Second-Order Godunov-Type Model for Free Surface Flow
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     This project involves the use of Godunov-type scheme which is an FMV
     method that solves analytically the Riemann problem; it shall be used for
    four types of scenarios for shallow water equation:

     1-Still water test: The simulation showed a constant water elevation
     across the channel and the model was able to keep a steady state
     solution, the velocity remained zero all along the simulation.

     2-Tidal Wave Over a Varying Bed: The simulation showed that
     the analytical and numerical solutions are similar,as the model
    was able to properly simulate the increasing level of water with
     time producing a non-oscillatory result.

     3-Dam Break:The simulation showed difficulties with appearance
     oscillation at sonic points ,these were eliminated with the use of MUSCL
     and slope limiter with the Godunov scheme .

     4-Tidal Wave Over Steps: The simulation showed that both analytical and
     numerical are compatible As for the velocity profile, we can notice that
     the half risen tidal flow at time 10,800 have maximum positive velocities
     and the half-ebb tidal flowat time 32,400 s have maximum negative velocities.



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Halim Richard Maamari
Water and Landscapes
Simulation figure; of Tidal Wave Over a Varying Bed; showing similar water level profiles for the analytical and the numerical solution.
Simulation figure; of Dam Break; showing difficulties at sonic points in rarefactions.
Simulation figure; of Tidal Wave Over Steps showing that the half risen (Coming from the sea to the shore) tidal flow at time 10,800 have maximum positive velocities.
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