MIKE 11 IntroductionNovember 2002 Part 1

Introduction to MIKE 11

Part 1• General• Hydrodynamics within MIKE 11

– Basic Equations– Flow Types

• Numerical Scheme

MIKE 11 IntroductionNovember 2002 Part 1

General

• Simulation of 1D Flow in– Estuaries,– Rivers and – Irrigation Systems, etc.

• Application for Inland Water System– Design, – Management and – Operation

MIKE 11 IntroductionNovember 2002 Part 1

Main Modules

• Rainfall-Runoff

• Hydrodynamics

• Advection-Dispersion and Cohesive Sediment

• Water Quality

• Non Cohesive Sediment Transport

MIKE 11 IntroductionNovember 2002 Part 1

Basic Equations

Assumptions• Constant Density• Small Bed Slope• Large Wave Length Compared to Water Depth• Uniform Velocity over the Cross Section• No Vertical Acceleration

MIKE 11 IntroductionNovember 2002 Part 1

de Saint Venant Equations

• (Mass and Momentum Conservation):

0

q

2

2

ARC

QgQ

x

hgA

x

AQ

t

Q

t

A

x

Q

where , Q - discharge, m3 s-1

A - flow area, m2

q - lateral flow, m2s-1

h - depth above datum, m C - Chezy resistance coefficient, m1/2s-1

R - hydraulic radius, m - momentum distribution coefficient

MIKE 11 IntroductionNovember 2002 Part 1

Variables

• Independent variables• space x• time t

• Dependent variables• discharge Q• water level h

• All other variables are function of the independent or dependent variables

MIKE 11 IntroductionNovember 2002 Part 1

Flow Types

– Neglect first two terms

• Diffusive wave ( backwater analysis)

0

2

2

ARC

QgQ

x

hgA

x

AQ

t

Q

MIKE 11 IntroductionNovember 2002 Part 1

Flow Types

– Neglect three terms

• Kinematic wave (relatively steep rivers without backwater effects)

0

2

2

ARC

QgQ

x

hgA

x

AQ

t

Q

MIKE 11 IntroductionNovember 2002 Part 1

Finite Difference Method

• Discretisation in time and space

t

xx

t

x nn

1

MIKE 11 IntroductionNovember 2002 Part 1

Numerical Scheme

•Equations are transformed to a set of implicit finite difference equations over a computational grid– alternating Q - and h points, where Q and h

are computed at each time step

MIKE 11 IntroductionNovember 2002 Part 1

Numerical Scheme

Example of discretization

j

nj

nj

nj

nj

x

QQQQ

x

Q

222

1111

11

• Implicit Finite Difference Scheme (Abbott-Ionescu)• Continuity equation - h centered• Momentum equation - Q centered

MIKE 11 IntroductionNovember 2002 Part 1

Boundary Conditions

• Boundary conditions– external boundary conditions - upstream and

downstream;– internal “boundary conditions” - hydraulic

structures ( here Saint Venant equation are not applicable)

• Initial condition – time t=0

MIKE 11 IntroductionNovember 2002 Part 1

Boundary Conditions

• Typical upstream boundary conditions– constant discharge from a reservoir– a discharge hydrograph of a specific event

• Typical downstream boundary conditions– constant water level– time series of water level ( tidal cycle)– a reliable rating curve ( only to be used with

downstream boundaries)

MIKE 11 IntroductionNovember 2002 Part 1

Limitations

• Hydraulic jump can not be modelled

• Stability conditions– Sufficiently fine topographic resolution (x)– time step

• fine enough for accurate representation of a wave• at structure smaller time step is required• Courant condition to determine time step

1

x

ghtCr