Abstract
We present a new semi‐discrete central scheme for two‐layer shallow water flows along channels with non‐uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it preserves steady‐states of rest (i.e., it is well balanced). Along with a detailed description of the scheme, we present a numerical examples to assess its well balance property. Comparison with exact solutions illustrate the accuracy and robustness of the numerical algorithm.
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