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francesco_capuano September 18, 2012 08:46

Dissipation and dispersion errors
 
Hi,

I'm looking for a good reference in which the concepts of dissipative and dispersive errors for finite-difference methods are explained clearly and comprehensively, e.g. including Fourier analysis, concept of modified wavenumber, analysis of centred, upwind and compact schemes, physical interpretation of dissipative and dispersive errors, concept of phase and group velocity, modified equation analysis, etc...

Any suggestions?

Thanks in advance,
Francesco

michujo September 18, 2012 09:32

Hi, have a look at C. Hirsch "Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics" (second edition, only one volume).

Cheers,
Michujo.

francesco_capuano September 18, 2012 10:32

Thanks for your reply. For those interested, I have also found an old but nice book: "Fourier analysis of numerical approximations of hyperbolic equations", by R. Vichnevetsky and J.B. Bowles.

FMDenaro September 18, 2012 10:50

I agree about the Hirsch book, I also suggest:

Morton K., Mayers D. Numerical solution of partial differential equations.. an introduction (2ed., CUP, 2005)(ISBN 0521607930)(293s)

as well as some reading of 9.2 in
Fletcher - Computational Techniques For Fluid Dynamics 1

and Chap.4 in
Tannehill & al. - Computational Fluid Mechanics & Heat Transfer- 1984.

However, I think that the concept can be simply associated to the modified equation in physical and wavenumber space ;)

francesco_capuano September 18, 2012 11:31

Thank you very much! I gave a look at all those references, and at first glance the Hirsch book seems to be the most clear and complete.

FMDenaro September 18, 2012 11:43

Quote:

Originally Posted by francesco_capuano (Post 382383)
Thank you very much! I gave a look at all those references, and at first glance the Hirsch book seems to be the most clear and complete.

yes, give also a look at Chap.4 in Tannehill, for each scheme the amplification factor is reported

francesco_capuano September 18, 2012 12:42

Quote:

Originally Posted by FMDenaro (Post 382388)
yes, give also a look at Chap.4 in Tannehill, for each scheme the amplification factor is reported

Thank you :)


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