Adjoint-based estimation and control of spatial, temporal and stochastic approximation errors in unsteady flow simulations

• Numerical error estimates in spatial, temporal and stochastic domains are derived.
• Verified error estimation strategy in a modular fashion in steady/unsteady problems.
• Proposed a new reconstruction strategy of the adjoint solution in temporal domain.
• Demonstrated the use of stochastic error estimates as a basis for adaptive sampling.

The ability to estimate various sources of numerical error and to adaptively control them is a powerful tool in quantifying uncertainty in predictive simulations. This work attempts to develop reliable estimates of numerical errors resulting from spatial, temporal and stochastic approximations of fluid dynamic equations using a discrete adjoint approach. Each source of error is isolated and the accuracy of the error estimation is verified. When applied to unsteady flow simulations of vertical axis wind turbines (VAWT), the procedure demonstrates good recovery of discretization errors to provide accurate estimate of the objective functional. The framework is then applied to a VAWT simulation with inherent stochasticity and is confirmed to effectively estimate errors in computing statistical quantities of interest. The ability to use these stochastic error estimates as a basis for adaptive sampling is also presented. Predictive science is typically constrained by finite computational resources and this work demonstrates the viability of adjoint-based approaches to budget available computational resources to effectively pursue uncertainty quantification.