Dynamic Channel Routing Preissmann Scheme
Dynamic Channel Routing Preissmann Scheme unconditionally stable for >=0.5 second-order accurate if 0.5, first order otherwise not valid for transcritical flow variations of Preissman scheme used in many models focus on FLDWAV here...
Flow is 1-D: flow characteristics (depth, velocity, etc.) vary only in the longitudinal x-direction of the channel. Water surface is horizontal across any section perpendicular to the longitudinal axis. Flow is gradually varied with hydrostatic pressure prevailing at all points in the flow. Longitudinal axis of the channel can be approximated by a straight line. Bottom slope of the channel is small, i.e., tan h = sin h. ( h =10% yields 1.5% variation). Bed of the channel is fixed, i.e., no scouring or deposition is assumed to occur. Resistance coefficient for steady uniform turbulent flow is considered applicable and an empirical resistance equation such as the Manning equation describes the resistance effect. Flow is incompressible and homogeneous in density. Assumptions in St. Venant Equations
Continuity Momentum
UPSTREAM BOUNDARY Flow or WSEL T.S. DOWNSTREAM BOUNDARY Flow, WSEL, or tide T.S or Rating Curve INITIAL CONDITIONS Initial flow & elevation at each cross section location; Lateral Flow, pool elevation, gate control switch at each location x DtDt DxDx ii+1 ContinuityMomentum t j j+1 t=0 Computational Grid
X X X X X X X X X UB … C1 … M1 … C2 … M2 … C3 … M3 … DB … -RUB -RC1 -RM1 -RC2 -RM2 -RC3 -RM3 -RDB = Dh1Dh1 DQ2DQ2 DQ1DQ1 Dh2Dh2 Dh4Dh4 Dh3Dh3 DQ3DQ3 DQ4DQ4 Matrix Format solved using Newton-Raphson method
The s parameter “filters” the inertial terms of the momentum equation based on the Froude number so that this equation transitions between the dynamic and diffusion equation in transition region. Local Partial Inertia
Expanded Equations Basic: DWOPER: off-channel storage, expansion/contraction, lateral inflow, wind: DAMBRK: add sinuosity, mud/debris flow, no wind: FLDWAV: all capabilities above:
Stage-Discharge Relationship Channel Properties: Geometry Slope Roughness Hydrograph Properties: Peak Flow Time to Peak Flow Average Flow Information Requirements
h B4B4 B3B3 B2B2 B1B1 BO 4 Off-channel storage Tributary River Plan View Datum B5B5 BO 5 BO= 0 Active Dead Storage Cross Section A-A Plan view of river with active and dead storage areas, and cross section view. A A
B5B5 B4B4 B3B3 B2B2 HS 5 HS 4 HS 3 HS 2 HS 1 Actual Cross Section Symmetrical Cross Section Top Width (B) Elevation (HS) Top Width vs. Elevation Curve Each cross section is cast as a top width vs. elevation curve. The shape of the actual cross section is not retained.
Sinuosity Coefficient: s 1 = L 1 /x 1 Right Floodplain Main Channel B5B5 B4B4 B3B3 B2B2 HS 5 HS 4 HS 3 HS 2 HS 1 Actual Cross Section BL 3 BR 3 BL 4 BR 4 BL 5 BR 5 The actual cross section is divided into three components: main channel, left floodplain and right floodplain. Each component is modeled as a separate channel using sinuosity and conveyance. Floodplains and Sinuosity
Single Channel River & Tributaries Canal & Distributaries River Delta Network Dendritic (tree-type) System Channel Configurations
1.Routes outflow hydrograph hydraulically through downstream river/valley system using expanded form of 1-D Saint-Venant equations Considers effects of: downstream dams, bridges, levees, tributaries, off-channel storage areas, river sinuosity, backwater from tides Flow may be Newtonian (water) or non-Newtonian (mud/debris) Produces output of: a. High water profiles along valley b. Flood arrival times c. Flow/stage/velocity hydrographs Exports data needed to generate flood forecast map: a. Channel location (river mile and latitude/longitude) b. Channel invert profile c. Water surface profile for area to be mapped d. Channel top width corresponding to water surface elevations in profiles FLDWAV Capabilities
B LQ B RC Q t Q t LQ B L B Tidal Boundary LEGEND B - bridge RC - rating curve - reservoir and dam LQ- lateral inflow - levee overtopping and/or failure L - lock and dam manually operated