A stable projection method for the incompressible Navier–Stokes equations on arbitrary geometries and adaptive Quad/Octrees

Guittet, Arthur; Theillard, Maxime; Gibou, Frédéric

doi:10.1016/j.jcp.2015.03.024

Cited by 62 publications

(50 citation statements)

References 65 publications

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“…We follow [23] in designing our finite volume scheme, and discretize (1) for every mesh K and component i = 1, 2 in the following way: The different equations (4) amount to a nonlinear system that can be written in matrix form (for example K ∇ • u ≈ D • U where D is a divergence matrix). We formally define the gradient matrix as −D t , that is, the discrete gradient is the dual operator of the discrete divergence [22,23,32].…”

Section: Pruningmentioning

confidence: 99%

High order time integration and mesh adaptation with error control for incompressible Navier–Stokes and scalar transport resolution on dual grids

N'Guessan

Massot

Séries

et al. 2021

Journal of Computational and Applied Mathematics

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Relying on a building block developed by the authors in order to resolve the incompressible Navier-Stokes equation with high order implicit time stepping and dynamic mesh adaptation based on multiresolution analysis with collocated variables, the present contribution investigates the ability to extend such a strategy for scalar transport at relatively large Schmidt numbers using a finer level of refinement compared to the resolution of the hydrodynamic variables, while preserving space adaptation with error control. This building block is a key part of a strategy to construct a low-Mach number code based on a splitting strategy for combustion applications, where several spatial scales are into play. The computational efficiency and accuracy of the proposed strategy is assessed on a well-chosen three-vortex simulation.

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Section: Pruningmentioning

confidence: 99%

High order time integration and mesh adaptation with error control for incompressible Navier–Stokes and scalar transport resolution on dual grids

N'Guessan

Massot

Séries

et al. 2021

Journal of Computational and Applied Mathematics

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“…English et al [2013a;2013b] constructed a nested (Chimera) grid scheme relying on the flexibility of the local Voronoi structure to stitch together the boundaries between regular grids of differing resolutions. Voronoi diagrams have similarly been exploited in computational physics: Guittet et al improved the ghost-fluid method for two-phase Poisson problems by aligning Voronoi faces with the fluid interface [Guittet et al 2015a], and separately used the Voronoi diagram of fluid face midpoints to treat viscosity on non-graded octrees [Guittet et al 2015b]. Fig.…”

Section: Tetrahedralmentioning

confidence: 99%

“…Another option to recover orthogonality would be the Voronoi diagram of the octree cell centers. For non-graded trees this can yield very general unstructured meshes that discard the regularity benefits of the tree structure (see e.g., [Guittet et al 2015b]). While the variety of mesh configurations can naturally be reduced by grading, the Voronoi topology still differs more strongly from the original tree than for the power diagram, even in the simpler 2D setting (see Figure 4(c)).…”

Section: Power Diagram Discretizationmentioning

confidence: 99%

Power diagrams and sparse paged grids for high resolution adaptive liquids

et al. 2017

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Fig. 1. (Left)Water filling a river bed surrounded by a canyon, with effective resolution 512 2 × 1024. Three refinement levels are used, based on proximity to the terrain. (Right) Sources inject water into a container and collide to form a thin sheet, with effective resolution 512 3 . Adaptivity pattern shown on background.We present an efficient and scalable octree-inspired fluid simulation framework with the flexibility to leverage adaptivity in any part of the computational domain, even when resolution transitions reach the free surface. Our methodology ensures symmetry, definiteness and second order accuracy of the discrete Poisson operator, and eliminates numerical and visual artifacts of prior octree schemes. This is achieved by adapting the operators acting on the octree's simulation variables to reflect the structure and connectivity of a power diagram, which recovers primal-dual mesh orthogonality and eliminates problematic T-junction configurations. We show how such operators can be efficiently implemented using a pyramid of sparsely populated uniform grids, enhancing the regularity of operations and facilitating parallelization. A novel scheme is proposed for encoding the topology of the power diagram in the neighborhood of each octree cell, allowing us to locally reconstruct it on the fly via a lookup table, rather than resorting to costly explicit meshing. The pressure Poisson equation is solved via a highly efficient, matrix-free multigrid preconditioner for Conjugate Gradient, adapted to the power diagram discretization. We use another sparsely † M. Aanjaneya and M. Gao are joint first authors. * M. Aanjaneya was with the University of Wisconsin -Madison during this work. This work was supported in part by National Science Foundation grants IIS-1253598, CCF-1423064, CCF-1533885 and by the Natural Sciences and Engineering Research Council of Canada under grant RGPIN-04360-2014. The authors are grateful to Nathan Mitchell for his indispensable help with modeling and rendering of examples. C. Batty would like to thank Ted Ying for carrying out preliminary explorations on quadtrees. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. populated uniform grid for high resolution interface tracking with a narrow band level set representation. Using the recently introduced SPGrid data structure, sparse uniform grids in both the power diagram discretization and our narrow band level set can be compactly stored and efficiently updated via streaming operations. Additionally, we present enhancem...

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“…The behavior of the fluid is described by the Navier-Stokes equations for incompressible flows. For details the interested reader can also see [20,10].…”

Section: Fsi Problemωmentioning

confidence: 99%

Coupling of Fluid Stucture Intraction Solver With a Vof Method for Multiphase Structure Interaction

Cerroni¹,

Vià²,

Manservisi³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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A stable projection method for the incompressible Navier–Stokes equations on arbitrary geometries and adaptive Quad/Octrees

Cited by 62 publications

References 65 publications

High order time integration and mesh adaptation with error control for incompressible Navier–Stokes and scalar transport resolution on dual grids

High order time integration and mesh adaptation with error control for incompressible Navier–Stokes and scalar transport resolution on dual grids

Power diagrams and sparse paged grids for high resolution adaptive liquids

Coupling of Fluid Stucture Intraction Solver With a Vof Method for Multiphase Structure Interaction

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