Vertex-Centered Mixed Finite Element-Finite Volume scheme for 2D anisotropic hybrid mesh adaptation

The scope of this paper is to propose an appropriate numerical strategy to extend the Mixed Finite Element-Finite Volume (MEV) scheme to adapted meshes composed of both triangular and quadrangular elements, called hybrid meshes (Kallinderis and Kavouklis, 2005; Ito et al., 2013) (also named mixed-element meshes (Marcum and Gaither, 1999; Mavriplis, 2000)). Con-vective, diffusive and source terms require specific gradient discretization to maintain a global second-order accuracy. The major contributions of this paper concern the specification of these gradients, the convective fluxes' discretization and an innovative framework for anisotropic metric-based adaptation on hybrid meshes. Particularly, the V4 scheme, traditionally developed for triangular elements, is extended to quadrilateral elements. This method maintains the same order of accuracy as the baseline version when upwind/downwind quadrilateral elements are aligned with the attached edge. Viscous fluxes are discretized using the APproximated Finite Element (APFE) method (Puigt et al., 2010), which is second-order accurate on regular quadrilaterals. Nodal gradients, which are considered at boundaries and for source terms, are discretized with a generalization of Clement's L2-operator on hybrid meshes. The mesh adaptation relies on a specific metric gradation process to favor the clustering of structured elements at wall boundaries. The proposed scheme is validated on a set of CFD simulations.