A more efficient anisotropic mesh adaptation for the computation of Lagrangian coherent structures

Fortin, A.; Briffard, Thomas; Garon, André

doi:10.1016/j.jcp.2015.01.010

Cited by 11 publications

(7 citation statements)

References 19 publications

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“…Hence, B and C are either two neighbouring siblings or two neighbouring ancestral elements E m , E n . If B and C have the same level from the first evaluation in line 2, it means that B is a sibling and a direct neighbour of A as described by the array (21) Face fA = 1…”

Section: Connectivity Assignment Of Neighbouring Cellsmentioning

confidence: 99%

“…H-type refinement results in the re-arrangement of the computational grid. This can be achieved either by relocating the nodes of the mesh [7,21,22,23] or by splitting existing elements in smaller ones [24,19,25,26]. The relocation of the mesh vertices allows us to retain the connectivity topology but eventually leads to highly anisotropic elements [23].…”

Section: Introductionmentioning

confidence: 99%

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An efficient Adaptive Mesh Refinement (AMR) algorithm for the Discontinuous Galerkin method: Applications for the computation of compressible two-phase flows

Papoutsakis

Sazhin

Begg

et al. 2018

Journal of Computational Physics

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We present an Adaptive Mesh Refinement (AMR) method suitable for hybrid unstructured meshes that allows for local refinement and de-refinement of the computational grid during the evolution of the flow. The adaptive implementation of the Discontinuous Galerkin (DG) method introduced in this work (ForestDG) is based on a topological representation of the computational mesh by a hierarchical structure consisting of oct-quad-and binary trees. Adaptive mesh refinement (h-refinement) enables us to increase the spatial resolution of the computational mesh in the vicinity of the points of interest such as interfaces, geometrical features, or flow discontinuities. The local increase in the expansion order (p-refinement) at areas of high strain rates or vorticity magnitude results in an increase of the order of accuracy in the region of shear layers and vortices. A graph of unitarian-trees, representing hexahedral, prismatic and tetrahedral elements is used for the representation of the initial domain. The ancestral elements of the mesh can be split into self-similar elements allowing each tree to grow branches to an arbitrary level of refinement. The connectivity of the elements, their genealogy and their partitioning are described by linked lists of pointers. An explicit calculation of these relations, presented in this paper, facilitates the on-the-fly splitting, merging and repartitioning of the computational mesh by rearranging the links of each node of the tree with a minimal computational overhead. The modal basis used in the DG implementation facilitates the mapping of the fluxes across the non conformal faces. The AMR methodology is presented and assessed using a series of inviscid and viscous test cases. Also, the AMR methodology is used for the modelling of the interaction between droplets and the carrier phase in a two-phase flow. This approach is applied to the analysis of a spray injected into a chamber of quiescent air, using the Eulerian-Lagrangian approach. This enables us to refine the computational mesh in the vicinity of the droplet parcels and accurately resolve the coupling between the two phases.

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Section: Connectivity Assignment Of Neighbouring Cellsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An efficient Adaptive Mesh Refinement (AMR) algorithm for the Discontinuous Galerkin method: Applications for the computation of compressible two-phase flows

Papoutsakis

Sazhin

Begg

et al. 2018

Journal of Computational Physics

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“…these are smooth approximations of Dirac impulses. The system (32) was numerically examined with c given by (38), with the choice of parameters A = 1 and δ = 0.1. The t-discretisation of the previous example was used, with the forward FTLE field computed at each time using the maximum available data (i.e., till T = 2).…”

Section: Time-discontinuous Examplementioning

confidence: 99%

Local Stable and Unstable Manifolds and Their Control in Nonautonomous Finite-Time Flows

Balasuriya

2016

J Nonlinear Sci

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It is well known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each instance in time is the focus of this article. Within a nearly autonomous setting, it is shown that these time-varying directions can be characterised through the accumulated effect of velocity shear. Connections to Oseledets spaces and projection operators in exponential dichotomies are established. Availability of data for both infinite-and finite-time intervals is considered. With microfluidic flow control in mind, a methodology for manipulating these directions in any prescribed time-varying fashion by applying a local velocity shear is developed. The results are verified for both smoothly and discontinuously time-varying directions using finite-time Lyapunov exponent fields, and excellent agreement is obtained.

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“…Miron et al [24] applied AMR in FTLE calculation in anisotropic mesh using a commercial software. Based on this, Fortin et al [6] compared various kinds of adaptive methods to provide a more accurate method. The refinement criterion of all these methods are based on the error of FTLE field.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed whole algorithm is shown as Alg. (1) in Sec.3.1.Several AMR methods in LCS use the traditional AMR method, which focuses on error ([6,8]) or the magnitude of FTLE ([22,32]). In this article, the proposed OAR criterion put refinement particles at the vicinity of LCS, which is discussed detailedly in Sec.3.2.…”

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confidence: 99%

An objective-adaptive refinement criterion based on modified ridge extraction method for finite-time Lyapunov exponent (FTLE) calculation

Hang

Xiang

et al. 2019

J Vis

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High-accuracy and high-efficiency finite-time Lyapunov exponent (FTLE) calculation method has long been a research hot point, and adaptive refinement method is a kind of method in this field. The proposed objectiveadaptive refinement (OAR) criterion can put adaptive particles at the vicinity of FTLE ridges. The FTLE ridge is extracted not simply by the magnitude of FTLE (would cause false negative refinement) and error (would cause false positive refinement) but by a modified gradient climbing method. Moreover, the refinement regions converge to some certain region because of the objectivity of the refinement region. Testing cases include Bickley jet, mild FTLE ridge, and experimental single vortex. The results demonstrate that the proposed algorithm can avoid useless refinement of other methods in some certain areas, and thus reduce error up to 25% compared with the other methods with little difference in the calculation burden.

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A more efficient anisotropic mesh adaptation for the computation of Lagrangian coherent structures

Cited by 11 publications

References 19 publications

An efficient Adaptive Mesh Refinement (AMR) algorithm for the Discontinuous Galerkin method: Applications for the computation of compressible two-phase flows

An efficient Adaptive Mesh Refinement (AMR) algorithm for the Discontinuous Galerkin method: Applications for the computation of compressible two-phase flows

Local Stable and Unstable Manifolds and Their Control in Nonautonomous Finite-Time Flows

An objective-adaptive refinement criterion based on modified ridge extraction method for finite-time Lyapunov exponent (FTLE) calculation

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