A Non-oscillatory Central Scheme for One-Dimensional Two-Layer Shallow Water Flows along Channels with Varying Width

Abstract

We present a new high-resolution, non-oscillatory semi-discrete central scheme for one-dimensional two-layer shallow-water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme extends existing central semi-discrete schemes for hyperbolic conservation laws and it enjoys two properties crucial for the accurate simulation of shallow-water flows: it preserves the positivity of the water height, and it is well balanced, i.e., the source terms arising from the geometry of the channel are discretized so as to balance the non-linear hyperbolic flux gradients. Along with a detailed description of the scheme and proofs of these two properties, we present several numerical experiments that demonstrate the robustness of the numerical algorithm.