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Most common ODE solver

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Old   February 3, 2012, 10:02
Default Most common ODE solver
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It's my understanding that the method of lines is quite commonly used in CFD. What is the most common ODE solver used with this approach? For example, LSODA, VODE, or simply 4th order Runge-Kutta?
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Old   February 3, 2012, 10:12
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Quote:
Originally Posted by Nereus View Post
It's my understanding that the method of lines is quite commonly used in CFD. What is the most common ODE solver used with this approach? For example, LSODA, VODE, or simply 4th order Runge-Kutta?

from my experience, RK4 is high up on the list!
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Old   February 3, 2012, 15:11
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It also depends on solved equations. If a problem is stiff, implicit numerical methods are more suitable for that task. For non-stiff problems Dorman-Prince method is the first shot integrator in many numerical solvers.
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Old   February 3, 2012, 18:56
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Originally Posted by cfdnewbie View Post
from my experience, RK4 is high up on the list!
Yes I agree with cfdnewbie. RK4 is known to be the most accurate method (if you exclude RK5, RK6 etc....)
But if you plan to use it to solve Navier-Stokes equations in an explicit way, RK4 is quite expensive in CPU time and storage. A special RK3 method has been specifically designed to lower that cost.
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Old   February 3, 2012, 19:05
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Dormand-Prince method is linked to RK method familly and seems to be more expensive than RK4. check this link for a gpl subroutine using this method.
http://www.unige.ch/~hairer/prog/nonstiff/dopri5.f
RK4 can be coded with 20 lines !!!
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