Application of the HLL Approximate Riemann Solver to One-Dimensional Open Channel Flows with Irregular Geometry

Recently, many researchers revealed that the conventional approximate Riemann solvers are inadequate to deal with the real-life one-dimensional open channel flows because of problems such as unrealistic flow caused by numerical imbalance as well as inaccuracy in the solution of discharge when the channel has complex geometry and a hydraulic jump is present. To overcome these deficiencies, several new techniques have been proposed, including: (1) adopting the form of the Saint Venant equations which include only one source term representing driving forces; (2) using water surface level as one of the primitive variables; (3) defining discharge at interface and evaluating it according to the flux obtained by the HLL Riemann solver. In this paper, the performance of this new scheme is evaluated by means of two dam-break flow problems. The comparisons of computed results with analytic solutions and data measured from the physical model show that the scheme is capable of satisfactorily reproducing open channel flows with irregular geometry.