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.