Advection Operators

🌀 Analytic Warp

sim_add_analytic_warp_operator(ctx, field, opts)

Nonlinear analytic deformation (digamma/trigamma/power/tanh/hyperexp/qhyperexp).

• profile (enum): digamma, trigamma, power, tanh, hyperexp, qhyperexp.
• delta (>0, default 1e-3): symmetric offset for gradient estimates.
• lambda (default 1.0): response gain.
• bias (default 0): pre-profile offset.
• exponent (power profile).
• hyperexp_epsilon, hyperexp_depth, hyperexp_q (hyperexp/qhyperexp profiles).
• complex_mode (enum): component or polar.
• continuity_mode (enum): none|strict|clamped|limited.
• continuity_clamp_min / continuity_clamp_max: bounds for clamped/limited.
• continuity_tolerance: blend radius for limited mode.

Examples:

sim.sim_add_analytic_warp_operator(ctx, field, {
    profile = "power",
    exponent = 1.5,
    lambda = 0.4
})

sim.sim_add_analytic_warp_operator(ctx, field, {
    profile = "hyperexp",
    hyperexp_depth = 16,
    hyperexp_epsilon = 0.25,
    complex_mode = "polar"
})

∇ Spatial Derivative

sim_add_spatial_derivative_operator(ctx, src, dst, opts)

Finite difference derivative df/dx (or df/dy).

• method (enum): central (default), forward, backward.
• axis (int, default 0): 0=x, 1=y.
• skew_forward (bool): bias central toward upwind.
• spacing (>0): dx scale.
• boundary (enum): periodic|neumann|dirichlet|reflective.
• accumulate (bool): add instead of overwrite.

Examples:

sim.sim_add_spatial_derivative_operator(ctx, u, ux, {
    method = "forward",
    spacing = 0.25
})

sim.sim_add_spatial_derivative_operator(ctx, u, uy, {
    method = "central",
    axis = 1,
    boundary = "dirichlet",
    accumulate = true
})

Read/modify an existing spatial-derivative operator

• sim_spatial_derivative_config(ctx, op_index) -> table|nil returns { input_field, output_field, spacing/dx, method, method_index, axis, skew_forward, boundary, accumulate }.
• sim_spatial_derivative_update(ctx, op_index, opts) -> true updates any subset of those fields. input_field / output_field accept a field handle or index; method accepts enum/string; boundary accepts periodic|neumann|dirichlet|reflective.

local cfg = sim.sim_spatial_derivative_config(ctx, op_index)
if cfg then
    sim.log("∂ axis=%d method=%s dx=%.3g", cfg.axis, cfg.method, cfg.dx)
end

-- Switch to backward upwind on y with tighter spacing
sim.sim_spatial_derivative_update(ctx, op_index, {
    axis = 1,
    method = "backward",
    spacing = 0.05,
    skew_forward = false,
    boundary = "neumann",
})