Comparison of Different Error Estimators for the p-Adaptive Discontinuous Galerkin Solution of Separated Flows

The use of high-order discontinuous Galerkin (dG) methods is gaining interest in the efficient and accurate simulation of flow problems to meet the growing demand for high-fidelity results. dG methods provide higher accuracy than standard industrial solvers on complex geometries, but they are computationally more expensive. This drawback has prompted the research on adaptive dG discretizations that can vary the level of spatial accuracy according to proper error estimators, reducing the computational effort. In this context the choice of the error indicator, which identifies where the spatial resolution is lacking and guides the refinement of the adaptation algorithm, is a key ingredient, as it can affect the capability of the solver to predict correctly the flow features. This study aims to contribute to the improvement of the computational efficiency of dG methods when applied to industrial applications with the assessment and comparison of two error estimators: (i) a 'simple' estimator based on the combination of the interface pressure jumps and the spectral decay of the coefficients of the modal expansion; (ii) an entropy-adjoint-based error estimator, which targets the generation of spurious entropy. Test cases used for the assessment involve laminar and turbulent flows around bluff bodies, providing insights into attached and separated boundary layers, instabilities, possibly laminar-to-turbulent transition, and vortex shedding.