Coupling of Continuous and Hybridizable Discontinuous Galerkin Methods: Application to Conjugate Heat Transfer Problem

A coupling strategy between hybridizable discontinuous Galerkin (HDG) and continuous Galerkin (CG) methods is proposed in the framework of second-order elliptic operators. The coupled formulation is implemented and its convergence properties are established numerically by using manufactured solutions. Afterwards, the solution of the coupled Navier-Stokes/convection-diffusion problem, using Boussinesq approximation, is formulated within the HDG framework and analysed using numerical experiments. Results of Rayleigh-Benard convection flow are also presented and validated with literature data. Finally, the proposed coupled formulation between HDG and CG for heat equation is combined with the coupled Navier-Stokes/convection diffusion equations to formulate a new CG-HDG model for solving conjugate heat transfer problems. Benchmark examples are solved using the proposed model and validated with literature values. The proposed CG-HDG model is also compared with a CG-CG model, where all the equations are discretized using the CG method, and it is concluded that CG-HDG model can have a superior computational efficiency when compared to CG-CG model.