On the Application of FMG to Variational Approximation of Flow Problems

Carré, Gilles; Dervieux, Alain

doi:10.1080/10618569908940817

Cited by 7 publications

(9 citation statements)

References 11 publications

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“…This scheme extended to compressible Navier-Stokes equations by Rostand and Stoufflet [14] is widely used in works of Eymard et al [6], Arminjon and Madrane [15], Carré and Dervieux [16], Debiez et al [17], Dervieux and Desideri [18], Farhat and Lanteri [19], Guillard [20], Guillard and Viozat [21], Lanteri [22], Le Ribault et al [23], Mer [24], etc. The method is based on the combination of a Galerkin finite element method for the diffusive part of the system and of a vertex finite volume scheme for the discretization of the convective part: indeed, the latter allows us to introduce flux splitting and upwinding techniques.…”

Section: Introductionmentioning

confidence: 99%

Footbridge between finite volumes and finite elements with applications to CFD

Pascal

Ghidaglia

2001

Numerical Methods in Fluids

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SUMMARYThe aim of this paper is to introduce a new algorithm for the discretization of second-order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier-Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided.

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Section: Introductionmentioning

confidence: 99%

Footbridge between finite volumes and finite elements with applications to CFD

Pascal

Ghidaglia

2001

Numerical Methods in Fluids

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“…The FMG theory 15 states that if the solution is fully converged at stage 1, then it is sufficient to converge the solution by one order of magnitude at stages 2, 3, etc. in order to achieve the global convergence on the finest mesh.…”

Section: Onmentioning

confidence: 99%

“…Moreover, anisotropic coarsening can automatically be handled using mesh adaptation. According to the FMG theory, 15 multigrid schemes can improve the convergence of the solution in the mesh adaptation loop. Indeed, it states that, if the solution is fully converged at stage 1, then it is sufficient to converge the solution by one order of magnitude at stages 2, 3, etc.…”

Section: 4mentioning

confidence: 99%

Multigrid Strategies Coupled with Anisotropic Mesh Adaptation

Menier

Loseille

Alauzet

2015

53rd AIAA Aerospace Sciences Meeting

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This paper is an attempt to combine a full multigrid (FMG) algorithm with the classical anisotropic mesh adaptation loop. The FMG algorithm aims at improving the convergence rate of the flow solver, while mesh adaptation tends to improve the tradeoff between CPU time and accuracy of the solution. Coupling these two methods consists, at each stage of the adaptation loop, in running a multigrid simulation using the previously adapted coarser meshes. The main benefits of this coupling are that (i) the convergence of mesh adaptation is improved thanks to the properties stated by the FMG theory, and (ii) anisotropic coarsening is automatically handled by mesh adaptation. First, the implementation and the validation of the multigrid procedures are described, and then the coupling is detailed. Results are presented in 2D and 3D for various flow prescriptions, including a real-life configuration.

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“…With the method proposed in this paper, many anisotropic strategies can be applied thanks to the way we parameterize our meshes, but this issue is not addressed in this paper.Second, for many complex applications, it has been remarked that FMG does not work, in the sense that the usual stopping criterion produces a discrete final solution with an accuracy deteriorated by an insufficient iterative resolution. See for example [7]. Let us examine a possible FMG failure scenario.…”

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confidence: 99%

A mesh‐adaptative metric‐based full multigrid for the Poisson problem

Brèthes

Allain

Dervieux

2015

Numerical Methods in Fluids

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Summary This paper studies the combination of the full‐multigrid (FMG) algorithm with an anisotropic metric‐based mesh adaptation algorithm. For the sake of simplicity, the case of an elliptic two‐dimensional partial differential equation is studied. Meshes are unstructured and non‐embedded, defined through the metric‐based parameterization. A rather classical MG preconditioner is applied, in combination with a quasi‐Newton fixed point. An anisotropic metric‐based mesh adaptation loop is introduced inside the FMG algorithm. FMG convergence stopping test is revisited. Applications to a few two‐dimensional continuous and discontinuous coefficient elliptic model problems show the efficiency of this combination. Copyright © 2015 John Wiley & Sons, Ltd.

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On the Application of FMG to Variational Approximation of Flow Problems

Cited by 7 publications

References 11 publications

Footbridge between finite volumes and finite elements with applications to CFD

Footbridge between finite volumes and finite elements with applications to CFD

Multigrid Strategies Coupled with Anisotropic Mesh Adaptation

A mesh‐adaptative metric‐based full multigrid for the Poisson problem

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