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 adapti ve grid is investigated. The flux-difference-splitting (FDS) scheme based o n 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, develo ped by Harten and Hyman, adjusts the grid by averaging the local characteri stic velocities with respect to the signal amplitude in such a way that a s hock always lies on a mesh point. This enables a scheme capable of perfectl y resolving a stationary shock to capture a shock that moves from mesh poin t to mesh point. The Roe's approximate Jacobian is used for conservation an d consistency, while theoretically sound treatment for satisfying entropy i nequality conditions ensures physically realistic solutions. Details about inclusion of source terms, often left out of analyses for the homogeneous p art of governing equations, are also explained. The numerical results for s ome exacting problems are compared with analytical as well as experimental results for examining improvements in resolution of discontinuities by the adaptive grid. Copyright (C) 2001 John Wiley & Sons, Ltd.