Abstract
We present a high-order accurate scheme for the reinitialization equation of Sussman et al.(J. Comput. Phys. 114:146-159, [1994]) that guarantees accurate computation of the interface's curvatures in the context of level set methods. This scheme is an extension of the work of Russo and Smereka (J. Comput. Phys. 163:51-67, [2000]). We present numerical results in two and three spatial dimensions to demonstrate fourth-order accuracy for the reinitialized level set function, third-order accuracy for the normals and second-order accuracy for the interface's mean curvature in the L 1- and L ∞- norms. We also exploit the work of Min and Gibou (UCLA CAM Report (06-22), [2006]) to show second-order accurate scheme for the computation of the mean curvature on non-graded adaptive grids.
| Original language | English |
|---|---|
| Pages (from-to) | 114-131 |
| Number of pages | 18 |
| Journal | Journal of Scientific Computing |
| Volume | 35 |
| Issue number | 2-3 |
| DOIs | |
| State | Published - Jun 2008 |
Bibliographical note
Funding Information:Isocontours of the curvature on a 128 × 128 grid in the case where 100 iterations of the algorithm detailed in [8] are used. The red curve corresponds to the curvature at the interface. The initial implicit function is given byφ :↼x↪y↽ ⤇ min↼↼x − 1.5↽2 + y2 − 1.3132↪ ↼x + 1.5↽2 + y2 − 1.3132↽ Acknowledgements The research of A. du Chéné and F. Gibou was supported in part by a Sloan Research Fellowship in Mathematics and by NSF under grant agreement DMS 0713858. The research of C. Min was supported in part by the Kyung Hee University Research Fund (KHU-20070608) in 2007.
Keywords
- Adaptive mesh refinement
- Level set method
- Reinitialization equation
- Second-order accurate curvature