Application of a Quasi-Acoustic Scheme to Solve Shallow-Water Equations with an Uneven Bottom

We describe the application of an explicit homogeneous conservative quasi-acoustic scheme to numerical solution of one-dimensional shallow-water equations with an uneven bottom. The scheme performs linear reconstruction of the numerical solution within a single numerical cell and partitions the linear reconstruction into small-perturbation horizontal layers. The quasi-acoustic scheme correctly reproduces the physical solution in the neighborhood of the sonic point without invoking artificial regularizers or tuning parameters. The scheme is verified on a number of test and prototype problems. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.