31 | | where delta_t is constrained by the delta_t <= delta_x/max[S(n)] <- here s(n) is a given wave speed. note this allows a wave to travel a full delta_x in a time-step |

32 | | |

33 | | we don't worry about wave-wave interaction based on linearity -- that is, assume wave interactions do not lead to wave accelerations |

34 | | |

35 | | we can specify the time constraint as follows, delta_t = cfl*delta_x/max[s(n)], if we let 0<cfl<=1. a cfl = 1 gives the most efficient time marching scheme (the largest time steps). max[s(n)] finds the max speed on the entire domain. |

36 | | |

37 | | u(i, n+1) = average over the cell |

| 31 | The time-step, is constrained by the CFL condition, which uses the max wave speed on the grid. The constraint used in the God. code here allows any given wave on the grid to travel a full delta_x in a time-step. In allowing this, we achieve a more efficient time-marching scheme, but with the assumption that wave interactions do not lead to wave accelerations. |