The present work proposes a new morphodynamic model for flow simulation in open channels. The governing one dimensional (1D) shallow water equations along with the Exner sediment continuity equation are solved here using coupled approach. A TVD based MacCormack predictor corrector method is used here for solution of the coupled governing equations. The developed numerical model is used to replicate several test cases of known experimental and approximate solutions. These cases include bed aggradation due to sediment overloading, bed degradation due to sediment shut-off, dam break flow over erodible bed and movable bump due to subcritical and transcritical flows. The results obtained are found to be excellent and free from oscillations near sharp gradient. The numerical model is also found to be capable of capturing the wave-fronts of both water surface and bed sediment. Quantitative analysis of the results in terms of two statistical parameters establishes the potential of the present model in more complicated practical problems.

本工作提出了一种新的形态动力学模型，用于明渠中的水流模拟。在这里使用耦合方法求解控制的一维（1D）浅水方程以及埃克纳沉积物连续性方程。这里使用基于TVD的MacCormack预测器校正器方法来求解耦合控制方程。开发的数值模型用于复制已知实验和近似解的多个测试用例。这些情况包括由于沉积物超载导致的床层凝结，由于沉积物的关闭而导致的床层退化，易蚀床层上的大坝溃决流以及由于亚临界和跨临界流而引起的活动颠簸。发现获得的结果是极好的，并且没有接近陡峭梯度的振荡。还发现该数值模型能够捕获水面和床底沉积物的波前。根据两个统计参数对结果进行定量分析，建立了本模型在更复杂的实际问题中的潜力。