A spurious increase in the computed energy of a numerical model over time that does not reflect physical input or true system dynamics, typically caused by discretization errors, unstable time integration, or improper coupling between submodels.

Principle

Numerical representations must respect the energetic balance of the continuous system: discretizations and coupling schemes should conserve, dissipate, or transfer energy in ways consistent with the underlying physics or controlled numerical regularization.

Demonstration

An explicit time-stepping scheme for a wave equation with insufficiently small time step produces growing discrete L2 energy; or a partitioned fluid–structure interaction algorithm injects energy at the interface because the coupling algorithm does not enforce reciprocal work balance.

Misapplication

Interpreting numerically induced energy growth as evidence of a real external forcing, or adding arbitrary damping without diagnosing the discrete source, which can mask model deficiencies and produce biased results.

Consequence

When present, artificial energy growth leads to nonphysical amplification of modes, loss of stability, incorrect long-term statistics, and potential solver divergence, undermining predictive value and error estimation.

Reversal

Energy-conserving or properly dissipative schemes produce non-increasing discrete energy consistent with physics; the reversed concept is numerical energy conservation or controlled dissipation rather than growth.

Boundary

Refers to computed energy in discrete numerical simulations and coupled solvers; excludes genuine physical energy input, parameter drift, measurement errors, or stochastic forcing explicitly modeled as energy sources.

Semantic Tension

Differs from model error or missing physics (which may also change energy) because artificial growth is a numerical artifact tied to discretization/coupling rather than to a mis-specified physical forcing; it can be confused with instability produced by nonlinear model behavior.

Synthesis

Artificial energy growth is the nonphysical rise of computed energy caused by the numerical method or coupling failure; diagnosing it requires checking discretization stability, invariants, and coupling work balances, and resolving it restores physically consistent energy behavior.