THE SIMULATION OF ONE-DIMENSIONAL SHALLOW WATER WAVE EQUATION WITH MACCORMACK SCHEMES

Abstract

Many practical problems can be modeled using the one-dimensional shallow water wave equation. Therefore, the solution to the one-dimensional shallow water wave equation will be discussed to solve this problem. The research method used was the study of literature related to the shallow water wave equation and its solution method. The one-dimensional shallow water wave equation can be derived from the law of conservation of mass and the law of conservation of momentum. In this study, one of the finite difference methods will be discussed, namely the MacCormack method. The MacCormack method consists of two steps, namely the predictor and corrector steps. The MacCormack method was used to perform numerical simulations of the pond and tsunami models for one-dimensional (1D) shallow water wave equations with flat and non-flat topography. The simulation results showed that the channel's topography could affect the water surface's height and velocity. At the same time, a channel with a non-flat topography had a slower water velocity than the water velocity of a channel with a flat topography.