Abstract
This paper introduces a well-balanced second-order finite volume scheme, based on the Q-scheme of Roe, for simulating granular type flows. The proposed method is applied to solve the incompressible Euler equations under Savage–Hutter assumptions. The model is derived in a local coordinate system along a non-erodible bed to take its curvature into account. Moreover, simultaneous appearance of flowing/static regions is simulated by considering a basal friction resistance which keeps the granular flow from moving when the angle of granular flow is less than the angle of repose. The proposed scheme preserves stationary solutions up to second order and deals with different situations of wet/dry transitions by a modified nonlinear wet/dry treatment. Numerical results indicate the improved properties and robustness of the proposed finite volume structure. In addition, the granular flow properties are estimated with a computational error of less than 5%. These errors are consistently less than those obtained by using similar existing finite volume schemes without the proposed modifications, which can result in up to 30% overestimation.
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