Coupling of hybridisable discontinuous Galerkin and finite volumes for transient compressible flows

Fast, high-fidelity solution workflows for transient flow phenomena is an important challenge in the computational fluid dynamics (CFD) community. Current low-order methodologies suffer from large dissipation and dispersion errors and require large mesh sizes for unsteady flow simulations. Recently, on the other hand, high-order methods have gained popularity offering high solution accuracy. But they suffer from the lack of robust, curvilinear mesh generators.A novel methodology that combines the advantages of the classical vertex-centred finite volume (FV) method and high-order hybridisable discontinuous Galerkin (HDG) method is presented for the simulation of transient inviscid compressible flows. The resulting method is capable of simulating the transient effects on coarse, unstructured meshes that are suitable to perform steady simulations with traditional low-order methods. In the vicinity of the aerodynamic shapes, FVs are used whereas in regions where the size of the element is too large for finite volumes to provide an accurate answer, the high-order HDG approach is employed with a non-uniform degree of approximation. The proposed method circumvents the need to produce tailored meshes for transient simulations, as required in a low-order context, and also the need to produce high-order curvilinear meshes, as required by high-order methods.FV and HDG methods for compressible inviscid flows with an implicit time-stepping method and capable of handling flow discontinuities is developed. A two-way coupling of the methods in a monolithic manner was achieved by the consistent application of the so-called transmission conditions at the FV-HDG interface. Numerical tests highlight the optimal convergence properties of the coupled HDG-FV scheme. Numeri-cal examples demonstrate the potential and suitability of the developed methodology for unsteady 2D and 3D flows in the context of simulating the wind gust effect on aerodynamic shapes.