Coupling of One-Dimensional and Two-Dimensional Hydrodynamic Models Using an Immersed-Boundary Method

Numerical simulations of flooding events through rivers and channels require coupling between one-dimensional (1D) and two-dimensional (2D) hydrodynamic models. The rivers and channels are relatively narrow, and the widths could be smaller than the grid size used in the background 2D model. The shapes of the rivers and channels are often complex and do not necessarily coincide with the grid points. The coupling between the 1D and 2D models are challenging. In this paper, a novel immersed-boundary (IB) type coupling is implemented. Using this method, no predetermined linking point is required, nor are the discharge boundary conditions needed to be specified on the linking points. The linkage will be dynamically determined by comparing the water levels in the 1D channel and the surrounding dry cell elevations on the 2D background. The linking-point flow conditions, thus, can be dynamically calculated by the IB type implementation. A typical problem of the IB treatment, which is the forming of the nonsmooth zigzag shaped boundary, has not been observed with this method. This coupling method enables more realistic and accurate simulations of water exchange between channels and dry lands during a flooding event.