Define initial conditions

Bind the initial state of a block from numpy arrays, then advance the run. This page assumes you already have a compiled Case; see Configure a simulation for that. The layout convention is row-major (ny, nx): index a field as arr[j, i], where j is the row (y axis) and i is the column (x axis).

Set a scalar density

Pass a block state through pops.bind. For a scalar block, ARR is an (n, n) array.

  1. Build the cell-center coordinates and the field.

    coord = (np.arange(n) + 0.5) / n * L

  2. Mesh the coordinates with indexing="xy" so both arrays have shape (ny, nx).

    xx, yy = np.meshgrid(coord, coord, indexing="xy")

  3. Fill the density array and bind it.

    ne = np.full((n, n), 1e-3)

    sim = pops.bind(compiled, state={"ne": ne})

For a periodic Poisson, fix a neutralizing background equal to the mean (n_i0 = ne.mean()) so the right-hand side is solvable.

Set a fluid state from primitives

For fluid models, bind the conservative state expected by the compiled block. Helper functions may prepare that array from primitive variables (rho, u, v, p) before binding.

U0 = conservative_from_primitives(rho=rho0, u=u0, v=v0, p=p0)
sim = pops.bind(compiled, state={"electrons": U0})

The conservative state uses the block’s component order and an (ncomp, n, n) layout.

Advance and check the result

After binding, sim.run(t_end, cfl=CFL) advances the simulation by CFL-limited steps up to t_end.

sim.run(0.1, cfl=0.4)

Read sim.density(NAME) for the field, sim.potential() for phi, and sim.mass(NAME) for the total mass. The mass is the conservation invariant; with periodic advective transport its drift stays near machine roundoff.

Next steps