In this paper, we introduce and test the enhanced stability recovery (ESR) scheme. It is a robust and compact approach to the computation of diffusive fluxes in the framework of discontinuous Galerkin methods. The scheme is characterized by a new recovery basis and a new procedure for the weak imposition of Dirichlet boundary conditions. These features make the method flexible and robust, even in the presence of highly distorted meshes. The implementation is simplified with respect to the original recovery scheme (RDG1x). Furthermore, thanks to the proposed approach, a robust implementation of p-adaptive algorithms is possible. Numerical tests on unstructured grids show a convergence rate equal to pC1, where p is the reconstruction order. Comparisons are shown with the original recovery scheme RDG1x and the widely used BR2 method. Results show a significantly larger stability region for the proposed discretization when explicit Runge- Kutta time integration is employed. Interestingly, this advantage grows quickly when the reconstruction order is increased. The proposed procedure for the weak imposition of Dirichlet boundary conditions does not need the introduction of ghost cells, and it is truly local because it does not require data exchange with other elements. It can be easily used with curvilinear wall elements. Several test cases are considered. They include some benchmark tests with the heat equation and compressible Navier-Stokes equations, with test cases designed also to evaluate the behaviour of the scheme with very stretched elements and separated flow

Supersonic inlets are a key component of present and future air-breathing propulsion systems for high-speed flight. The inlet design is challenging because of several phenomena that must be taken under control: shock waves, boundary layer separation and unsteadiness. Furthermore, the intensity of these phenomena is strongly influenced by the working conditions and so active control systems can be particularly useful in off-design conditions. In this work, a mixed compression supersonic inlet with a double wedge ramp is considered. The flow field was numerically investigated at different values of Mach number. The simulations show that large separations appear at the higher Mach numbers on both the upper and lower walls of the duct. In order to improve the performances of the inlet two different control strategies were investigated: plasma actuators and bleed. Different locations of the plasma actuator are considered in order to also apply this technology to configurations with a diverter which prevents boundary layer ingestion. The potential of the proposed solutions is investigated in terms of total pressure recovery, flow distortion and power consumption.