Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

The objective of this paper is to present an alternative approach to the conventional level set methods for solving two-dimensional moving-boundary problems known as the passive transport. Moving boundaries are associated with time-dependent problems and the position of the boundaries need to be determined as a function of time and space. The level set method has become an attractive design tool for tracking, modeling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. Recent research on the numerical method has focused on the idea of using a meshless methodology for the numerical solution of partial differential equations. In the present approach, the moving interface is captured by the level set method at all time with the zero contour of a smooth function known as the level set function. A new approach is used to solve a convective transport equation for advancing the level set function in time. This new approach is based on the asymmetric meshless collocation method and the adaptive greedy algorithm for trial subspaces selection. Numerical simulations are performed to verify the accuracy and stability of the new numerical scheme which is then applied to simulate a bubble that is moving, stretching and circulating in an ambient flow to demonstrate the performance of the new meshless approach.

Keywords

Moving-boundary problems, Stefan problems, Level set method, Multiquadric, Partial differential equations, Adaptive greedy algorithm

Publication Date

2010

Source Publication Title

Computers & Fluids

Volume

39

Issue

9

Start Page

1480

End Page

1490

Publisher

Elsevier

Peer Reviewed

1

DOI

10.1016/j.compfluid.2010.04.015

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.compfluid.2010.04.015

ISSN (print)

00457930

Included in

Mathematics Commons

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