Improving multi-block sigma-coordinate for 3D simulation of sediment transport and steep slope bed evolution

•A multi-block sigma–coordinate is developed to simulate bed evolutions for the first time.•A multi-block sigma–coordinate can easily increase depth directional resolution.•A multi-block sigma–coordinate follows bed evolution by different numbers of horizontal layers.•A multi-block sigma–coordinate has no significant impact on the time steps within the application range. This paper aims at developing a multi-block sigma-coordinate to simulate morphological evolutions. The developed multi-block sigma-coordinate can represent a steep slope topography smoothly with different numbers of horizontal layers, without producing any truncation error and artificial flux (PGFE). The multi-block sigma–coordinate can easily increase the depth-direction resolution of the sediment transport module in the sub-regions, without the aggregation of computational points in the shallow areas which may be caused by using high resolution over the entire domain. The model is beneficial for long-term simulation of morphological evaluations in lakes where the bed slope near delta region (the sedimentary area which forms where a river enters a lake/ocean) is mostly steep, and delta keeps advancing down the lake. The multi-block sigma approach at the block interface, where the number of horizontal layers varies, allocates the flux to the neighboring cells according to two essential factors, namely “the common border length” and “satisfying continuity” which lead to defining the virtual cells. A series of numerical tests have been performed. Comparison between the numerical results, the analytical solutions, and the experimental data demonstrated an appreciable accuracy, a satisfactory performance and the efficiency of this scheme.