Point Cloud Generation for Meshfree Methods: An Overview

Suchde, Pratik; Jacquemin, Thibault; Davydov, Oleg

doi:10.1007/s11831-022-09820-w

Cited by 27 publications

(9 citation statements)

References 193 publications

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“…Nevertheless, due to the flexibility of mesh‐free schemes, the point cloud generation can be considerably easier than manual mesh generation. A detailed review of point generation methods can be found in Reference 27.…”

Section: Numerical Methodologiesmentioning

confidence: 99%

Assessment of implicit adaptive mesh‐free CFD modelling

Zhang,

Barakos

2024

Numerical Methods in Fluids

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SummaryThis work presents details and assesses implicit and adaptive mesh‐free CFD modelling approaches, to alleviate laborious mesh generation in modern CFD processes. A weighted‐least‐squares‐based, mesh‐free, discretisation scheme was first derived for the compressible RANS equations, and the implicit dual‐time stepping was adopted for improved stability and convergence. A novel weight balancing concept was introduced to improve the mesh‐free modelling on highly irregular point clouds. Automatic point cloud generations based on strand and level‐set points were also discussed. A novel, polar selection approach, was also introduced to establish high‐quality point collocations. The spatial accuracy and convergence properties were validated using 2D and 3D benchmark cases. The impact of irregular point clouds and various point collocation search methods were evaluated in detail. The proposed weight balancing and the polar selection approaches were found capable of improving the mesh‐free modelling on highly irregular point clouds. The mesh‐free flexibility was then exploited for adaptive modelling. Various adaptation strategies were assessed using simulations of an isentropic vortex, combining different point refinement mechanisms and collocation search methods. The mesh‐free modelling was then successfully applied to transonic aerofoil simulations with automated point generation. A weighted pressure gradient metric prioritising high gradient regions with large point sizes was introduced to drive the adaptation. The mesh‐free adaptation was found to effectively improve the shock resolution. The results highlight the potential of mesh‐free methods in alleviating the meshing bottleneck in modern CFD.

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Section: Numerical Methodologiesmentioning

confidence: 99%

Assessment of implicit adaptive mesh‐free CFD modelling

Zhang,

Barakos

2024

Numerical Methods in Fluids

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“…This is because inter-point distances are controlled to fixed multiples of h. The minimum distance between two points is controlled to be greater than r min h, and maximum hole size in the point cloud is given by r max h. This is enforced by merging particles that come too close, and adding them in holes where no points are present. For more details of these addition / deletion procedures, we refer to [15,51,57,59].…”

Section: Notationmentioning

confidence: 99%

“…The point clouds used in the present work are irregularly spaced, without any background grid or mesh. All points clouds are generated using an advancing front point generation method [57,54].…”

Section: Notationmentioning

confidence: 99%

“…Their biggest advantage lie in avoiding the generation of a mesh to discretize the computational domain. Meshfree domain discretization procedures that produce a point cloud or a particle cloud are faster, and can be automated to a higher degree, even for complex domains [57]. Another major advantage of meshfree methods, especially when used in a Lagrangian framework, is the ease of capturing large deformations and displacements in the computational domain.…”

Section: Introductionmentioning

confidence: 99%

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Volume and Mass Conservation in Lagrangian Meshfree Methods

Suchde¹,

Leithäuser²,

Kuhnert³

et al. 2023

Preprint

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Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass conservation does not imply discrete volume conservation. On the other hand, meshfree collocation methods typically do not use any notion of mass. As a result, they are neither mass conservative nor volume conservative at the discrete level. In this paper, we give an overview of various sources of conservation errors across different meshfree methods. The present work focuses on one specific issue: unreliable volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing especially in meshfree collocation methods. Using these, we introduce an artificial compression or expansion in the fluid to rectify errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour, even for complex industrial test cases such as automotive water crossing.

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“…Another possible approach is to use randomlygenerated nodes [17,22]; this approach has been used (with some modifications) in areas such as compressive sensing [1] and function approximation in high dimensions [24]. Other approaches include iterative optimization [12,19,15], sphere-packing [16], QR factorization [34], and repulsion [9,35]. It is generally accepted that quasi-uniformly-spaced node sets improve the stability of meshless methods [36].…”

Section: Introductionmentioning

confidence: 99%

Discretization of non-uniform rational B-spline (NURBS) models for meshless isogeometric analysis

Urban¹,

Shankar²,

Kosec³

2023

Preprint

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We present an algorithm for fast generation of quasi-uniform and variable density spatial nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new algorithm enables the solution of partial differential equations (PDEs) within the volumes enclosed by these CAD models using (collocation-based) meshless numerical discretizations. Our hierarchical algorithm first generates quasi-uniform node sets directly on the NURBS surfaces representing the domain boundary, then uses the NURBS representation in conjunction with the surface nodes to generate nodes within the volume enclosed by the NURBS surface. We provide evidence for the quality of these node sets by analyzing them in terms of local regularity and separation distances. Finally, we demonstrate that these node sets are well-suited (both in terms of accuracy and numerical stability) for meshless radial basis function generated finite differences (RBF-FD) discretizations of the Poisson, Navier-Cauchy, and heat equations. Our algorithm constitutes an important first in bridging the field of node generation for meshless discretizations with mesh generation for isogeometric analysis.

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Point Cloud Generation for Meshfree Methods: An Overview

Cited by 27 publications

References 193 publications

Assessment of implicit adaptive mesh‐free CFD modelling

Assessment of implicit adaptive mesh‐free CFD modelling

Volume and Mass Conservation in Lagrangian Meshfree Methods

Discretization of non-uniform rational B-spline (NURBS) models for meshless isogeometric analysis

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