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Old   June 22, 2004, 13:34
Default linearizing euler equation
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kalyan
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Dear friends , I just entered into the concepts of CFD . I would like to know : Is there any method to linearize a nonlinear euler equation in conservative form (no source terms )? If so please provide me with an Example so as to implement the finite difference technique .
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Old   June 22, 2004, 23:44
Default Re: linearizing euler equation
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Praveen
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It is a good excercise to carry out the calculations yourself. It is really simple. Write every quantity u as u = U + u' where U is a constant function. Plug this into the equations and neglect all terms which are of order O(u'*u') and above. The remaining terms will be linear in u' and its derivatives.
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Old   June 23, 2004, 08:59
Default Re: linearizing euler equation
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Apurva
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Hi

Refer this two papers by Mike Giles:

D.R. Lindquist and M.B. Giles. `Validity of linearized unsteady Euler equations with shock capturing'. AIAA Journal, 32(1):46-53, 1994

M.S. Campobasso and M.B. Giles. `Stabilization of a linearized Navier-Stokes solver for turbomachinery aeroelasticity' in Computational Fluid Dynamics 2002. Springer-Verlag, 2003

You can get the copy of second paper from : http://web.comlab.ox.ac.uk/oucl/work.../journals.html

Hope it helps

Good Luck

Apurva
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Old   June 23, 2004, 14:43
Default Re: linearizing euler equation
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kalyan
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thanks for the suggestions praveen & apurva .
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