[francesco_capuano]

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]

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]

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]

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]

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]

Originally Posted by francesco_capuano

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]

Originally Posted by FMDenaro

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

Thank you