Discretisation of diffusive fluxes on hybrid grids

Puigt, Guillaume; Auffray, V.; Müller, Jens-Dominik

doi:10.1016/j.jcp.2009.10.037

Cited by 19 publications

(10 citation statements)

References 29 publications

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“…Towards highly efficient and accurate viscous simulations by Navier-Stokes codes, a great deal of effort has recently been devoted to the development of diffusion schemes with particular emphases on high-order methods [1][2][3][4][5][6][7][8][9] and unstructured grid methods [10][11][12][13][14][15][16][17]. A background approach of constructing diffusion schemes common to many methods is to evaluate the solution gradient on a control volume boundary (e.g., by reconstruction) and compute the diffusive flux directly with them.…”

Section: Introductionmentioning

confidence: 99%

Robust and accurate viscous discretization via upwind scheme – I: Basic principle

Nishikawa

2011

Computers & Fluids

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Section: Introductionmentioning

confidence: 99%

Robust and accurate viscous discretization via upwind scheme – I: Basic principle

Nishikawa

2011

Computers & Fluids

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“…Coirier & Powell 1996). While our method for estimating the advective fluxes remains the MUSCL-Hancock scheme, the technique for estimating the diffusive fluxes is essentially contained in the estimation of the velocity gradients at each interface (see Coirier 1994; Puigt et al 2010, for a series of tests on different interface gradient estimates). Looking for better accuracy, we have chosen to couple these two otherwise independent procedures by correcting/biasing the linear extrapolation of the velocity field (stage (I) in Section 3.1) with a viscous source term.…”

Section: (A) Viscosity Kicksmentioning

confidence: 99%

Multidimensional, compressible viscous flow on a moving Voronoi mesh

Muñoz

Springel

Marcus

et al. 2012

Monthly Notices of the Royal Astronomical Society

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Numerous formulations of finite volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes. In many applications, more flexible mesh geometries that can dynamically adjust to the problem at hand and move with the flow in a (quasi) Lagrangian fashion would, however, be highly desirable, as this can allow a significant reduction of advection errors and an accurate realization of curved and moving boundary conditions. Here we describe a novel formulation of viscous continuum hydrodynamics that solves the equations of motion on a Voronoi mesh created by a set of mesh-generating points. The points can move in an arbitrary manner, but the most natural motion is that given by the fluid velocity itself, such that the mesh dynamically adjusts to the flow. Owing to the mathematical properties of the Voronoi tessellation, pathological mesh-twisting effects are avoided. Our implementation considers the full Navier-Stokes equations and has been realized in the AREPO code both in 2D and 3D. We propose a new approach to compute accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a finite volume solver of the Navier-Stokes equations. Through a number of test problems, including circular Couette flow and flow past a cylindrical obstacle, we show that our new scheme combines good accuracy with geometric flexibility, and hence promises to be competitive with other highly refined Eulerian methods. This will in particular allow astrophysical applications of the AREPO code where physical viscosity is important, such as in the hot plasma in galaxy clusters, or for viscous accretion disk models.

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“…For such codes, a coupled finite volume / finite element formalism is generally used: the finite volume formalism for convection defined at dual mesh facets is combined with a finite element approach which provides the definition of gradient inside mesh elements through the use of finite element shape functions. On multi-element shapes, the computation of the gradient for diffusion is a key point, and a new approach has been proposed recently 36 for non simplex elements.…”

Section: B Input / Output Strategymentioning

confidence: 99%

Development of a new hybrid compressible solver inside the CFD elsA software

Puigt

Gazaix²,

Montagnac

et al. 2011

20th AIAA Computational Fluid Dynamics Conference

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A new fully integrated environment for compressible flow simulation on structured and unstructured zones coexisting within the same hybrid mesh is presented. This environment originates from the existing elsA a CFD software tool, developed by ONERA and CERFACS for structured grids, and widely used both in industry and research.Some configurations can not be easily addressed with a fully structured mesh approach. An efficient way to overcome this drawback is to combine structured and unstructured zones in a single hybrid mesh. Structured zones are kept for sake of accuracy in boundary layers, wall clock efficiency and low memory consumption. Unstructured zones enable an easier mesh generation / adaptation process. This paper describes the extension of elsA to unstructured multi-element zones composed of hexahedra, tetrahedra, prisms and pyramids. A key feature is the treatment of structured / unstructured zone interfaces, performed with a mismatched abutting grid interface algorithm.We demonstrate that the Object-Oriented (OO) programming approach is useful and efficient to integrate unstructured data structures and numerical methods into the original software to form a single computational CFD kernel.Software design, numerical algorithm, structured/unstructured block interface treatment, CPU efficiency and parallel scalability, are discussed. Finally, validation examples demonstrating the project status are given.

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Discretisation of diffusive fluxes on hybrid grids

Cited by 19 publications

References 29 publications

Robust and accurate viscous discretization via upwind scheme – I: Basic principle

Robust and accurate viscous discretization via upwind scheme – I: Basic principle

Multidimensional, compressible viscous flow on a moving Voronoi mesh

Development of a new hybrid compressible solver inside the CFD elsA software

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