A meshfree interface-finite element method for modelling isothermal solutal melting and solidification in binary systems

作者：Ghoneim A^*

来源：Finite Elements in Analysis and Design, 2015, 95: 20-41.

DOI：10.1016/j.finel.2014.10.002

• Level set method
• Radial basis functions
• Meshfree methods
• Finite elements
• Solidification
• Melting

In this paper, numerical modelling of isothermal solutal melting and solidification in binary systems is done using a new meshfree interface-finite element method (MI-FEM) where the implicitly represented liquid-solid interface is allowed to arbitrarily intersect the finite elements. A meshfree radial basis functions (RBFs) method is used for solving a distance-regularized level set (DRLS) equation such that re-initialization is completely eliminated and fast marching algorithms for interfacial velocity extension are not necessary resulting in a more efficient solution with excellent volume conservation. In the proposed method, intersection points between the mesh and the zero level set are used as meshiree nodes such that at the interface-embedded elements interpolants are constructed using meshfree RBFs ensuring both the partition of unity and Kronecker-delta properties are satisfied allowing for precise and easy imposition of Dirichlet boundary conditions (DBCs) on each side of the interface. A coupling of the MI-FEM with a new meshfree automata (MA) method is used to efficiently predict the microstructural evolution during solidification. Benchmark problems with strong discontinuities were solved where very good accuracy was obtained. The solute conservation and interfacial equilibrium equations describing solutal phase transformation in binary systems were solved using the newly developed method. Mathematical formulation and implementation followed by numerical results and analysis will be presented and discussed.

• 出版日期2015-3