Abstract: To address the issue of moving grids adapted to intense bank erosion in a wandering river reach, a two-dimensional mathematical model is developed based on moving grids and an orthogonal curvilinear body-fitted coordinate system using the arbitrary Lagrangian-Eulerian method, aimed at the unsteady flow and sediment transport in a wandering reach of the lower Yellow River. Then, for the grid moving terms of the basic equations of flow and sediment transport under the orthogonal curvilinear body-fitted coordinates, a new formula is derived that allows the equations to obey the geometric conservation law. We also develop an approach to moving the grid nodes on the moving boundary through an algorithm of transfinite arc length interpolation. Finally, we verify this new model against the 2013 measurements of the wandering reach between Huayuankou and Gaocun. The results demonstrate that this grids-moving model is able to reproduce flow and sediment transport, river bed aggradation and degradation, and bank-floodplain scour and retreat in the studied wandering reach, and that it is also applicable to the other lower Yellow River reaches.

Key words: river dynamics, bank erosion and collapse, two dimensional water-sediment mathematical model, moving grids, arbitrary Lagrangian-Eulerian method, wandering reach, lower Yellow River