##  [Artificial Energy Growth](/artificial-energy-growth-0) 

 Definition

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

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

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

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

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

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

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

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

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.