Fast Numerical Methods for Evolving Interfaces

free boundary;moving boundary;eikonal equation;sand piles

Kuster, Christopher M. ; Stephen L. Campbell, Committee Member,Pierre A. Gremaud, Committee Chair,Zhilin Li, Committee Member,Carl T. Kelley, Committee Member,Kuster, Christopher M. ; Stephen L. Campbell ; Committee Member ; Pierre A. Gremaud ; Committee Chair ; Zhilin Li ; Committee Member ; Carl T. Kelley ; Committee Member

University:North Carolina State University

关键词: free boundary;    moving boundary;    eikonal equation;    sand piles;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/4952/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

Free and/or moving boundary problems occur in a wide range of applications. These boundaries can obey either local or global conditions. In this dissertation, new numerical techniques for solving some of these problems are developed, analyzed, implemented and tested. The new techniques for free and moving boundary problems are 1) a second order method for solving moving boundary problems and 2) a hybrid level set/boundary element method for solving some free boundary problems. The main tool used in both is the Fast Marching method, a fast algorithm for solving the eikonal equation. An application using Fast Marching to solve a model for sand pile formation in domains with obstacles is shown. A new, second order Fast Marching scheme for domains with obstacles is introduced. We look at the stability and accuracy of discretizations commonly used with Fast Marching. The performance of Fast Marching is compared that of Fast Sweeping, another eikonal solver. The second order method for solving moving boundary problems is applied to some simple examples. Finally, a globally defined free boundary problem inspired by fluid dynamics, the Bernoulli problem, is solved using the hybrid method.