An adaptive level set method based on two‐level uniform meshes and its application to dislocation dynamics

Wang, Hanquan; Xiang, Yang

doi:10.1002/nme.4463

Cited by 10 publications

(7 citation statements)

References 52 publications

(164 reference statements)

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“…The first step devoted to calculating some quantities under the assumption that the design boundaries are fixed, and the second step predicts and moves the nodes on the design boundaries in the desired direction. The update scheme (38), that is, the expression of the iterative scheme to find new coordinates of nodes on the design boundaries, was coupled with the algorithm of geometric adaptive methods during the shape or topology optimization process, so that the design boundaries are moved in the desired direction until the final shape reached within a certain tolerance. The goal of the adaptive procedure presented is to achieve a desired resolution around the interfaces or boundaries.…”

Section: Numerical Algorithmmentioning

confidence: 99%

“…In this calculation, the shape modifications determined by the optimization algorithm are imposed on the previous mesh. Then, the mesh for the new shape is obtained from the previous mesh by solving the Stokes equation and updated by the scheme (38). The update time is very short compared with solving the Stokes problem.…”

Section: Numerical Algorithmmentioning

confidence: 99%

“…Details of adaptive finite element methods and related literature please refer to [30][31][32]. Up to now, there are some adaptive methods to improve the efficiency and accuracy in the literature [33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

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Optimality criteria coupled adaptive mesh method for optimal shape design of Stokes flow

Duan

Qin

2016

Math Methods in App Sciences

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An adaptive mesh method combined with the optimality criteria algorithm is applied to optimal shape design problems of fluid dynamics. The shape sensitivity analysis of the cost functional is derived. The optimization problem is solved by a simple but robust optimality criteria algorithm, and an automatic local adaptive mesh refinement method is proposed. The mesh adaptation, with an indicator based on the material distribution information, is itself shown as a shape or topology optimization problem. Taking advantages of this algorithm, the optimal shape design problem concerning fluid flow can be solved with higher resolution of the interface and a minimum of additional expense. Details on the optimization procedure are provided. Numerical results for two benchmark topology optimization problems are provided and compared with those obtained by other methods. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Numerical Algorithmmentioning

confidence: 99%

Section: Numerical Algorithmmentioning

confidence: 99%

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Optimality criteria coupled adaptive mesh method for optimal shape design of Stokes flow

Duan

Qin

2016

Math Methods in App Sciences

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“…The focus of this study is to smoothen the discontinuous initial concentration field by solving the Hamilton-Jacobi equation introduced in [36,37]. Then, UCCD scheme [25] is adopted, which introduces less dispersion and dissipation errors into the formulation and thus enables simultaneously approximating both first and second derivatives in the concentration transport equation.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Turbidity Current over a Three-Dimensional Seafloor

Yu¹,

Zhao²,

Wen³

et al. 2019

CiCP

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Turbidity current over a Gaussian-bump is investigated numerically using the upwinding combined compact difference (UCCD) scheme and the immersed boundary (IB) method in Cartesian grids. In the prediction of lock-exchange gravity-driven flow motion, the initial discontinuous concentration field is smoothed to avoid numerical oscillation by solving the Hamilton-Jacobi equation. The UCCD spatial scheme with sixth-order accuracy which introduces less dispersion errors is then used to discretize advection and diffusion terms in the calculation of concentration transport equation. Direct forcing IB method is employed to treat solid object bumps in the fluid flow. The incompressible Navier-Stokes solutions are obtained through the projection method. Analysis of the smoothing procedure, grid sensitivity and the effect of the Schmidt numbers is performed for the turbidity current problem to validate the proposed numerical algorithm, which is shown to be capable of accurately demonstrating their results. Finally, several problems of turbidity current over a three-dimensional seafloor are investigated. The front locations of the currents interacting with the bump are predicted under different Reynolds numbers. Also, the current properties, namely the suspended particle mass, sedimentation rate and energy budget, are compared with the available numerical results.

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“…Element subdivision methods have been successfully implemented either on structured Cartesian meshes based on finite difference method or unstructured meshes based on finite element method (FEM) . Barth and Sethian employed an element subdivision scheme for LS calculations on 2D triangular meshes.…”

Section: Introductionmentioning

confidence: 99%

A multi‐level adaptive mesh refinement method for level set simulations of multiphase flow on unstructured meshes

Ngo

Choi

2016

Numerical Meth Engineering

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An adaptive mesh refinement (AMR) technique is proposed for level set simulations of incompressible multiphase flows. The present AMR technique is implemented for two-dimensional/three-dimensional unstructured meshes and extended to multi-level refinement. Smooth variation of the element size is guaranteed near the interface region with the use of multi-level refinement. A Courant-Friedrich-Lewy condition for zone adaption frequency is newly introduced to obtain a mass-conservative solution of incompressible multiphase flows. Finite elements around the interface are dynamically refined using the classical element subdivision method. Accordingly, finite element method is employed to solve the problems governed by the incompressible Navier-Stokes equations, using the level set method for dynamically updated meshes. The accuracy of the adaptive solutions is found to be comparable with that of non-adaptive solutions only if a similar mesh resolution near the interface is provided. Because of the substantial reduction in the total number of nodes, the adaptive simulations with two-level refinement used to solve the incompressible Navier-Stokes equations with a free surface are about four times faster than the non-adaptive ones. Further, the overhead of the present AMR procedure is found to be very small, as compared with the total CPU time for an adaptive simulation. Figure 14. Free surface propagation over time with adapted meshes based on initial mesh M2 at selected times, where shadow area represents water: (a) t D 0, (b) t D 1:3, (c) t D 2:6, (d) t D 4:2, (e) t D 5:6, (f) t D 6:6, and (g) t D 8.

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An adaptive level set method based on two‐level uniform meshes and its application to dislocation dynamics

Cited by 10 publications

References 52 publications

Optimality criteria coupled adaptive mesh method for optimal shape design of Stokes flow

Optimality criteria coupled adaptive mesh method for optimal shape design of Stokes flow

Numerical Study of Turbidity Current over a Three-Dimensional Seafloor

A multi‐level adaptive mesh refinement method for level set simulations of multiphase flow on unstructured meshes

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