Mesh Generation Using Unstructured Computational Meshes and Elliptic Partial Differential Equation Smoothing

Karman, Steve L.; Anderson, W. Kyle; Sahasrabudhe, Mandar

doi:10.2514/1.15929

Cited by 31 publications

(12 citation statements)

References 6 publications

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“…where r in e is the current value of the element insphere radius andr in is the predefined target value. The definition (28) of the fictitious volumetric straiñ * v is motivated by the outcome of numerical experiments in the works of Karman et al 26 and Yang and Mavriplis, 27 where elastic properties inversely proportional to the element volume are shown to lead to a faster convergence of sliver elements toward the desired shape, avoiding the problem of element inversion. In fact, looking at the evolution of̃ * v with r in e shown in Figure 2, one can see that element configurations with r in e <r in are highly penalized, generating a high fictitious pressure p * e = K * ̃ * v,e , tending to infinity for vanishing r in e .…”

Section: Definition Of the P-smoothing Elastic Analogy Problemmentioning

confidence: 99%

“…The result obtained with this coarse mesh will be used as a reference for assessing the effect of the P-Smoothing on the solution accuracy. Table 1 shows a comparison of the fluid front positions at different time instants, varying the parameter a defined in Equation (26). This parameter controls the size of the smoothing domain and consequently the influence of the nodal P-Smoothing on the results of the analysis.…”

Section: Dam Breakmentioning

confidence: 99%

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An efficient runtime mesh smoothing technique for 3D explicit Lagrangian free‐surface fluid flow simulations

Meduri

Cremonesi

Perego

2018

Numerical Meth Engineering

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Summary A fast runtime mesh smoothing algorithm for explicit Lagrangian simulations of 3D weakly compressible viscous fluid flows, implemented in conjunction with the particle finite element method (PFEM), is proposed. The formulation for weakly compressible fluids allows for the use of an explicit time integration scheme. Explicit solvers are appealing for large‐scale engineering problems characterized by fast dynamics and/or a high degree of nonlinearity. However, the conditional stability of these schemes requires the use of small time increments, proportional to the size of the element in the mesh with the worst geometrical quality. The Lagrangian description of the PFEM requires an efficient and robust runtime mesh generator algorithm, such as the Delaunay tessellation, to create new meshes during the analysis, whenever the current ones get too distorted because of the motion of the mesh nodes. When 3D problems are considered, a computationally effective mesh‐improving algorithm is also required because, in 3D, the Delaunay tessellation loses some of its optimality properties holding in 2D so that badly shaped tetrahedra are frequently included in the triangulation, leading to unacceptably small stable time step sizes for the explicit solver. To this purpose, a novel and efficient mesh smoothing technique is here proposed, exploiting an elastic analogy that allows for the use of the same explicit and parallelizable architecture of the fluid solver. This smoothing algorithm has been specifically designed to ensure reasonably large critical time step sizes at an acceptable computational cost. This is particularly appealing for the application of explicit Lagrangian PFEM in large‐scale 3D engineering problems, but it could be conveniently applied also to regularize the mesh and improve the solution of implicit solvers.

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Section: Definition Of the P-smoothing Elastic Analogy Problemmentioning

confidence: 99%

Section: Dam Breakmentioning

confidence: 99%

An efficient runtime mesh smoothing technique for 3D explicit Lagrangian free‐surface fluid flow simulations

Meduri

Cremonesi

Perego

2018

Numerical Meth Engineering

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“…Arbitrary Lagrangian-Eulerian is implemented through a remap following the Lagrangian motion at every cycle. When a remap is employed here, the computational mesh is continuously relaxed at every cycle in one of two ways, either by retaining fixed Eulerian nodal positions or by solving the 3D Winslow equations [33] to iteratively smooth interior nodal points while allowing boundary points to move with a fixed velocity. The remap algorithm, itself, is an extension of a common swept-face method described previously in two dimensions [32].…”

Section: Arbitrary Lagrangian-eulerianmentioning

confidence: 99%

A 3D finite element ALE method using an approximate Riemann solution

Chiravalle

Morgan

2016

Numerical Methods in Fluids

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Summary Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann‐like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann‐like problem. Two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well‐known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented. Copyright © 2016 John Wiley & Sons, Ltd.

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“…In order to simulate the moving boundary problems, two types of grid deformation scheme prevail, which can be based on either an algebraic scheme (Liu et al, 2006;Morton, Melville, & Visbal, 1998;Sheng & Allen, 2013) or a physical-analogy technique (Blom, 2000;Clarence, 2004;Degand & Farhat, 2002;Karman, Anderson, & Sahasrabudhe, 2006;Stein, Tezduyar, & Benney, 2004;Sun, Zhang, & Ren, 2012;Zeng & Ethier, 2005;Zhou & Xu, 2010). The algebraic scheme defines the interior grid node movement as an algebraic function of the boundary node positions.…”

Section: The Grid Deformation Algorithmmentioning

confidence: 99%

“…However, because the algebraic functions are usually geometrically based and have little physical meaning, the control of the behavior of the grid deformation process by the algebraic scheme is often relatively weak and limited. In contrast, physical-analogy techniques such as the linear elastic technique (Karman et al, 2006;Stein et al, 2004) and the spring-analogy technique (Batina, 1991;Blom, 2000;Clarence, 2004;Degand & Farhat, 2002;Zeng & Ethier, 2005) provide the user with more flexibility to control the grid deformation by adjusting the physical parameters in an element-wise or edge-wise manner. For instance, badly-shaped elements can be more stiffened than those well-shaped elements to prevent the early appearance of an element with an unacceptable level of shape quality.…”

Section: The Grid Deformation Algorithmmentioning

confidence: 99%

An improved local remeshing algorithm for moving boundary problems

Zheng

Chen

Zheng

et al. 2016

Engineering Applications of Computational Fluid Mechanics

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Three issues are tackled in this study to improve the robustness of local remeshing techniques. Firstly, the local remeshing region (hereafter referred to as 'hole') is initialized by removing low-quality elements and then continuously expanded until a certain element quality is reached after remeshing. The effect of the number of the expansion cycle on the hole size and element quality after remeshing is experimentally analyzed. Secondly, the grid sources for element size control are attached to moving bodies and will move along with their host bodies to ensure reasonable grid resolution inside the hole. Thirdly, the boundary recovery procedure of a Delaunay grid generation approach is enhanced by a new grid topology transformation technique (namely shell transformation) so that the new grid created inside the hole is therefore free of elements of extremely deformed/skewed shape, whilst also respecting the hole boundary. The proposed local remeshing algorithm has been integrated with an in-house unstructured grid-based simulation system for solving moving boundary problems. The robustness and accuracy of the developed local remeshing technique are successfully demonstrated via industry-scale applications for complex flow simulations. ARTICLE HISTORY

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Mesh Generation Using Unstructured Computational Meshes and Elliptic Partial Differential Equation Smoothing

Cited by 31 publications

References 6 publications

An efficient runtime mesh smoothing technique for 3D explicit Lagrangian free‐surface fluid flow simulations

An efficient runtime mesh smoothing technique for 3D explicit Lagrangian free‐surface fluid flow simulations

A 3D finite element ALE method using an approximate Riemann solution

An improved local remeshing algorithm for moving boundary problems

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