Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A front-tracking method for dendritic solidification
Journal of Computational Physics
A simple level set method for solving Stefan problems
Journal of Computational Physics
A conserving discretization for the free boundary in a two-dimensional Stefan problem
Journal of Computational Physics
The fast construction of extension velocities in level set methods
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
A mathematical model for the dissolution of particles in multi-component alloys
Journal of Computational and Applied Mathematics
A moving mesh method for the solution of the one-dimensional phase-field equations
Journal of Computational Physics
Solution of vector Stefan problems with cross-diffusion
Journal of Computational and Applied Mathematics
Hi-index | 31.45 |
A sharp interface method is proposed for the dissolution of stoichiometric particles in multi-component alloys occurring during the heat treatments of as-cast aluminium alloys prior to hot extrusion. In the mathematical model, a number of non-linearly coupled diffusion equations are given to determine the position of the particle interface and the interfacial concentrations. A level set method is used to determine the interface position at each time step. Once the front position is known, a fixed-point iteration is used to find the interfacial concentrations. The model is applicable to both complete and incomplete dissolution in two and three spatial dimensions, and handles topological changes in a natural fashion. The numerical solution is compared with steady-state and self-similar exact solutions available for simple particle geometries. Subsequently, the model is applied to an AlMgSi-alloy to investigate the influence of the particle morphology in the dissolution kinetics.