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Topic: ? influence of temporal discretization
Replies: 1   Last Post: May 30, 2012 10:12 AM

 Dieter Britz Posts: 20 Registered: 6/17/10
Re: ? influence of temporal discretization
Posted: May 30, 2012 10:12 AM

On Fri, 25 May 2012 09:41:02 +0000, AMX wrote:

> On Sat, 19 May 2012 05:02:55 -0700 (PDT), Cosine <asecant@gmail.com>
> wrote:

>> Hi:
>>
>> Suppose we have a diffusion eqn: dT/dt = a*div(grad(T))+Q in non-
>> dimensional form.
>>

> [..]
>

>> Can we discretize the time using dt as 0.1 sec or should we use a dt
>> even smaller? How do we estimate the appropriate value of dt?

>
> It mostly depends on method of integrating over time.
>
> AMX

For any method of time integration, you can measure the order wrt dt
and get an estimate of the error by setting the spatial intervals
very small, and trying with dt, dt/2 and dt/4, choosing some resulting
quantity as the test, say q1, q2, q4, resp. Then q1 - q4 is close to
the error, and log_2 of the ratio (q1 - q2) / (q2 - q4) gives you the
order wrt dT.
--
Dieter Britz