In recent decades, a few Godunov-type, finite volume two-dimensional (2D) unstructured grid, coupled flow, and sediment models (GF2DUCM) have been developed for flows over erodible beds. These kinds of models are generally analyzed as a Vertex Model (VM) that define topography at the cell vertex, which can lead to the non-conservation of mass regarding flow, sediment, and bed evolution. Here, a full cell-cantered variable storage method (Central Model or CM) is applied as the solution of the GF2DUCM. In this method, terrain elevation is defined at the cell centroids; this accurately describes the physical relations between the water depth and topography deformation. This approach can fully eliminate calculation errors in topography deformation at local cells caused by the interpolation of topography deformation at the cell vertex, and reduced uncertainty in the computation of the GF2DUCM. The model performance is systematically tested using a series of laboratory experiments, which demonstrate the mass conservation feature and high accuracy in reproducing hydrodynamic and morphological processes.

近几十年来，已经开发了一些Godunov型有限体积二维（2D）非结构化网格，耦合流和沉积物模型（GF2DUCM），用于侵蚀床上方的流。通常将这些类型的模型作为顶点模型（VM）进行分析，该模型定义了单元顶点的形貌，这可能导致流量，沉积物和床层演化方面的质量守恒。在此，将完整的单元格固定变量存储方法（中央模型或CM）用作GF2DUCM的解决方案。在这种方法中，在单元质心处定义了地形高程。这准确地描述了水深和地形变形之间的物理关系。这种方法可以完全消除由单元顶点处的地形变形插值引起的局部单元的地形变形的计算误差，并减少了GF2DUCM计算的不确定性。使用一系列实验室实验系统地测试了模型的性能，这些实验证明了质量守恒特征和再现水动力和形态过程的高精度。