Finite element simulation of planar instabilities during solidification of an undercooled melt
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Computing minimal surfaces via level set curvature flow
Journal of Computational Physics
Variational algorithms and pattern formation in dendritic solidification
Journal of Computational Physics
Computation of dendrites using a phase field model
Proceedings of the twelfth annual international conference of the Center for Nonlinear Studies on Nonlinearity in Materials Science
Microstructural evolution in inhomogeneous elastic media
Journal of Computational Physics
Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
A level-set method for simulating island coarsening
Journal of Computational Physics
Discontinuous enrichment in finite elements with a partition of unity method
Finite Elements in Analysis and Design - Special issue on Robert J. Melosh medal competition
Some Improvements of the Fast Marching Method
SIAM Journal on Scientific Computing
Modelling dendritic solidification with melt convection using the extended finite element method
Journal of Computational Physics
Hi-index | 31.45 |
A sharp-interface numerical formulation using an Eulerian description aimed at modeling diffusional evolution of precipitates produced by phase transformations in elastic media, is presented. The extended finite element method (XFEM) is used to solve the field equations and the level set method is used to evolve the precipitate-matrix interface. This new formulation is capable of handling microstructures with arbitrarily shaped particles and capturing their topological transitions without needing the mesh to conform with the precipitate-matrix interface. The XFEM makes it possible to model the precipitate and the matrix to be both elastically anisotropic and inhomogeneous with ease. The interface evolution velocity is evaluated using a domain integral scheme [1] that is consistent with the sharp interface. Numerical examples modeling two distinct phases of particle evolution, growth (dendritic evolution) and equilibration (Ostwald ripening) are presented. To overcome the issue of grid anisotropy in growth simulations, a random grid rotation scheme is implemented in conjunction with a bicubic spline interpolation scheme. Growing shapes are dendritic while equilibrium shapes are squarish and in this respect our simulation results are in agreement with those presented in the literature [2-4].