Dry and wet boundary treatment and improvement of a TVD‐MacCormack scheme in shallow water flow

Abstract To solve shallow water equation, this paper proposes a simple and easy‐to‐operate dry‐wet boundary treatment method based on the total variation diminishing (TVD)‐ MacCormack scheme. The method requires to judge dry and wet nodes before the calculation of prediction step and correction step, respectively. Then, the dry nodes are fictitiously celled and the topographic variables are reset. Moreover, previous researches show that when the same differential scheme was used, the left and right traveling waves showed over predicted computational fluxes during the downstream dry bed flow evolution, which led to distorted values and non‐real physical phenomena. To solve the problem, the difference scheme for prediction step and correction step is modified, and a new finite difference scheme improvement method is proposed. Finally, the numerical solutions are compared with the analytical solution results by five classical cases to verify the rationality of the proposed method in this paper.