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

TL;DR

This paper introduces a robust time-split explicit/implicit numerical method for 2D hydrodynamic models, demonstrating stability, accuracy, and application to flood simulation in Cameroon’s far north region.

Contribution

The paper presents a new stable, accurate, and efficient time-split explicit/implicit scheme for 2D hydrodynamic modeling with real flood application in Cameroon.

Findings

The method is spatial fourth-order accurate.

The method is temporal second-order convergent.

Numerical examples confirm stability and accuracy.

Abstract

This paper deals with a time-split 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 Cameroon far north region is considered and discussed.