A preconditioning for the spectral solution of incompressible variable-density flows

Reynier, L.; Di Pierro, B.; Alizard, F.; Cadiou, A.; Le Penven, L.; Buffat, M.

doi:10.1016/j.compfluid.2023.106024

Cited by 2 publications

(2 citation statements)

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“…The DRBEM and DBEM could also be effective for the numerical solutions of incompressible variable density flows (Almgren et al 1998, Di Pierro and Abid et al 2013, Reynier et al 2023. In this case, the density can be obtained from the additional density equation by approximating easily the space derivatives in this equation with the DRBEM coordinate matrix; which is one of the main advantage of boundary element approaches.…”

Section: Test Problem 2: Lid-driven Cavity Flowmentioning

confidence: 99%

“…One-sided lid-driven cavity flow problem has been investigated and they have obtained reasonable results for higher values of Reynolds number (Re = 10.000). In Almgren et al (1998), Di Pierro and Abid et al (2013), Reynier et al (2023), the variable density incompressible NS equations are solved by using an adaptive projection method, a projection method for the spectral solution, and a combination of fraction-step and finite difference method, respectively.…”

Section: Introductionmentioning

confidence: 99%

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On the BEM solution of convection–diffusion type equations involving variable convective coefficients

Fendoğlu,

Bozkaya,

Tezer-Sezgin

2024

Fluid Dyn. Res.

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In this study, numerical solutions of the unsteady convection–diffusion type equations of variable convective coefficients are investigated by two effective techniques alternative to direct boundary element method (BEM). That is, the domain boundary element and the dual reciprocity BEMs with the fundamental solution of convection–diffusion equation are used in space to transform the governing differential equations into equivalent integral equations while a backward finite difference scheme is utilized in time discretization. The fruitfulness of these combined techniques are shown by the implementation of the techniques for some widely investigated fluid dynamics problems. In fact, the lid-driven cavity flow is solved, and precise results are attained as benchmarks for assessing the accuracy of the aforementioned methods. Further, the application of the methods is extended for the natural convection flow which is governed mainly by the convection–diffusion type equations accompanied by the velocity components as variable convective coefficients. The obtained numerical results reveal that the domain BEM which uses the fundamental solution of convection–diffusion equation captures the characteristics and physical advancement of the fluid flow quite well at various combined values of the problem physical parameters.

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Section: Test Problem 2: Lid-driven Cavity Flowmentioning

confidence: 99%