages are based on the PhD thesis "Cluster-Based Parallelization of Simulations on Dynamically Adaptive Grids and Dynamic Resource Management" by Martin Schreiber.
There is also more information and a PDF version available.

3.1 Simulation: grid, data and communication management

For our simulations, the grid management has to allow adaptivity during runtime due to demands on the resolution to be increased by refining the grid in feature-rich areas (e.g. close to the wave front) and coarsening the grid in areas which do not have a large contribution to the final result.

The shallow water equations are frequently used models to research wave-propagations and a simulation of them only requires a two-dimensional domain discretization. Therefore, we focus on efficient simulations of two-dimensional scenarios with triangles as the basic primitives. Despite its two-dimensional nature, particular domain triangulations can be created to assemble a two-dimensional surface on a sphere (see Sec. 6.5). Using multiple layers in each cell, this leads to further possible applications such as weather simulations (see Sec. 6.6).

For the simulation of our considered hyperbolic equations, we particularly focus on the following requirements: