A non-linear filter for one- and two-dimensional open channel flows with shocks

Modeling flows with shocks creates numerical challenges due to the oscillations in the vicinity of the discontinuity. This paper presents the advantage of using a non-linear filter for obtaining oscillatory free solution for one- and two-dimensional open channel flows. Numerical results are compared with those of other conventional high-resolution schemes to demonstrate the accuracy of the solution. As discussed in the course of this document, the present formulation is computationally faster, and simpler to code while maintaining consistent results with the standard schemes.