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
Computation of three dimensional dendrites with finite elements
Journal of Computational Physics
Adaptive mesh refinement computation of solidification microstructures using dynamic data structures
Journal of Computational Physics
Robustness and Scalability of Algebraic Multigrid
SIAM Journal on Scientific Computing
Algebraic Multigrid Based on Element Interpolation (AMGe)
SIAM Journal on Scientific Computing
A Level Set Approach for the Numerical Simulation of Dendritic Growth
Journal of Scientific Computing
On Multi-Mesh H-Adaptive Methods
Journal of Scientific Computing
A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids
Journal of Computational Physics
Efficient computation of dendritic growth with r-adaptive finite element methods
Journal of Computational Physics
Edge Detection by Adaptive Splitting II. The Three-Dimensional Case
Journal of Scientific Computing
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In this paper, we propose an efficient multi-mesh h-adaptive algorithm to solve the level set model of dendritic growth. Since the level set function is used to provide implicitly the location of the phase interface, it is resolved by an h-adaptive mesh with refinement only around the phase interface, while the thermal field is approximated on another h-adaptive mesh. The proposed method not only can enjoy the merits of the level set function to handle complex evolution of the free boundary, but also can achieve the similar accuracy as the front tracking method for the sharp interface model with about the same degrees of freedom. The algorithm is applied to the simulation of the dendritic crystallization in a pure undercooled melt. The accuracy is verified by comparing the computational dendrite tip velocity with solvability theory. Numerical simulations, both in 2D and 3D cases, are presented to demonstrate its capacity and efficiency.