Development of modified beta distribution tailored for channel application at inflow boundary

Abstract

Accurate representation of inflow boundary conditions is critical for hydrodynamic simulations in natural and open channel systems, where irregular topographies often result in complex flow patterns. Traditional methods, such as uniform or simplified velocity distributions, fail to capture the variability of flow velocities and water depths along the channel cross-section. This limitation leads to inaccurate predictions, particularly in simulations involving pollutant transport, sediment movement, and flood risk assessments. To address these challenges, this study proposes a Modified Beta Distribution (MBD) tailored to account for varying water depths at the inflow boundary. Building upon the traditional Beta Distribution, the MBD introduces a depth-weighting factor, ensuring that inflow discharge and velocity profiles are accurately represented in channels with irregular topography. The model was validated through simulations on rectangular, triangular, parabolic, and asymmetric channel cross-sections, demonstrating improved accuracy and stability compared to existing methods. The results showed that MBD outperformed traditional methods in channels with non-uniform cross-sections, significantly reducing velocity prediction errors. This enhanced accuracy improves the simulation of flow characteristics, making the MBD an essential tool for environmental modeling, urban flood management, and water resource engineering.