This paper develops a time-split linearized explicit/implicit approach for solving a two-dimensional hydrodynamic flow model with appropriate initial and boundary conditions. The time-split technique is employed to upwind the convection term and to treat the friction slope so that the numerical oscillations and stability are well controlled. A suitable time step restriction for stability and convergence accurate of the new algorithm is established using the $L^{\infty}(0,T; L^{2})$-norm. Under a time step requirement, some numerical examples confirm the theoretical studies and suggest that the proposed computational technique is spatial fourth-order accurate and temporal second-order convergent. An application to floods observed in the far north region of Cameroon is considered and discussed.

翻译：本文发展了一种时间分裂线性化显式/隐式方法，用于求解具有适当初始和边界条件的二维水动力流动模型。该时间分裂技术用于对对流项进行迎风处理并处理摩擦坡度，从而有效控制数值振荡和稳定性。利用 $L^{\infty}(0,T; L^{2})$-范数，为所提新算法的稳定性和收敛精度建立了合适的时间步长限制条件。在满足时间步长要求的前提下，若干数值算例验证了理论分析，并表明所提出的计算技术在空间上具有四阶精度，在时间上具有二阶收敛性。本文还考虑并讨论了该方法在喀麦隆极北地区观测洪水中的应用。