Abstract2018-05-24T12:52:58+00:00

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"
}