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Dynamic Channel Routing. Preissmann Scheme. Dynamic Channel Routing. Preissmann Scheme. unconditionally stable for q >=0.5 second-order accurate if q = f = 0.5, first order otherwise not valid for transcritical flow variations of Preissman scheme used in many models.

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Dynamic Channel Routing

Preissmann Scheme


Dynamic Channel Routing

Preissmann Scheme

  • unconditionally stable for q>=0.5

  • second-order accurate if q = f = 0.5, first order otherwise

  • not valid for transcritical flow

  • variations of Preissman scheme used in many models

focus on FLDWAV here...


Assumptions in St. Venant Equations

  • 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.


Continuity

Momentum


Dt

Momentum

Continuity

Dx

Computational Grid

t

1

2

3

4

5

6

7

DOWNSTREAM BOUNDARY

Flow, WSEL, or tide T.S or Rating Curve

UPSTREAM BOUNDARY

Flow or WSEL T.S.

j+1

j

x

t=0

i

i+1

INITIAL CONDITIONS

Initial flow & elevation at each cross section location;

Lateral Flow, pool elevation, gate control switch at each location


Matrix Format

UB …

C1 …

M1 …

C2 …

M2 …

C3 …

M3 …

DB …

X X

X X X X

X X X X

X X X X

X X X X

X X X X

X X X X

X X

Dh1

-RUB

-RC1

-RM1

-RC2

-RM2

-RC3

-RM3

-RDB

DQ1

Dh2

DQ2

=

Dh3

DQ3

Dh4

DQ4

solved using Newton-Raphson method


Local Partial Inertia

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.


Expanded Equations

Basic:

DWOPER: off-channel storage, expansion/contraction, lateral inflow, wind:

DAMBRK: add sinuosity, mud/debris flow, no wind:

FLDWAV: all capabilities above:


Information Requirements

Stage-Discharge Relationship

Channel Properties:

  • Geometry

  • Slope

  • Roughness

    Hydrograph Properties:

  • Peak Flow

  • Time to Peak Flow

  • Average Flow


BO

= 0

Plan View

A

River

Off-channel storage

A

Tributary

B5

BO5

BO4

B4

B3

Active

h

B2

Dead Storage

B1

Datum

Cross Section A-A

Plan view of river with active and dead storage areas, and cross section view.


Actual Cross Section

B5

HS5

B4

HS4

B3

HS3

B2

HS2

HS1

Each cross section is cast as a top width vs. elevation curve. The shape of the actual cross section is not retained.

Top Width vs. Elevation Curve

Symmetrical Cross Section

Elevation (HS)

Top Width (B)


L

1

x

1

Left Floodplain

L

x

2

2

Floodplains and Sinuosity

Main Channel

Actual Cross Section

B5

BL5

BR5

HS5

B4

BL4

BR4

Right Floodplain

HS4

BL3

BR3

B3

HS3

B2

HS2

HS1

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.

Sinuosity Coefficient:

s1 = L1/x1


Channel Configurations

Single Channel

Dendritic (tree-type) System

River & Tributaries

Canal & Distributaries

River Delta

Network


FLDWAV Capabilities

  • 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


LQ

Q

t

LQ

Q

B

t

B

RC

RC

LEGEND

B - bridge

RC - rating curve

- reservoir and dam

- lateral inflow

LQ

- levee overtopping and/or failure

B

L - lock and dam manually operated

L

B

Tidal Boundary


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