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I want to simulate 2D plane Poiseuille flow using molecular dynamics (velocity verlet algorithm) but not able to understand exactly to how to do this. Boundary condition is fine, I am confused about the forces to use in the verlet algorithm, I may use Lennard Jones but not sure if it is okay to use. Please help me with the algorithm only and suggest suitable references. Thanks.

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Probably the best reference is Nonequilibrium molecular dynamics: theory, algorithms and applications by Billy D Todd and Peter J Daivis, Cambridge University Press (2017). Chapter 9 discusses how to set up a simulation of this kind. They recommend applying a constant external force per atom in the flow direction, confining the system between parallel walls consisting of atoms (for example, Lennard-Jones atoms) and applying periodic boundary conditions in other directions. The fluid atoms would interact with each other, for example also with LJ forces, and with the wall atoms, once more with LJ interactions. You can choose to make the fluid-fluid, and fluid-wall, interactions of different strength.

There is a small subtlety in this choice of external force: it implies that the pressure gradient, which is proportional to the number density multiplied by the force per atom, is not constant across the cavity (because the number density varies, near the walls). However they argue that this is still OK.

There is more subtlety associated with the choice to either fix the wall atoms or allow them to vibrate, connected to each other by springs, as they would in a real solid. I've seen both methods used: I think they generally prefer to allow these atoms to move, otherwise the collisions of fluid atoms with them can be a bit unphysical (specular reflection or rebounding), but this may not worry you too much. Finally, you'll need to thermostat the system, otherwise it will heat up. Many people apply the thermostat to all the atoms, but I think Todd and Daivis prefer the more physical approach of just thermostatting the wall atoms, so the heat is conducted away through the walls. Again, this may not be a critical issue for you.

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