A non-conforming finite volume element method of weighted upstream type for the two-dimensional stationary Navier–Stokes system

Djadel, Karim; Nicaise, Serge

doi:10.1016/j.apnum.2007.01.012

Cited by 8 publications

(3 citation statements)

References 18 publications

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“…The non-linear convective term is discretized using an upstream approach with weight as in (see for instance, Schieweck and Tobiska, 1989;Djadel and Nicaise, 2008).…”

Section: Flow Discretizationmentioning

confidence: 99%

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A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows

Younès

Makradi

Zidane

et al. 2014

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -The purpose of this paper is to develop an efficient non-iterative model combining advanced numerical methods for solving buoyancy-driven flow problems. Design/methodology/approach -The solution strategy is based on two independent numerical procedures. The Navier-Stokes equation is solved using the non-conforming Crouzeix-Raviart (CR) finite element method with an upstream approach for the non-linear convective term. The advectiondiffusion heat equation is solved using a combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods. To reduce the computational time due to the coupling, the authors use a non-iterative time stepping scheme where the time step length is controlled by the temporal truncation error. Findings -Advanced numerical methods have been successfully combined to solve buoyancy-driven flow problems on unstructured triangular meshes. The accuracy of the results has been verified using three test problems: first, a synthetic problem for which the authors developed a semi-analytical solution; second, natural convection of air in a square cavity with different Rayleigh numbers (103-108); and third, a transient natural convection problem of low Prandtl fluid with horizontal temperature gradient in a rectangular cavity. Originality/value -The proposed model is the first to combine advanced numerical methods (CR, DG, MPFA) for buoyancy-driven flow problems. It is also the first to use a non-iterative time stepping scheme based on local truncation error control for such coupled problems. The developed semi analytical solution based on Fourier series is also novel.

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“…The non-linear convective term is discretized using an upstream approach with weight as in (see for instance, Schieweck and Tobiska, 1989;Djadel and Nicaise, 2008).…”

Section: Flow Discretizationmentioning

confidence: 99%

“…In the following, we recall the main stages for the discretization of the Navier-Stokes equation (1) with the CR triangular elements. The non-linear convective term is discretized using an upstream approach with weight as in (see for instance, Schieweck and Tobiska, 1989;Djadel and Nicaise, 2008).…”

Section: Flow Discretizationmentioning

confidence: 99%

A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows

Younès

Makradi

Zidane

et al. 2014

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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show abstract

“…Several other approaches pertinent to this problem are also available, as, for example, the finite volume element methods, and the mimetic finite difference methods. Since there is a huge amount of literature concerning these latter techniques, we just refer the interested reader to [9,17] for a recent overwiew.…”

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confidence: 99%

The Discrete Duality Finite Volume Method for Convection-diffusion Problems

Coudière¹,

Manzini²

2010

SIAM J. Numer. Anal.

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In this paper we extend the Discrete Duality Finite Volume (DDFV) formulation to the steady convection-diffusion equation. The discrete gradients defined in DDFV are used to define a cellbased gradient for the control volumes of both the primal and dual meshes, in order to achieve a higher-order accurate numerical flux for the convection term. A priori analysis is carried out to show convergence of the approximation and a global first-order convergence rate is derived. The theoretical results are confirmed by some numerical experiments.

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A new benchmark with high accurate solution for hot–cold fluids mixing

et al. 2015

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International audienceA new benchmark is proposed for the verification of buoyancy-driven flow codes. The benchmark deals with mixing hot and cold fluids from the opposite boundaries of an open channel. A high accurate solution is developed using the Fourier–Galerkin (FG) method and compared to the results of an advanced finite element (FE) model. An excellent agreement is observed between the FG and FE solutions for different Reynolds numbers which demonstrates the viability of the solutions in benchmarking buoyancy-driven flow numerical codes

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A non-conforming finite volume element method of weighted upstream type for the two-dimensional stationary Navier–Stokes system

Cited by 8 publications

References 18 publications

A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows

A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows

The Discrete Duality Finite Volume Method for Convection-diffusion Problems

A new benchmark with high accurate solution for hot–cold fluids mixing

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