P-adaptive hybridized flux reconstruction schemes

Abstract

This paper presents p-adaptive hybridized flux reconstruction schemes to reduce the computational cost of implicit discretizations. We first introduce spatial and temporal discretization and discuss the adaptation algorithm via a nondimensional vorticity indicator for hybridized methods with globally continuous and globally discontinuous numerical traces. At each adaptation level, projection operations are applied to determine the new space based on the element-wise projected solution and transmission conditions. We validate our implementation and analyze performance via numerical examples. Specifically, we show via an isentropic vortex that p-adaptive hybridization of both HFR and EFR methods results in comparable numerical error to standard p-adaptive and p-uniform FR discretizations with a fraction of degrees of freedom. Results for a cylinder at Re=150 showcase speedup factors in excess of 6 for hybridized methods in comparison with p-adaptive standard FR schemes and up to 40 against p-uniform FR discretizations. Similarly, results for a NACA 0012 airfoil at Re=10,000 demonstrate speedup factors close to 6 against p-adaptive FR discretizations and up to 33 against p-uniform conventional FR. Hence, combining hybridization with adaptation yields a significant reduction in computational cost compared with standard implicit discretizations.