Gridindependent

Grid independence refers to the property of a numerical simulation where the computed solution becomes insensitive to further grid refinement. In practice, a grid-independent (or grid-converged) solution is sought when discretization errors are reduced below the level of other model uncertainties. It is a key part of verification and validation in computational science and engineering.

To assess grid independence, researchers perform a grid convergence study. They solve the problem on a sequence of meshes with increasing resolution and monitor quantities of interest such as drag, lift, maximum velocity, or temperature at specified points. If changes between successive refinements fall below a predefined tolerance, the solution is considered grid independent. Techniques like Richardson extrapolation can be used to estimate the continuum solution and quantify discretization error.

Refinement strategies include h-refinement (smaller elements), p-refinement (higher-order basis functions), and hp-refinement (a combination). Grid quality metrics such as skewness, aspect ratio, and orthogonality are important, and the mesh should adequately resolve important features, including boundary layers and sharp gradients.

Cautions include that grid independence does not guarantee model accuracy; it only indicates consistency with respect to grid resolution. Excessive refinement can incur high computational cost with little gain. In transient problems, time-step size and solver convergence criteria should be coordinated with spatial resolution. Adaptive mesh refinement uses error estimators to target refinement where it most affects the quantities of interest, helping achieve grid independence efficiently.

Grid independence is commonly pursued in computational fluid dynamics, finite element analysis, heat transfer, and electromagnetics to support reliable conclusions from simulations.