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#1 |
Member
Francesco Capuano
Join Date: May 2010
Posts: 81
Rep Power: 16 ![]() |
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 |
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#2 |
Senior Member
Join Date: Dec 2011
Location: Madrid, Spain
Posts: 134
Rep Power: 15 ![]() |
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. |
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#3 |
Member
Francesco Capuano
Join Date: May 2010
Posts: 81
Rep Power: 16 ![]() |
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.
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#4 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,830
Rep Power: 73 ![]() ![]() ![]() |
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 ![]() |
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#5 |
Member
Francesco Capuano
Join Date: May 2010
Posts: 81
Rep Power: 16 ![]() |
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.
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#6 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,830
Rep Power: 73 ![]() ![]() ![]() |
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#7 |
Member
Francesco Capuano
Join Date: May 2010
Posts: 81
Rep Power: 16 ![]() |
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Tags |
discretization errors, finite differences |
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