Multislope MUSCL method applied to solve shallow water equations

Based on a classical multislope MUSCL (monotone upstream scheme for conservation law) method, this paper addresses a new multislope MUSCL method which is used to extrapolate the values of flow variables at the midpoints of cell edges. The main merit of the new method is its more straightforward implementation than that of the classical one. The new method is incorporated into a two-dimensional unstructured cell-centered Godunov-type finite volume model to simulate shallow water flows. The performance of the model with the new multislope MUSCL method is demonstrated by simulating three test cases including both theoretical and practical ones. It is verified that the new method is more efficient than the classical one and is able to produce slightly better or similar numerical results.

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