CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

BCs of hyperbolic Shallow Water Equation

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   November 9, 2000, 07:20
Default BCs of hyperbolic Shallow Water Equation
  #1
Kang, S. K.
Guest
 
Posts: n/a
I am a graduate student who studies hydrodynamics. I want to solve hyperbolic 2-D shallow water equations (1 continuity eq, 2 momentum eqs) by Finite Volume Method using limiter with unstructued grid. For 1-D Saint-Venant equation, when flow is subcritical we specify 1 boundary condition (discharge or flow velocity) at upstream end and another one(water depth) is calculated from characteristic equation at upstream end. I got to know it becomes complicated when the problem is 2D. The characeristic line is no longer expressed in 2D plane. In 2D shallow water equation the unknowns are u, v, h (u,v=x,y velocity; h=water depth). For subcritical flow two variables(u, v) are known and one variable(h) us unknown at inflow boundary. How should I determine h ?
  Reply With Quote

Old   November 20, 2000, 12:15
Default Re: BCs of hyperbolic Shallow Water Equation
  #2
Sergei Zhubrin
Guest
 
Posts: n/a
You might find the answer by looking at a few demonstration cases describing the main details of how PHOENICS , finite-volume code, has been taught to deal with Shallow Water Equations for the sub- and super-critical flows to simulate:
  • <a href="http://www.simuserve.com/cfd-shop/uslibr/freesurf/fs4.htm">

    Water elevation in an open U-bend</a>
  • <a href="http://www.simuserve.com/cfd-shop/uslibr/freesurf/fs5.htm">

    Whirlpool in a pond</a> and
  • <a href="http://www.simuserve.com/cfd-shop/uslibr/freesurf/fs6.htm">

    Hydraulic jump</a>
ROSA, one of the PHOENICS Special Purpose Programes , makes use of this technique to simulate the dispersion of oil spills and other chemicals in natural rivers.
Regards
Sergei Zhubrin
  Reply With Quote

Old   November 20, 2000, 23:33
Default Re: BCs of hyperbolic Shallow Water Equation
  #3
Kang, S. K.
Guest
 
Posts: n/a
Thanks for your reply. I visited PHOENICS sites that you said. But the demonstration cases also used fixed flux at inlet boundary,ie. all (3) boundary values are imposed at inlet boundary by Dirichlet type. Anyway, I greatly appreciate your answer.

Regards

Kang, S. K.
  Reply With Quote

Old   November 21, 2000, 05:16
Default Re: BCs of hyperbolic Shallow Water Equation
  #4
Sergei Zhubrin
Guest
 
Posts: n/a
If one introduces the terms representing the elevation of bed above arbitrary horizontal datum as a momentum sources, the depths at the inlet and outlet planes can be calculated as a part of the solution without imposing the fixed inlet fluxes.
The corresponding changes of BC are straightforward to derive and implement.
Regards
Sergei Zhubrin
  Reply With Quote

Old   November 21, 2000, 22:20
Default Re: BCs of hyperbolic Shallow Water Equation
  #5
Kang, S. K.
Guest
 
Posts: n/a
Then, can you please send me the derivations of the terms for super- and sub-critical case privately.

Thanks for your reply.

Regards

Kang, S. K.
  Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Vorticity in inviscid shallow water equations sonsiest Main CFD Forum 0 June 7, 2011 14:10
Problems with BCs in muliphase flow with water falling from a reservoir Paul_l FLUENT 2 March 11, 2011 05:59
Looking for "numerical methods for shallow water flows" book novan tofany Lounge 0 February 10, 2011 19:28
Constant velocity of the material Sas CFX 15 July 13, 2010 08:56
mass flow in is not equal to mass flow out saii CFX 2 September 18, 2009 08:07


All times are GMT -4. The time now is 14:04.