An implicit friction source term treatment for overland flow simulation using shallow water flow model

Aiming at resolving the numerical problems caused by the improper friction source term treatment when simulating overland flow using 2D shallow water flow models, a proposed implicit method computing the friction source term is developed in this work. The method is able to not only accurately evaluate the tricky thin overland flow by considering the flow velocity varying in a single time step, but also eliminates the redundant iterations for regular implicit approach through converting the implicit scheme to an explicit equation. It is therefore an improved one in terms of accuracy and efficiency comparing to the existing methods. Furthermore, it is an independent part and can be straightforwardly and universally incorporated into any FVM based shallow water flow model. Such performances are validated against three test cases involving theoretical and practical overland flow problems. The results prove the proposed method treating friction source term could simulate overland flow problems in a relatively more accurate and efficient way, and therefore can effectively help extend the applicability of the shallow water models reliably computing both the open channel and overland flows.