High resolution flux-difference-splitting scheme on adaptive grid for open-channel flows

The effectiveness and usefulness of further enhancing the shock resolution of a second-order accurate scheme for open-channel flows by using an adaptive grid is investigated. The flux-difference-splitting (FDS) scheme based on the Lax-Wendroff numerical flux is implemented on a fixed as well as on a self-adjusting grid for this purpose. The grid-adjusting procedure, developed by Harten and Hyman, adjusts the grid by averaging the local characteristics velocities with respect to the signal amplitude in such a way that a shock always lies on a mesh point. This enables a scheme capable of perfectly resolving a stationary shock to capture a shock that moves from mesh point. The Roe's approximate Jacobian is used for conservation and consistency, while theoretically sound treatment for satisfying entropy inequality conditions ensures physically realistic solutions. Details about inclusions of source terms, often left out of analyses for the homogeneous part of governing equations, are also explained. The numerical results for some exacting problems are compared with analytical as well as experimental results for examining improvements in resolution of discontinuities by the adaptive grid.