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

1D wave equation

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

Reply
 
LinkBack Thread Tools Display Modes
Old   October 27, 2003, 14:44
Default 1D wave equation
  #1
rvndr
Guest
 
Posts: n/a
Hi

I am trying to solve 1D wave equation using eulers explicit scheme.After Discretization I am getting the following equation.

[Ui^(n+1)]=[v^2*U(i-1)^n]+[2(1-v^2)*Ui^n]+[v^2*U(i+1)^n]-[Ui^(n-1)].

The problem that I am facing is with the last term -Ui^(n-1).Because the values at (n-1) level are not known.We know only boundary conditions at nth level and are trying to find out at n+1 level.Then how to solve this equation.

Where v=c*(delta t/delta x);

Any help in this regard is higly solicilated.Thanks in advance.

regards rvndr

  Reply With Quote

Old   October 28, 2003, 03:43
Default Re: 1D wave equation
  #2
Roman
Guest
 
Posts: n/a
at first time stpe say n=1 i.e n+1=2,n=1,n-1=0. You should use value of variable at n at n-1 are equal.One you solve everything at that time step the next time n=2 i.e n+1=3,n=2,n-1=1. Now you value of variable in n-1=1 and n=2 so you can proceed. Roman
  Reply With Quote

Old   October 30, 2003, 09:30
Default Re: 1D wave equation
  #3
rvndr
Guest
 
Posts: n/a
thanks..............i did the same way
  Reply With Quote

Old   November 3, 2003, 20:01
Default Re: 1D wave equation
  #4
Peter
Guest
 
Posts: n/a
"You should use value of variable at n at n-1 are equal."

If you do that then you've effectively implemented u(x,0)=f(x) and u_t(x,0)=0 where the u_t equation is discretized with a one-sided approximation to the time derivative. Are these the initial conditions the original poster wanted ?
  Reply With Quote

Old   November 5, 2003, 05:13
Default Re: 1D wave equation
  #5
Tom
Guest
 
Posts: n/a
The easiest way to initialise the problem

u_tt = c^2.u_xx with u=f(x), u_t = g(x) at t=0

is to use Taylor series

u = u(x,0) + dt.u_t(x,0) + (1/2)dt^2.u_tt + O(dt^3)

~ f(x) + dt.g(x) + (1/2)dt^3.c^2.f''(x) + O(dt^3)

you can use this formula to obtain u at time level n=1,

Tom.

  Reply With Quote

Old   December 5, 2003, 21:28
Default Re: 1D wave equation
  #6
vasanth
Guest
 
Posts: n/a
Use forward difference if U_t is not specified at the boundary
  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
Calculation of the Governing Equations Mihail CFX 7 September 7, 2014 06:27
Wave equation, wave velocity components mztcu CFX 1 May 4, 2010 02:14
what is the condition to use the wave equation? mmff Main CFD Forum 0 January 26, 2010 05:25
Assistance with one-way wave equation Frank Main CFD Forum 5 March 14, 2007 11:56
Wave equation with COMSOL Jeff NUMECA 0 December 6, 2006 03:27


All times are GMT -4. The time now is 17:18.