Adaptive grid refinement using cell-level and global imbalances

A methodology for local solution-adaptive mesh refinement in computational fluid dynamics (CFD) using cell-level and global kinetic energy balances is formulated and tested. Results are presented for two two-dimensional steady incompressible laminar benchmark problems: a lid-driven cavity (Reynolds number Re = 1000) and a backward-facing step (Re = 400). It is demonstrated that local kinetic energy imbalance correlates with local solution accuracy, that normalized global imbalance is an appropriate criterion for halting mesh refinement and that a specified level of accuracy is realized at lower computational effort using local refinement compared with a uniform finer mesh.