zoomy_core.analysis.linearisation module

Generic linearisation around a base state for a SystemModel.

Replaces every state slot q in the SystemModel’s operator-form residual M·∂_t Q + ∂_x F + ∂_x P + B·∂_x Q − S with q_0 + ε δq, expands to first order in ε, and returns a new SystemModel whose state is the perturbation vector δq.

Works for arbitrary state shapes — differential or algebraic rows (zero mass-matrix rows pass through unchanged in form). The base values q_0 may themselves be expressions in coordinates (useful when the steady state is non-uniform, e.g. a varying bottom profile b(x)).

zoomy_core.analysis.linearisation.linearise(sm, base_state, *, eps=None, simplify=True)

Insert Q = Q_0 + ε δQ, expand, return O(ε) SystemModel.

Parameters:

• sm (SystemModel) – Input operator-form system.

• base_state (dict) – Maps each entry in sm.state to its base value (a scalar or an expression in coordinates).

• eps (sympy Symbol, optional) – Small parameter; created internally if None.

• simplify (bool) – Apply sp.expand to each linearised operator entry.

Returns:

New SystemModel whose state is [δq_0, …, δq_{n-1}] and whose operator matrices are linearised around base_state.

Return type:

SystemModel