I am new to LAMMPS, but is it possible to create a boundary condition that is like a Couette flow, with a horizontal velocity Vx, but also includes a vertical velocity, which is defined as Vy = (P-Pwall)L/c, where P is the applied pressure in the -ve y direction, Pwall is the pressure of the particles on the wall in the +ve y direction, L is the length of the wall in x direction and c is a damping coefficient? (The attached diagram hopefully describes it better).
In steady state, the vertical velocity should be zero, as the pressures should balance. I ask this because I am trying to test the method in this paper:
The x and y motion of the wall can be specified by different
fixes (or initial conditions). See fix aveforce for how
to apply a y-pressure to a set of atoms.
The examples/flow dir has 2 scripts. One for Couette flow,
the other for Poiseuille flow. The latter uses fix aveforce
to equilibrate the wall in y.
If you want to use an idealized wall, e.g. fix wall/lj93, then
its position can also be specified with a variable that could
implement a condition to balance forces, like your equation.
You could also use the fix controller command to equilibrate
something like wall position as a function of applied force (pressure).