Flux-difference splitting schemes for 2D flood flows

Two numerical models for 2D flood flows are presented. One model is first-o rder accurate and another is second-order accurate. Roe's numerical flux is used to develop the first-order accurate model, while second-order accurac y, in space and time, is obtained by using the Lax-Wendroff numerical flux. A simple operator splitting is found to yield the same results as that obt ained by using more complicated, and thus, time consuming, operator splitti ng. Roe's approximate Jacobian is used for conservative properties and Hart en and Hyman's procedure is followed for the entropy inequality condition. Flux limiter is used in the second-order accurate model that removes oscill ations while maintaining the order of accuracy. The models are verified aga inst available experimental data of a 2D flood wave due to partial dam-brea k. Numerical experiments are conducted to verify the models' ability to cor rectly predict behavior of the free surface, in addition to prediction of d epth and velocity.