Session: 17-01-01: Research Posters

Paper Number: 144458

144458 - Convolution Finite Element Level Set Method: Application to Additive Manufacturing Simulations 

Level set method is widely adopted for interface tracking and has been applied for many computational science and engineering problems, such as multiphase flow simulations and additive manufacturing modeling. Traditional level set method is usually implemented using finite difference or low order finite element schemes with reinitialization techniques. Regardless of their efficiency, these level set schemes can still encounter stability issues when dealing with complex interface changes. As a result, non-physical oscillations can be observed in solutions of level set equations. The weighted essentially nonoscillator (WENO) [1,2] method has thus been developed to improve the smoothness and accuracy of level set solutions and can mitigate oscillations to some extent. However, this approach still has some limitations due the finite difference nature.

This work proposes an alternative numerical scheme for level set method based on the newly developed convolutional finite element method (C-FEM) [3]. C-FEM is a finite element technique that can enable arbitrarily high order approximations without modifying the mesh. In another word, C-FEM can construct high order approximation based on only linear finite element meshes. Different from conventional high order finite elements, C-FEM offers great advantages in terms of computational costs and flexible adaptivity, as the mesh remains unchanged compared to linear finite elements. It has been demonstrated that C-FEM solutions can have superior accuracy and smoothness with several orders of magnitude improvement, compared to that of traditional linear finite elements. The idea of C-FEM shares some similarity to WENO and is based on the use of a convolution patch on the top of an element to construct high order approximations. Therefore, C-FEM is expected to improve the stability of level set solutions as the WENO method. Moreover, C-FEM can be compatible with many other numerical techniques used in the level set method, such as reinitialization, narrow-band level sets, and the Fast Marching Method, based on a single initial grid. The C-FEM based level set method will be validated against several benchmark problems with extreme flow fields and compared with traditional finite elements and the WENO method. Applications to additive manufacturing simulations will be discussed.

References:

[1] G.S. JIANG, C.W. SHU. (1996). “Efficient Implementation of Weighted ENO Schemes.” Journal of Computational Physics, 126(1), 202–228.

[2] Gibou, F., Fedkiw, R., & Osher, S. (2018). A review of level-set methods and some recent applications. Journal of Computational Physics, 353, 82–109.

[3] Y. Lu, H. Li, L. Zhang, C. Park, S. Mojumder, S. Knapik, Z. Sang, S. Tang, D. W. Apley, G. J. Wagner, and W. K. Liu, (2023). Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond. Computational Mechanics, 72(2), 333-362.

 

Presenting Author: Chaoqian Yuan University of Maryland Baltimore County

Presenting Author Biography: N/A

Authors:

Chaoqian Yuan University of Maryland Baltimore County
Ye Lu University of Maryland Baltimore County