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.

There is also more information and a PDF version available.

Continuity equation and applications

Mathematical descriptions of scenarios should conserve particular quantities. We use the continuity equation as the underlying equation, which conserves these quantities for our considered simulations and start with a short derivation of this equation. This is followed by presenting two typical applications which are used in this work and introduce a notation for the conserved quantities. These conserved quantities are then successively discretized in the upcoming chapters.

1.1 Continuity equation

1.2 Examples of hyperbolic systems

1.2.1 Shallow water equations

1.2.2 Euler equations

1.2 Examples of hyperbolic systems

1.2.1 Shallow water equations

1.2.2 Euler equations