Adaptive domain decomposition for the bound method: Application to the incompressible Navier–Stokes and Energy equations in three space dimensions Original Research Article

Large-scale numerical simulations of the flow and associated transport phenomena governed by the Navier–Stokes and Energy equations are routinely calculated in engineering practice. Nevertheless, the uncertainty due to spatial discretization limits the confidence of practitioners in numerical solutions. An approach to provide information about the accuracy of the quantity of interest is proposed here-in. The novel a posteriori error estimation technique – the bound method – is based on relaxing Lagrange multipliers that enforces continuity between sub-domains. The method provides fast, efficient, asymptotic but reliable lower and upper bounds to the output of underlying partial differential equations (PDEs). Herein, we highlight the method when applied to outputs of the steady incompressible Navier–Stokes and Energy equations. The bound method i