In this work, a novel 2D depth-integrated numerical model for highly sediment-laden shallow flows over non-uniform erodible beds is presented, including variable density and exchange between the bed layer and the water–sediment mixture flow. The system of equations is formed by the 2D conservation equations for the mass and momentum of the mixture, the mass conservation equation for the different sediment size-classes transported in the flow and the bed evolution equation. The depth-averaged mixture density varies according to the volumetric concentration of the different sediment size-classes that can be incorporated from the bed to the flow and transported as suspended materials. The rheological behaviour of the flow is directly controlled by the properties of the mixture. A new x-split augmented Roe (xA-Roe) scheme is derived to solve the coupled flow and suspended solid-phase equations in both structured and unstructured meshes. The numerical scheme is defined to properly include density variations and momentum source terms, retaining a well-balanced flux formulation in steady states and the correct treatment of the wet–dry fronts. The numerical scheme is assessed with steady and transient cases involving highly sediment-laden flows, demonstrating its accuracy, stability and robustness in the presence of complex bed topography, wetting–drying fronts and rapid morphological changes.

在这项工作中，提出了一种新颖的二维深度积分数值模型，用于在非均匀易蚀床层上高度含沙的浅水流，包括可变的密度以及床层与水沙混合物流之间的交换。方程组由混合物的质量和动量的2D守恒方程，在流中传输的不同沉积物尺寸类别的质量守恒方程和床层演化方程组成。深度平均混合物密度根据不同沉积物尺寸类别的体积浓度而变化，这些沉积物尺寸类别可以从床层引入流中并作为悬浮物运输。流动的流变行为直接由混合物的性质控制。推导了一种新的x分裂增强Roe（xA-Roe）方案，以解决结构化和非结构化网格中的耦合流动方程和悬浮固相方程。定义数值方案时要适当地包括密度变化和动量源项，在稳态下保持良好平衡的通量公式，并正确处理湿干前沿。该数值方案在稳态和瞬态情况下进行评估，涉及高含沙量的水流，证明了其在复杂的床层地形，湿润干燥前沿和快速形态变化的情况下的准确性，稳定性和鲁棒性。在稳态下保持良好平衡的助焊剂配方，并正确处理湿干前沿。该数值方案在稳态和瞬态情况下进行评估，涉及高含沙量的水流，证明了其在复杂的床层地形，湿润干燥前沿和快速形态变化的情况下的准确性，稳定性和鲁棒性。在稳态下保持良好平衡的助焊剂配方，并正确处理湿干前沿。该数值方案在稳态和瞬态情况下进行评估，涉及高含沙量的水流，证明了其在复杂的床层地形，湿润干燥前沿和快速形态变化的情况下的准确性，稳定性和鲁棒性。