##  [Pinning](/pinning-0) 

 Definition

The arrest or anomalous slowing of an interface, front, or moving discontinuity in a numerical model caused by local heterogeneities, discretization artifacts, or imposed constraints rather than underlying physical pinning mechanisms.

 

 

 

 

 

 





## Principle

Principle

Numerical heterogeneities — e.g., local mesh changes, thresholding, or small discretization-induced energy barriers — can produce static metastable configurations where a continuous front should propagate, effectively trapping the interface.

 

 

 

 

 





## Demonstration

Demonstration

In a phase-field simulation, a moving phase boundary halts at mesh refinement transitions or at grid nodes with slight property perturbations; in combustion front models, a flame front ceases to advance when crossing coarse-to-fine mesh transitions despite sufficient global driving force.

 

 

 

 

## Misapplication

Misapplication

Interpreting a halted interface as a new physical equilibrium or using it to claim material pinning without verifying mesh and solver sensitivity; applying localized corrective source terms that mask the numerical origin.

 

 

 

 

 





## Consequence

Consequence

Recognizing pinning leads to remedies such as mesh smoothing, consistent interpolation across refinement interfaces, implicit time stepping with smaller tolerances, or explicit unpinning terms; if uncorrected, predictions of front speed, location, or stability become unreliable.

 

 

 

 

## Reversal

Reversal

The reversal is a physically pinned interface whose position is invariant under mesh refinement, parameter perturbation, and solver changes, indicating a true material or geometric pinning mechanism.

 

 

 

 

 





## Boundary

Boundary

Occurs in moving-boundary problems, interface-capturing methods, and nonlinear front propagation schemes; excluded are genuine microscale pinning due to material heterogeneity, modeling errors that intentionally include obstacles, and convergence failures unrelated to front dynamics.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Often confused with numerical stick-slip or with physically modeled contact pinning — the distinction lies in sensitivity tests: numerical pinning moves or disappears under mesh/resolution modifications, physical pinning does not.

 

 

 

 

 





## Synthesis

Synthesis

Pinning in numerical models is the spurious immobilization of an interface caused by discretization or solver artifacts; diagnosing it requires systematic mesh, timestep, and solver-parameter variation to separate numerical traps from true physical pinning.