Instituto Superior Técnico instituto superior técnico Lake Ha!Ha! Case Study mathematical model and results Instituto Superior Técnico Rui Ferreira João Leal A. H. Cardoso A. B. Almeida instituto superior técnico

instituto superior técnico Introduction Structure of the presentation: geometry for 1D computations model presentation initial and boundary conditions flood propagation over mobile bed conclusions and discussion instituto superior técnico

instituto superior técnico Geomertry raw data (362 sections with a 10 m discretization) is converted into trapezoidal sections elevation and width of the thalweg and inverse bank slope are retained m 1 Bf instituto superior técnico

instituto superior técnico Geomertry slope is corrected in order to eliminate counter-inclined reaches thalweg width and bank slope are subjected to a moving average and splining smoothening process a linear interpolation process generates sections every Dx = 10 m instituto superior técnico

instituto superior técnico Geomertry River Ha!Ha! is divided in seven reaches (roughly at bedrock emergence points) instituto superior técnico

instituto superior técnico Mathematical Model conservation equations closure equations water mass total momentum sediment mass transport layer bed load concentration total concentration bed shear stress characterisitc diameter of the sediment: ds = 0.01 m instituto superior técnico

instituto superior técnico Mathematical Model numerical discretization: flux vector splitting scheme with Roe approximations (first order version only) for the equations of conservation of the water constituent box scheme for the equation of conservation of sediment uncoupled model with water depth correction at the end of each time step instituto superior técnico

Initial & Boundary Conditions upstream: combined hydrograph at the upstream section of reach A sediment hydrograph in every generic reach downstream: transmissive boundary condition downstream for the water depth outflow hydrograph of each reach is used as upstream hydrograph for the following reach note: method of characteristics is used on both boundaries to determine the remaining hydrodynamic variables instituto superior técnico

Initial & Boundary Conditions initial condition is a steady flow over fixed bed and Q = 35 m3/s fixed bed flow evolves from finite depth (0.5 m typically), zero discharge initial flow after a warm-up run note that subcritical and supercritical flow coexist separated by hydraulic jumps Ks = 75 m1/3s-1 instituto superior técnico

instituto superior técnico Flood Propagation water depths variation of bed elevation note that subcritical flow disapears when mobile flow simulation starts instituto superior técnico

instituto superior técnico Flood Propagation longitudinal profiles during the maximum discharge instituto superior técnico

Conclusions & Discussion difficulties encountered steady flow difficult to attain downstream boundary condition is a source of non-physical waves large simulation time instituto superior técnico