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## 3.2.3 Stability

In time integration schemes, such as the first-order forward Euler method, information from a grid point to a neighbor grid point can at most propagate with the velocity given by the ratio of the grid spacing and the time increment, . In order to calculate the movement of a surface, its maximum speed must be smaller than this critical value

 (3.15)

This condition needs to be fulfilled in order to guarantee a stable time integration and is known as the Courant-Friedrichs-Lewy (CFL) condition [24].

For each integration step the time increment must be adapted to fulfill the CFL condition. In practice, a positive constant , the so-called CFL number, is defined and an appropriate time increment is chosen according to

 (3.16)

Next: 3.2.4 Surface Velocity Extension Up: 3.2 Solving the Level Previous: 3.2.2 Lax-Friedrichs Scheme

Otmar Ertl: Numerical Methods for Topography Simulation