A robust time-split linearized explicit/implicit technique for solving a two-dimensional hydrodynamic model: an application to floods in Cameroon far north region

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.