2021
DOI: 10.3390/math9182316
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A Massively Parallel Hybrid Finite Volume/Finite Element Scheme for Computational Fluid Dynamics

Abstract: In this paper, we propose a novel family of semi-implicit hybrid finite volume/finite element schemes for computational fluid dynamics (CFD), in particular for the approximate solution of the incompressible and compressible Navier-Stokes equations, as well as for the shallow water equations on staggered unstructured meshes in two and three space dimensions. The key features of the method are the use of an edge-based/face-based staggered dual mesh for the discretization of the nonlinear convective terms at the … Show more

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Cited by 16 publications
(22 citation statements)
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“…To solve the incompressible RANS equations in combination with the k − ε turbulence model, we extend the family of hybrid finite volume/finite element methods described in [27][28][29][30][31][32]. This methodology relies on a specific combination of explicit and implicit FV and FE methods to solve the subsystems obtained from the flux splitting introduced in the previous section.…”
Section: The Hybrid Finite Volume/finite Element Methodsmentioning
confidence: 99%
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“…To solve the incompressible RANS equations in combination with the k − ε turbulence model, we extend the family of hybrid finite volume/finite element methods described in [27][28][29][30][31][32]. This methodology relies on a specific combination of explicit and implicit FV and FE methods to solve the subsystems obtained from the flux splitting introduced in the previous section.…”
Section: The Hybrid Finite Volume/finite Element Methodsmentioning
confidence: 99%
“…Throughout this section, capital letters refer to the discrete variables, and the super-index * denotes intermediate approximations, that is, if the state vector is defined as w = (w v , w k , w ε ) T = (ρu, ρv, ρw, ρk, ρε) then, W n is the discrete approximation of w(x, t n ) = (ρu(x, t n ), ρv(x, t n ), ρw(x, t n ), ρk(x, t n ), ρε(x, t n )) T , and W * and W * * are the intermediate approximations. For the sake of simplicity, the hybrid FV/FE method is in the following only presented in two space dimensions, but it has already been implemented as well for the unstructured three-dimensional case, see [27,28,30,31].…”
Section: The Hybrid Finite Volume/finite Element Methodsmentioning
confidence: 99%
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