HYDRODYNAMICS OF LAKE ITASY: OPTIMIZING A NUMERICAL MODEL FOR STABILITY AND MASS CONSERVATION USING ADAPTIVE COURANT-FRIEDRICHS-LEWY CRITERION

Abstract

Hydrodynamic modeling of inland water bodies is crucial for effective water resource management, flood forecasting, and environmental monitoring. This study focuses on Lake Itasy, Madagascar, and aims to enhance the numerical stability and mass conservation of a shallow water equation (SWE)-based hydrodynamic model. The methodology combines remote sensing (NDWI on Sentinel-2 imagery), geospatial analysis (SRTM DEM), and numerical simulation, integrating physical processes such as tributary inflows, precipitation, evaporation, wind forcing, and outlet boundary conditions. Satellite data analysis revealed a reduction in lake surface area in 2024 compared to 2023, providing a relevant hydrological context. A key innovation lies in the implementation of an adaptive Courant-Friedrichs-Lewy (CFL) criterion, which dynamically adjusts the time step to maintain stability without compromising computational efficiency. The results demonstrate that a CFL value of 0.01 ensures high accuracy and numerical stability, albeit at the cost of increased computation time. Overall, this work establishes a robust and reliable modeling framework, offering a valuable tool for future hydrological studies and sustainable water management in the Itasy region.