Numerical modeling of free-surface flow over a mobile bed with predominantly bedload sediment transport can be done by solving the shallow water and Exner equations using coupled and splitting approaches. The coupled method uses a coupling of the governing equations at the same time step leading to a non-conservative solution. The splitting method solves the Exner and the shallow water equations in a separate manner, and is only capable of modeling weak free-surface and bedload interactions. In the current study, an extended version of a Godunov-type wave propagation algorithm is presented for modeling of morphodynamic systems using both coupled and splitting approaches. In the introduced coupled method the entire morphodynamic system is solved in the form of a conservation law. For the splitting technique, a new wave Riemann decomposition is defined which enables the scheme to be utilized for mild and strong interactions. To consider the bedload sediment discharge within the Exner equation, the Smart and Meyer-Peter & Müller formulae are used. It was found that the coupled solution gives accurate predictions for all investigated flow regimes including propagation over a dry-state using a Courant-Friedrichs-Lewy (CFL) number equal to 0.6. Furthermore, the splitting method was able to model all flow regimes with a lower CFL number of 0.3.

通过使用耦合和分裂方法求解浅水方程和Exner方程，可以对流动床中主要以床荷输沙为主的自由表面流进行数值模拟。耦合方法在同一时间步使用控制方程的耦合，从而导致非保守解。分裂方法以单独的方式求解Exner方程和浅水方程，并且仅能够对薄弱的自由表面和床荷相互作用进行建模。在当前的研究中，提出了Godunov型波传播算法的扩展版本，用于使用耦合和分裂方法对形态动力学系统进行建模。在引入的耦合方法中，以守恒律的形式解决了整个形态动力学系统。对于分割技术，定义了新的波黎曼分解，从而使该方案可用于温和强烈的相互作用。为了考虑Exner方程中的床层沉积物排放，使用了Smart和Meyer-Peter＆Müller公式。已发现，耦合解决方案使用等于0.6的Courant-Friedrichs-Lewy（CFL）值对所有研究的流态（包括在干燥状态下的传播）给出准确的预测。此外，分裂方法能够以较低的CFL值为0.3建模所有流动状态。已经发现，耦合解决方案使用等于0.6的Courant-Friedrichs-Lewy（CFL）数对所有研究的流态（包括在干燥状态下的传播）给出准确的预测。此外，分裂方法能够以较低的CFL值为0.3建模所有流动状态。已经发现，耦合解决方案使用等于0.6的Courant-Friedrichs-Lewy（CFL）数对所有研究的流态（包括在干燥状态下的传播）给出准确的预测。此外，分裂方法能够以较低的CFL值为0.3建模所有流动状态。