Abstract
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.
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