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

Quasi, Non -linear....pde

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

LinkBack Thread Tools Display Modes
Old   November 4, 2003, 11:28
Default Quasi, Non -linear....pde
Posts: n/a
With regard to partial differential equations, can anyone tell me what the following mean:

What does Quasi-linear mean? What does Non-linear mean? What does Linear mean?

I know I can go to a book, but I want a simpler answer than most books provide.

Thanks all.
  Reply With Quote

Old   November 4, 2003, 15:55
Default Re: Quasi, Non -linear....pde
Posts: n/a

a subtle point but:

1. Linear is when the dependant varibles and derivatives of dependant variables are all to the first power and each term in the equation may be multipied only by a constant.

2.Quasi-linear is when the derivatives are linear ie: d(v)/d(x) but the may be multiplied by other variables such as u*d(u)/d(x)

The Navier Sokes equations are quasi linear according to this definition but are often simply called non-linear. I am not sure if it makes too much of a difference to most of us, pedantry aside?


  Reply With Quote

Old   November 5, 2003, 08:54
Default Re: Quasi, Non -linear....pde
P. Birken
Posts: n/a
Ok, nonlinear is easy: any equation that is not linear is nonlinear ;-)

Linear means, as BAK_FLOW said that the coefficients of your problem do not depend on the variables themselves.

For example, the PDEs

u_t + a*u_x = 0 and

u_t + a(t)*u_x

are linear, but the PDEs

u_t + u*u_x = 0 and

u_t + a(u)*u_x = 0

are both nonlinear (if a(u) does indeed depend on u). Actually, they are also both quasilinear. Quasilinear means: the PDE looks linear, but is actually not. So if you have a coefficient matrix appearing in your PDE, than the PDE is quasilinear. Whether it is linear or nonlinear depends on the coefficients. If they depend on u, the equation is nonlinear, otherwise it is linear.


  Reply With Quote

Old   November 5, 2003, 09:28
Default Re: Quasi, Non -linear....pde
Posts: n/a
Excellent...thanks guys! Can anyone shed some light on the Entropy condition and methods used to ensure that the Entropy condition is not violated in solutions to certain hyperbolic pde's? Also, what books/s would you guys recommend to someone wishing to get a deeper understanding of pde's and their analytical solutions...something for a Engineer (rather than very theoretical), but not sacrificing completeness.

  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
please help me which solver is better for my application Ger_US OpenFOAM 8 January 8, 2013 13:29
solution diverges when linear upwind interpolation scheme is used subash OpenFOAM 0 May 29, 2010 01:23
IdeasUnvToFoam Bug amp Fix benru OpenFOAM Bugs 42 November 13, 2009 08:59
Water pump OpenFOAM 15 ANSYS CFX 110 comparation waynezw0618 OpenFOAM Running, Solving & CFD 39 March 5, 2009 13:57
Linear Iterative Solver + Elliptic PDE cfd101 Main CFD Forum 0 November 14, 2005 19:59

All times are GMT -4. The time now is 18:02.