We present a comparison between hybridized and non-hybridized discontinuous Galerkin methods in the context of target-based hp-adaptation. Using a discrete-adjoint approach, sensitivities with respect to output functionals are computed to drive the adaptation. From the error distribution given by the adjoint-based error estimator, h-or p-refinement is chosen based on the smoothness of the solution which can be quantified by properly-chosen smoothness indicators. Numerical results are shown for inviscid subsonic and transonic, and laminar viscous flow around the NACA0012 airfoil.

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In this work, we propose a new way of splitting the flux function of the isentropic compressible Euler equations at low Mach number into stiff and non-stiff parts. Following the IMEX methodology, the latter ones are treated explicitly, while the first ones are treated implicitly. The splitting is based on the incompressible limit solution, which we call reference solution (RS). An analysis concerning the asymptotic consistency and numerical results demonstrate the advantages of this splitting.

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In this publication, we consider IMEX methods applied to singularly perturbed ordinary differential equations. We introduce a new splitting into stiff and non-stiff parts that has a direct extension to systems of conservation laws and investigate its performance analytically and numerically. We show that this splitting can in some cases improve the order of convergence, demonstrating that the phenomenon of order reduction is not only a consequence of the method but also of the splitting.