I look at these equations by taking out the streaming velocity, which in LAMMPS is always assumed to be a linear profile. Normal thermal fluctuation principles apply once transform into this frame of reference, with the exception of the kinetic contribution as a result of the flow field. The capital P you are referring to does not arise from a flow field, as you can see from the comparison between eqn 2 and 33. This means, that such a term should also not be extra in just the nvt/slodd fix. Comparison between the nvt and nvt/sllod fixes shows the additional flow field corrections in the latter. The nvt fix encompasses the acceleration term as you call it.
Dr. Pieter J. in 't Veld
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06/08/2010 07:15 PM
Steve Plimpton [email protected], [email protected]
Re: Re: [lammps-users] questions about nvt/sllod code
Thank you so much for your comprehensive reply. First, I might mislead the discuss because of ambiguously using term “lab-frame of reference”. In my question, the lab-frame of reference is actually a fixed frame of reference without any translational velocity. In your reply, the lab-frame of reference means a moving frame of reference with herein the streaming velocity. Am I correct?
So my question is still there. In eqn 33 of Heyes, the capital P in the equation is peculiar momenta wrt the lab-frame of reference you mentioned. Thus, the dP/dt is the particle accelerations in the lab-frame of reference, this is the reason SLLOD correction comes in. However, according to my understanding, you use this acceleration to get the velocity increment at t+1/2dt. Should this lab-frame of reference acceleration should be used to advance the velocity or the acceleration in the fixed frame of reference? I think it should be the acceleration in the fixed frame of reference. Actually, if you try to differentiate eqn 32 wrt time and substitute eqn 33, this will give the expression for acceleration in the fixed frame of reference d^2(q)/dt^2 (eqn 21 in Tuckerman et al. J. Chem. Phys 106, 1997). This is how the SLLOD correction term cancels and time-dependent strain rate term comes out. Thus, the key problem remains as which acceleration should be used.