Simulation of the Steady Shocks using Finite Volume and Finite Difference Methods

In this article the behavior of steady oblique shocks in open channels is studied using both the finite
volume (FVM) and the finite difference (FDM) methods. In the FVM, the Van Leer scheme with an
advanced slope limiting function is implemented on unstructured triangular grids. The bed slope is
modeled using an upwind method including a modified hydrostatic pressure term. The Manning
equation is used for the bed friction and the mixing length is applied for turbulence modeling. In the
FDM, the two step MacCormack scheme with the Jameson's artificial viscosity algorithm is applied.
These schemes are used to simulate the oblique shocks produced by a lateral barrier in an open
channel. comparison of the numerical results with laboratory measurements proves robustness of both
the schemes in simulation of shock fronts. However the Van Leer scheme is more consistent with
experimental findings.