Grid refinement

Parameter refine_adx

Grid refinement is controlled by several parameters. Usually the most import one is

# Refine if alpha*dx is larger than this value:
refine_adx = 1.0

The idea behind this parameter is that the electron density will locally approximately increase like \( n_e(x) \sim e^{\alpha x} \), where \( \alpha \) is the ionization coefficient. To accurately capture this growth, one should resolve the length scale \( 1/\alpha \). The code will therefore mark cells where alpha(E) * dx > refine_adx for refinement. To get an idea of the convergence of a model, one can run it several times, using for example:

refine_adx = 2.0
refine_adx = 1.0
refine_adx = 0.5

Other refinement parameters

Some of the other parameters that control refinement are shown below:

    call cfg_add_get(cfg, "refine_buffer_width", refine_buffer_width, &
         "The refinement buffer width in cells (around flagged cells)")
    call cfg_add_get(cfg, "refine_per_steps", refine_per_steps, &
         "The number of steps after which the mesh is updated")
    call cfg_add_get(cfg, "refine_min_dx", refine_min_dx, &
         "The grid spacing will always be larger than this value (m)")
    call cfg_add_get(cfg, "refine_max_dx", refine_max_dx, &
         "The grid spacing will always be smaller than this value (m)")
    call cfg_add_get(cfg, "refine_adx", refine_adx, &
         "Refine if alpha*dx is larger than this value")
    call cfg_add_get(cfg, "derefine_dx", derefine_dx, &
         "Only derefine if grid spacing if smaller than this value")
    call cfg_add_get(cfg, "refine_init_time", refine_init_time, &
         "Refine around initial conditions up to this time")
    call cfg_add_get(cfg, "refine_init_fac", refine_init_fac, &
         "Refine until dx is smaller than this factor times the seed width")
    call cfg_add_get(cfg, "refine_electrode_dx", refine_electrode_dx, &
         "Ensure grid spacing around electrode is less than this value (m)")

Using a static grid for a specific region in the domain

The user can specify a specific region of the domain to have fixed grid spacing. The following flags are utilized for that purpose:

• refine_regions_dr: the minimum grid spacing in the region
• refine_regions_rmin: the starting boundary of the region
• refine_regions_rmax: the closing boundary of the region

The flag refine_regions_rmin should have two values if working in a two dimensional domain and three values if in a three dimensional domain. The same is the case for refine_regions_rmax. The values are separated by spaces. For example, having refine_regions_rmin = 0.0 0.0 and refine_regions_rmax = 6.0e-4 5.0e-2 in a cylindrically symmetric simulation corresponds to the region bounded by the lines r = 0.0, z = 0.0, r = 6.0e-4, and z = 5.0e-2.