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

artificial viscosity

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

LinkBack Thread Tools Display Modes
Old   March 2, 2004, 09:50
Default artificial viscosity
Posts: n/a

when modelling 1D wave eqn. the dissipation error is due to artificial viscosity(For first order schemes).Can anybody explain how this artificial viscosity came into picture as there is no viscosity term either in the model eqn or modified eqn.

Model eqn:du_dt=-a du_dx

Modified eqn:du_dt=-a du_dx+ [(a*Delta x/2)*(1-c)*(d^2u_dx^2)].

where "a" is speed of sound and "C" is courant number.

As per text book the second term in the model eqn that is [(a*Delta x/2)*(1-c)] is called artificial viscosity. How this will become a viscous term ? Any help in this regard is highly appreciated.


  Reply With Quote

Old   March 2, 2004, 11:24
Default Re: artificial viscosity
Posts: n/a
Artificial viscosity (= parabolic diffusive character) is often added to a numerical method to stabilize it and obtain non-oscillating solutions. This is achieved by adding a (negative = diffusive, as opposed to anti-diffusive) second order spatial derivative. To see how this is diffusive: treat the numerical solution as Fourier modes, ~ A_k * exp(i*k . x), and look at the eigenvalues of these operators,

d/dx = i*k (purely imaginary, so dispersive)

d^2/dx^2 = -k^2 (real and negative, so diffusive)

Is this of any help?
  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
Artificial Viscosity Luiz Eduardo Bittencourt Sampaio Main CFD Forum 12 November 13, 2011 11:21
Artificial Viscosity MAB CFX 1 July 30, 2008 22:00
Artificial viscosity rads CFX 2 July 31, 2006 07:02
Jameson-type Artificial Viscosity Steve Allison Main CFD Forum 1 February 19, 2003 09:50
Artificial Viscosity Girish Bhandari Main CFD Forum 5 January 13, 2001 14:22

All times are GMT -4. The time now is 22:10.