This present study develops a 2-D numerical scheme to simulate the velocity and depth on the actual terrain by using shallow water equations. The computational approach uses the HLL scheme as a basic building block, treats the bottom slope by lateralizing the momentum flux, then refines the scheme using the Strang splitting to deal with the frictional source term. Besides, a decoupled algorithm...

We build an augmentation of the Masur-Minsky marking complex by Groves-Manning combinatorial horoballs to obtain a graph we call the augmented marking complex, AMpSq. Adapting work of Masur-Minsky, we show this augmented marking complex is quasiisometric to Teichmüller space with the Teichmüller metric. A similar construction was independently discovered by Eskin-Masur-Rafi [EMR13]. We also com...

An increase in the flow velocity in flowthrough large porous media and deflection of flow regime from Darcy law causes a nonlinear relationship between hydraulic gradient and pore velocity of media. So many investigations have done previously in such Medias. One of the most important subjects in flowthrough large porous media is relationship between friction coefficient and flow characteristics...