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Re: Are our systems conservatives?

 

On 7 May 2010 15:51, chiara modenese <c.modenese@xxxxxxxxx> wrote:

>
>
> On 7 May 2010 13:31, Bruno Chareyre <bruno.chareyre@xxxxxxxxxxx> wrote:
>
>>
>>> Ok, can I change something in Shop for the dt/2 shift or should I save
>>> velocities and accelerations and then interpolate?
>>>
>>>
>> You can change in shop.
>>
> I changed in shop the kinetic as
>
>
> ret+=.5*(b->state->mass*(b->state->vel+b->state->accel*dt/2).SquaredLength()+(b->state->angVel+b->state->angAccel*dt/2).Dot(diagMult(b->state->inertia,(b->state->angVel+b->state->angAccel*dt/2))));
>
> I tried the sample example with the two balls and the time step estimated
> by PWave. I attach the figure.
> Now I suppose that if the kinetic energy is computed correctly (is it?) the
> problem relies on the elastic energy. You said yourself that the total
> energy is "approximately" constant. Is this approximation due to the
> numerical scheme, is not it? If so the time step plays a role also on the
> total energy, no?
>

To also note that the total energy computed considering the corrected
kinetic energy at time step t+dt/2, it is less close to the expected value
than the case in which kinetic energy is not shifted. Now I guess if
computing the kinetic energy through the linear interpolation of the
velocities we are actually altering the numerical scheme.. Not sure here..


>
>
>
>> Another note : your remark on different dt for different problems is
>> correct. PWave and GSTS both consider a dense packing.
>> If you have problems where fast collisions between particles matter, there
>> is another constraint on dt. In short, particles must not go through each
>> other in only one time-step. It results in a definition of dt based on size
>> of particles and incident velocities only, disregarding mass and stiffness.
>>
>>
>>
>> Bruno
>>
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>
>

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