Simulation of Dam-Break Problem using Random Choice Method

• Glimm’s Random Choice Method is used to the 1-D shallow water equations.
• The results obtained from RCM and the FORCE schemes are compared.
• A Hybrid method is applied to the two dimensional case.
• RCM is applied to the continuous parts.
• FORCE method is applied at large pressure jumps.

In the present study we investigate the application of Glimm’s Random Choice Method to the one dimensional homogenous shallow water equations of the Dam-Break Problem and extend the same to two-dimensional case using operator splitting procedure. A comparison is drawn between the Random Choice Method and the FORCE (First Order Centered) scheme. It was observed that the Random Choice Method gives sharper shock resolution as compared to FORCE method which causes the smearing of discontinuities. On further analysis of the two-dimensional case via operator splitting procedure, we observe that the result is highly erroneous and haphazard due to the presence of shocks oblique to the cell interfaces. We resolve this error by applying a Hybrid method to the two dimensional case; the Glimm’s method is applied to the continuous parts of the flow while the FORCE method is applied at large pressure jumps. This increases the accuracy of the results and provides good shock capture as well.