R. Vacondio, B. D. Rogers, P. K. Stansby and P. Mignosa A correction for balancing discontinuous bed slopes in two-dimensional smoothed particle hydrodynamics shallow water modeling International Journal for Numerical Methods in Fluids 71
The imbalance introduced by a bed or bottom discontinuity is eradicated from the smoothed particle hydrodynamics calculation of the water depth by means of a corrected mass. The imbalance in the source terms in the momentum equation is also removed by using this corrected mass within the bed gradients. The numerical scheme has been tested against a set of analytical and experimental test cases (including dam breaks over steps) showing that the numerical scheme is able to reproduce reference solutions with improved accuracy.
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