TY - JOUR

T1 - A second order accurate level set method on non-graded adaptive cartesian grids

AU - Min, Chohong

AU - Gibou, Frédéric

N1 - Funding Information:
The research of F. Gibou was supported in part by the Alfred P. Sloan Foundation through a research fellowship in Mathematics.

PY - 2007/7/1

Y1 - 2007/7/1

N2 - We present a level set method on non-graded adaptive Cartesian grids, i.e. grids for which the ratio between adjacent cells is not constrained. We use quadtree and octree data structures to represent the grid and a simple algorithm to generate a mesh with the finest resolution at the interface. In particular, we present (1) a locally third order accurate reinitialization scheme that transforms an arbitrary level set function into a signed distance function, (2) a second order accurate semi-Lagrangian methods to evolve the linear level set advection equation under an externally generated velocity field, (3) a second order accurate upwind method to evolve the non-linear level set equation under a normal velocity as well as to extrapolate scalar quantities across an interface in the normal direction, and (4) a semi-implicit scheme to evolve the interface under mean curvature. Combined, we obtain a level set method on adaptive Cartesian grids with a negligible amount of mass loss. We propose numerical examples in two and three spatial dimensions to demonstrate the accuracy of the method.

AB - We present a level set method on non-graded adaptive Cartesian grids, i.e. grids for which the ratio between adjacent cells is not constrained. We use quadtree and octree data structures to represent the grid and a simple algorithm to generate a mesh with the finest resolution at the interface. In particular, we present (1) a locally third order accurate reinitialization scheme that transforms an arbitrary level set function into a signed distance function, (2) a second order accurate semi-Lagrangian methods to evolve the linear level set advection equation under an externally generated velocity field, (3) a second order accurate upwind method to evolve the non-linear level set equation under a normal velocity as well as to extrapolate scalar quantities across an interface in the normal direction, and (4) a semi-implicit scheme to evolve the interface under mean curvature. Combined, we obtain a level set method on adaptive Cartesian grids with a negligible amount of mass loss. We propose numerical examples in two and three spatial dimensions to demonstrate the accuracy of the method.

KW - Adaptive mesh refinement

KW - Extrapolation in the normal direction

KW - Ghost fluid method

KW - Level set method

KW - Motion by mean curvature

KW - Motion in an externally generated velocity field

KW - Motion in the normal direction

KW - Non-graded Cartesian grids

UR - http://www.scopus.com/inward/record.url?scp=34447280147&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2006.11.034

DO - 10.1016/j.jcp.2006.11.034

M3 - Article

AN - SCOPUS:34447280147

SN - 0021-9991

VL - 225

SP - 300

EP - 321

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -