CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum

stability of alternate direction implicit scheme

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

LinkBack Thread Tools Display Modes
Old   September 21, 2012, 05:41
Default stability of alternate direction implicit scheme
New Member
Aniket Sachdeva
Join Date: Mar 2012
Posts: 22
Rep Power: 7
thegodfather is on a distinguished road
In the ADI scheme for solving 2 dimensional unsteady diffusion problem, the pentadiagonal matrix is expressed as sum of two tridiagonal matrices along horizontal and vertical directions at half and full time steps respectively. For stability of a numerical scheme all the contribution coefficients must be positive. But, in this case the coefficient of Tn (Temperature at nth time level) in the expression of Tn+1 has a coefficient 1-gamma*dt/dx^2, where gamma is the diffusion coefficient, dt full time step value. This can become negative for gamma > dx^2/dt, thus imposing a stability criterion in the implicit scheme. Is this true? Can implicit schemes also be unstable in some cases, or am I making some mistake?
thegodfather is offline   Reply With Quote


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
How L-norms are used to study stability of a numerical scheme? Ravindra Shende Main CFD Forum 7 April 22, 2012 17:15
2D Implicit HLLC scheme harish_0689@ Main CFD Forum 2 January 21, 2012 14:22
Is it feasible to apply implicit scheme in LES EagleGao Main CFD Forum 2 October 24, 2011 14:04
time_step, implicit scheme, number of iterations Isa Main CFD Forum 3 May 11, 2006 12:27
Physical Reason for stability of Implicit Schemes? radhakrishnan Main CFD Forum 25 December 7, 2000 16:25

All times are GMT -4. The time now is 04:40.