A locally implicit time-reversible sonic point processing algorithm for one-dimensional shallow-water equations

Abstract

In this paper, we introduce a new locally implicit sonic point processing algorithm for one-dimensional shallow-water equations. The algorithm is based on transferring the shallow-water invariants along the characteristics around the sonic point, and it can be coupled with conservative-characteristic methods, which have problems modelling the transonic flows. For each sonic point, a system of two non-linear equations should be solved, which allows to use the proposed method with explicit methods for subsonic or supersonic flows without noticeable increase in calculation time. The important features of the algorithm include the second order of approximation in time and space and the property of time reversibility if monotonization procedures are disabled. Coupled with the CABARET scheme, the proposed method has been tested on several Riemann problems, including the Toro tests for transonic flows. The results have shown that the algorithm allows to obtain solutions with accurate transonic rarefaction and shock waves in both cases of wet and dry beds.