Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Crystal growth and dendritic solidification
Journal of Computational Physics
A fast adaptive vortex method in three dimensions
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
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
Journal of Computational Physics
Front-tracking finite element method for dendritic solidification: 765
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Level Set Approach for the Numerical Simulation of Dendritic Growth
Journal of Scientific Computing
A partial differential equation approach to multidimensional extrapolation
Journal of Computational Physics
Local level set method in high dimension and codimension
Journal of Computational Physics
A node-centered local refinement algorithm for Poisson's equation in complex geometries
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A second order accurate level set method on non-graded adaptive cartesian grids
Journal of Computational Physics
Journal of Computational Physics
A hybrid level set-volume constraint method for incompressible two-phase flow
Journal of Computational Physics
Journal of Scientific Computing
A Multigrid Method on Non-Graded Adaptive Octree and Quadtree Cartesian Grids
Journal of Scientific Computing
Hi-index | 31.46 |
We present a level set approach to the numerical simulation of the Stefan problem on non-graded adaptive Cartesian grids, i.e. grids for which the size ratio between adjacent cells is not constrained. We use the quadtree data structure to discretize the computational domain and a simple recursive algorithm to automatically generate the adaptive grids. We use the level set method on quadtree of Min and Gibou [C. Min, F. Gibou, A second order accurate level set method on non-graded adaptive Cartesian grids, J. Comput. Phys. 225 (2007) 300-321] to keep track of the moving front between the two phases, and the finite difference scheme of Chen et al. [H. Chen, C. Min, F. Gibou, A supra-convergent finite difference scheme for the poisson and heat equations on irregular domains and non-graded adaptive Cartesian grids, J. Sci. Comput. 31 (2007) 19-60] to solve the heat equations in each of the phases, with Dirichlet boundary conditions imposed on the interface. This scheme produces solutions that converge supralinearly (~1.5) in both the L^1 and the L^~ norms, which we demonstrate numerically for both the temperature field and the interface location. Numerical results also indicate that our method can simulate physical effects such as surface tension and crystalline anisotropy. We also present numerical data to quantify the saving in computational resources.