Eikonal equation‐based front propagation for arbitrary complex configurations

Wang, Y.; Guibault, François; Camarero, R.

doi:10.1002/nme.2063

Cited by 11 publications

(12 citation statements)

References 28 publications

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“…Accordingly, the computation of marching directions is defined in the solution space of the adopted governing equation rather than in the geometric space. For example, the marching direction at a point could be defined as the gradient vector of the solution at that point [25]. At present, a frequently adopted governing equation is the Eikonal equation, and the adopted numerical schemes for the solution include the fast-marching method [25,28], fast sweeping method [29], the finite element method and the finite difference method.…”

Section: On Computation Of Marching Directionsmentioning

confidence: 99%

“…For example, the marching direction at a point could be defined as the gradient vector of the solution at that point [25]. At present, a frequently adopted governing equation is the Eikonal equation, and the adopted numerical schemes for the solution include the fast-marching method [25,28], fast sweeping method [29], the finite element method and the finite difference method. To harness these numerical schemes, an additional volume background mesh is always created [24][25][26][27].…”

Section: On Computation Of Marching Directionsmentioning

confidence: 99%

“…At present, a frequently adopted governing equation is the Eikonal equation, and the adopted numerical schemes for the solution include the fast-marching method [25,28], fast sweeping method [29], the finite element method and the finite difference method. To harness these numerical schemes, an additional volume background mesh is always created [24][25][26][27]. Recently, the Laplacian equation has been chosen as the governing PDE but changed from the scalar function to a vector one [1].…”

Section: On Computation Of Marching Directionsmentioning

confidence: 99%

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Hybrid Grid Generation for Viscous Flow Simulations in Complex Geometries

Liu

Chen

et al. 2020

Preprint

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In this paper, we present a hybrid grid generation approach for viscous flow simulations by marching a surface triangulation on viscous walls along certain directions. Focuses are on the computing strategies used to determine the marching directions and distances since these strategies determine the quality of the resulting elements and the reliability of the meshing procedure to a large extent. With respect to marching direction, three strategies featured with different levels of efficiencies and robustness performance are combined to compute the initial normals at front nodes to balance the trade-off between efficiency and robustness. A novel weighted strategy is used in the normal smoothing scheme, which evidently reduce the possibility of early stop of front generation at complex corners. With respect to marching distances, the distance settings at concave and/or convex corners are locally adjusted to smooth the front shape at first; a further adjustment is then conducted for front nodes in the neighbourhood of gaps between opposite viscous boundaries. These efforts, plus other special treatments such as multi-normal generation and fast detection of local/global intersection, as a whole enable the setup of a hybrid mesher that could generate qualitied viscous grids for geometries with industry-level complexities.

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Section: On Computation Of Marching Directionsmentioning

confidence: 99%

Section: On Computation Of Marching Directionsmentioning

confidence: 99%

Section: On Computation Of Marching Directionsmentioning

confidence: 99%

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Hybrid Grid Generation for Viscous Flow Simulations in Complex Geometries

Liu

Chen

et al. 2020

Preprint

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“…In his seminal work, Sethian proposes a method to advance structured meshes by solving the Eikonal equation [23]. Another front propagation method based on the Eikonal equation is presented in [24]. In [25,26], the authors show how to obtain the medial axis transform (MAT) by means of the Eikonal equation.…”

Section: Related Workmentioning

confidence: 99%

The receding front method applied to hexahedral mesh generation of exterior domains

Ruiz‐Gironés

Roca

Sarrate

2011

Engineering with Computers

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Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside-outside approach. On the other hand, advancing front methods generate highquality hexahedra near the boundary using an outside-inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside-outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.

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“…Recently, Wang et al . proposed generating boundary-layer meshes in three dimensions using a fast marching method with unit speed [31, 39]. However, their method does not allow for the adaptation of the marching based on the geometry or physics, and difficulties still remain in reconstructing the connectivities [39].…”

Section: Background and Related Workmentioning

confidence: 99%

Variational generation of prismatic boundary‐layer meshes for biomedical computing

Dyedov

Einstein

Jiao

et al. 2009

Numerical Meth Engineering

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SUMMARYBoundary-layer meshes are important for numerical simulations in computational fluid dynamics, including computational biofluid dynamics of air flow in lungs and blood flow in hearts. Generating boundary-layer meshes is challenging for complex biological geometries. In this paper, we propose a novel technique for generating prismatic boundary-layer meshes for such complex geometries. Our method computes a feature size of the geometry, adapts the surface mesh based on the feature size, and then generates the prismatic layers by propagating the triangulated surface using the faceoffsetting method. We derive a new variational method to optimize the prismatic layers to improve the triangle shapes and edge orthogonality of the prismatic elements and also introduce simple and effective measures to guarantee the validity of the mesh. Coupled with a high-quality tetrahedral mesh generator for the interior of the domain, our method generates high-quality hybrid meshes for accurate and efficient numerical simulations. We present comparative study to demonstrate the robustness and quality of our method for complex biomedical geometries.

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Eikonal equation‐based front propagation for arbitrary complex configurations

Cited by 11 publications

References 28 publications

Hybrid Grid Generation for Viscous Flow Simulations in Complex Geometries

Hybrid Grid Generation for Viscous Flow Simulations in Complex Geometries

The receding front method applied to hexahedral mesh generation of exterior domains

Variational generation of prismatic boundary‐layer meshes for biomedical computing

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