Moving beds represented by immersed boundaries: numerical experiments using large eddy simulation

Abstract

The Immerse Boundary Method (IBM) was used to evaluate the sediment transport over deformable beds. Large Eddy Simulation (LES) procedures were used for the mathematical treatment of turbulence, and the advection-diffusion equation was used to calculate sediment concentration. The Finite Differences Method with staggered grid was applied for the numerical solution of the governing equations (filtered Navier-Stokes, Continuity and advection-diffusion equations). Spatial derivatives were discretized using second order centered differences. A second order explicit Adams-Bashforth scheme was used for the time evolution in the advection-diffusion equation, while a fourth order Adams-Bashforth scheme was used for the filtered Navier-Stokes equations. The numerical simulation reproduced flow structures like large eddies after the dune crests and counter-rotative vortices, which are important in sediment transport. Resuspension fluxes and sedimentation (dependent on particle concentration) were calculated using equations proposed in this study. The deformations of the bed caused by erosion and deposition may be well followed through the present procedures, showing that this methodology is adequate to evaluate bed modifications and sediment transport in alluvial flows.