An Unconditionally Stable Explicit Finite Difference Method for a Non-Dimensional Mathematical Model of Shoreline Evolution with a Twin Groins Structure

Abstract

The development of a more effective model and the prediction of trends in shorelines were the two goals of this study. For simulations of shoreline evolution utilizing the straight twin groin structure, we used two mathematical models. A one-dimensional evolution model makes up the initial model. The first model is transformed into a non-dimensional evolution model in the second model. We propose a method for transforming one-dimensional models into non-dimensional models, that involves creating initial and boundary conditions for each model. The forward time centered space (FTCS) technique and the Saulyev finite difference technique were applied to approximately represent shoreline evolution each year. Their simulation results demonstrate that when the engineering structure was built on the nearby shorelines, shoreline evolution accelerated annually. As the Saulyev finite difference technique is not restricted by the stability conditions, it produces better simulations.