Unintended loss or artificial flux of conserved quantities (mass, energy, momentum, probability, etc.) across a nominal boundary in a simulation or discretized model caused by discretization errors, inconsistent coupling, ghost-cell treatments, or incorrect numerical fluxes.

Principle

When discrete fluxes, coupling operators, or boundary treatments do not exactly balance conservation laws or are mismatched between subdomains or components, conserved quantities can leak across the intended boundary, producing nonphysical gain or loss in one region and violating global conservation.

Demonstration

In a finite-volume solver, incorrectly computed numerical flux at the domain edge or between coupled meshes results in net mass leaving the computational domain. In coupled multi-physics simulations, inconsistent variable extrapolation between solvers can produce spurious transport of energy across the interface.

Misapplication

Attributing small global conservation errors to modelling physics rather than to spurious boundary leakage, or fixing leakage by adding artificial sinks/sources inside the domain rather than correcting the boundary treatment, thereby obscuring and compounding the error source.

Consequence

Accumulated leakage produces biased conservation diagnostics, degraded accuracy, and potentially runaway errors in long simulations; coupled systems can display artificial equilibration between subdomains and invalid physical conclusions.

Reversal

Ensure conservative discretizations and flux-consistent boundary formulations, enforce inter-domain compatibility (conservative coupling, flux matching), use consistent ghost-cell or penalty formulations, and perform balance checks and local conservation repairs at interfaces rather than global ad hoc fixes.

Boundary

Specifically concerns unintended cross-boundary transfer in discrete/computational settings; excludes intended physical boundary fluxes prescribed by the continuous model and internal numerical diffusion that does not produce net cross-boundary transfer.

Semantic Tension

Close to boundary artifact but distinct: leakage denotes real (numerical) transfer across the boundary affecting global balances, while an artifact is a localized nonphysical feature without net transfer. Also overlaps conceptually with open-boundary modelling errors that intentionally allow flux.

Synthesis

Boundary leakage is the unintended numerical transfer of conserved quantities across a computational boundary caused by inconsistent or nonconservative treatments; it is diagnosed by violation of global balances and corrected by enforcing conservative, compatible interface fluxes and coupling.