Study and Analysis of Flow Regime Transitions in Straight Channels Using the Lattice Boltzmann Method for Shallow Water

The objective of this work is to examine the unexplored dynamics of flow regime changes in linear channels, with a specific emphasis on the impact of relaxation time, channel width, and external forces on the shift from laminar to turbulent flow.This study intends to improve understanding of how the parameters associated with the Lattice Boltzmann model for shallow water equations (LABSWE) can be modified to change flow regimes using a D2Q9 approach for domain discretization.Our investigations demonstrate that a decrease in relaxation time prompts a shift from a parabolic (laminar) to a logarithmic (turbulent) velocity distribution, evidenced by significant fluctuations in the central channel velocity and an increase in the Reynolds number.This study also reveals that broader channel widths lead to turbulent flow, marking a notable departure from the laminar flow observed in narrower settings.The application of external forces further intensifies this transition, showcasing their pivotal role in influencing flow regimes.This study presents significant scientific novelty by offering new insights into the conditions that foster flow regime transitions, thereby addressing a gap in the current fluid mechanics literature.Our findings suggest practical ways to manipulate these factors to optimize flow behaviors, providing valuable insights for the engineering and environmental management of water systems.