A Novel Least-Squares Level Set Method by Using Polygonal Elements

Các tác giả

  • Tran Ba Dinh Nguyen Japan Technology and Engineering Co. Ltd, Viet Nam
  • Hoang Son Nguyen Ton Duc Thang University, Vietnam
  • Duc-Huynh Phan Ho Chi Minh City University of Technology and Education, Vietnam

Email tác giả liên hệ:

huynhpd@hcmute.edu.vn

DOI:

https://doi.org/10.54644/jte.72A.2022.1232

Từ khóa:

Polygonal Elements, Level Set Method, Convection-diffusion, Least-squares method, Re-initialization

Tóm tắt

In this study, we apply an artificial viscosity method to convert an unsteady level set (LS) convection equation into an unsteady LS convection-diffusion transport equation to stabilize the numerical solution of the convection term. Then a novel least-square polygonal finite element method is used to solve an unsteady LS convection-diffusion problem. The least-squares method provided good mathematical properties such as natural numerical diffusion and the positive definite symmetry of the resulting algebraic systems for the convection-diffusion and re-initialization equations. The proposed method is evaluated numerically in two different benchmark problems: a rigid body rotation of Zalesak’s disk, and a time-reversed single-vortex flow. In comparison with conventional triangular (T3) and quadrilateral (Q4) elements, polygonal elements are capable of providing greater flexibility in mesh generation for complicated problems as well as more accurate in solving the LS equations. In addition, the numerical results are also compared with the results which obtained from essentially non-oscillatory type formulations and particle LS methods. The results show that the proposed method completely matches the previously published results.

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Tiểu sử của Tác giả

Tran Ba Dinh Nguyen, Japan Technology and Engineering Co. Ltd, Viet Nam

Ba-Dinh Nguyen-Tran. received the B.S degree in mechanical engineering from Ho Chi Minh City University of Technology and Education, Ho Chi Minh, Viet Nam, in 2017 and the M.S. degree in engineering mechanics from Ho Chi Minh City University of Technology and Education, Ho Chi Minh, Viet Nam, in 2019.

From 2019 to present, he is a staff in Japan Technology and Engineering Co. Ltd, Ho Chi Minh, Viet Nam. His research interest includes: computational mechanics, fluid-Structure interaction.

Hoang Son Nguyen, Ton Duc Thang University, Vietnam

Son H. Nguyen. is a full-time researcher in Institute for Computational Science at Ton Duc Thang University. His research interests are in the area of computational solid mechanics with a particular emphasis on topology optimization using the level set method and polygonal elements.

Duc-Huynh Phan, Ho Chi Minh City University of Technology and Education, Vietnam

Duc-Huynh Phan.  received the B.S. degree in aeronautical engineering from HCMC University of Technology, Ho Chi Minh, Viet Nam, in 2001, the M.S. degree in mechanics of constructions from University of Liège, Wallonia, Belgium, in 2003, and the Ph.D. degree in Structural control from Ritsumeikan University, Kyoto, Japan, in 2008.

From 2008 to present, he is a lecturer in HCMC University of Technology and Education, Ho Chi Minh, Viet Nam. His research interest includes: structural stability, computational mechanics, fluid-Structure interaction, and multi-body dynamics.

Tài liệu tham khảo

S.H. Nguyen and H.-G. Kim, "Stress-constrained shape and topology optimization with the level set method using trimmed hexahedral meshes," Methods Appl. Mech. Engrg., vol. 366, pp. 061-113, 2020.

C. Basting, D. Kuzmin, "A minimization-based finite element formulation for interface-preserving level set reinitialization," Computing, vol. 95, no. 1, pp. 13-25, 2012.

S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Verlag New York: Springer, 2003.

M. Sussman, P. Smereka, S. Osher, "A level set approach for computing solutions to incompressible two-phase flow," J. Comput. Phys., vol. 144, no. 1, pp. 146-159, 1994.

H.G. Choi, "A least-square weighted residual method for level set simulation," Int. J. Numer. Meth. Fluids, vol. 68, pp. 887-904, 2012.

J.A. Sethian, "A fast marching level set method for monotonically advancing fronts," Proc. Natl. Acad. Sci. USA, vol. 93, no. 4, pp. 1591-1595, 1996.

R.N. Elias, M.A.D. Martins, and A.L.G.A. Coutinho, "Simple finite element-based computation of distance functions in unstructured grids," Int. J. Numer. Methods Engrg, vol. 72, pp. 1095-1110, 2007.

H. N.-Xuan, S. N.-Hoang, T. Rabczuk, and K. Hackl, "A polytree-based adaptive approach to limit analysis of cracked structures," Computer Methods in Applied Mechanics and Engineering, vol. 313, pp. 1006-1039, 2017.

H. N.-Xuan, "A polygonal finite element method for plate analysis," Computers & Structures, vol. 188, pp. 45-62, 2017.

T.J. Barth and J.A. Sethian, "Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains," J. Comput. Phys., vol. 145, pp. 1-40, 1998.

C. Lin, H. Lee, T. Lee, and L.J. Weber, "A LS characteristic Galerkin finite element method for free surface flows," Int. J. Numer. Meth. Fluids, vol. 49, pp. 521-547, 2005.

E. Marchandise, J.-F. Remacle, and N. Chevaugeon, "A quadrature-free discontinuous Galerkin method for the level set equation," J. Comput. Phys., vol. 212, pp. 338-357, 2006.

M.H. Cho, H.G. Choi, and J.Y. Yoo, "A direct reinitialization approach of level-set/splitting finite element method for simulating incompressible two-phase flows," Int. J. Numer. Meth. Fluids, vol. 67, pp. 1637-1654, 2011.

J. Donea and A. Huerta, Finite element methods for flow problems, Chichester: Wiley, 2003.

M.S. Floater, A. Gillette, and N. Sukumar, "Gradient bounds for Wachspress coordinates on polytopes," SIAM Journal of Numerical Analysis, vol. 52, no. 1, pp. 515-532, 2014.

S. E. Hieber and P. Koumoutsakos, “A Lagrangian particle level set method,” Journal of Computational Physics., vol. 204, no. 1, pp. 342-367, 2005.

D. Enright, R. Fedkiw, J. Ferziger, and I. Mitchell, “A Hybrid Particle Level Set Method for Improved Interface Capturing,” Journal of Computational Physics., vol. 183, no. 1, pp. 83-116, 2002.

Tải xuống

Đã Xuất bản

2022-10-28

Cách trích dẫn

[1]
T. B. D. . Nguyen, H. S. Nguyen, và D.-H. Phan, “A Novel Least-Squares Level Set Method by Using Polygonal Elements”, JTE, vol 17, số p.h 5, tr 45–53, tháng 10 2022.

Số

T. 17 S. 5 (2022)

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