Coupling of continuous and hybridizable discontinuous Galerkin methods. Application to conjugate heat transfer problem.
Author (s): Paipuri, M.; Tiago, C. and Fernández-Méndez, S.
Journal: Journal of Scientific Computing
Volume: 78
Pages: 321 – 350
Date: 2019
Abstract:
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-Bénard 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.
Bibtex:
@Article{Paipuri2019, author="Paipuri, Mahendra and Tiago, Carlos and Fern{\'a}ndez-M{\'e}ndez, Sonia", title="Coupling of Continuous and Hybridizable Discontinuous Galerkin Methods: Application to Conjugate Heat Transfer Problem", journal="Journal of Scientific Computing", year="2019", month="Jan", day="01", volume="78", number="1", pages="321--350", abstract="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--B{\'e}nard 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.", issn="1573-7691", doi="10.1007/s10915-018-0769-8", url="https://doi.org/10.1007/s10915-018-0769-8" }