A Hybrid Method for Moving Interface Problems with Application to the Hele–Shaw Flow

✍ Scribed by Thomas Y. Hou; Zhilin Li; Stanley Osher; Hongkai Zhao

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 613 KB
• Volume: 134
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1997.5689

✦ Synopsis

are examples of this type; see, e.g., the recent review paper [12] for references. The disadvantage of front tracking

In this paper, a hybrid approach which combines the immersed interface method with the level set approach is presented. The fast methods is that it requires explicit tracking of the front. version of the immersed interface method is used to solve the This is, in general, difficult for interfaces with complicated differential equations whose solutions and their derivatives may be geometry and topological change and particular so in three discontinuous across the interfaces due to the discontinuity of the dimensions. Front capturing, in particular, the level set coefficients or/and singular sources along the interfaces. The movmethod as derived by Osher and Sethian in [26], on the ing interfaces then are updated using the newly developed fast level set formulation which involves computation only inside some small other hand, avoids the explicit tracking of the front. The tubes containing the interfaces. This method combines the advanmoving front is implicitly captured on an Eulerian grid.

tage of the two approaches and gives a second-order Eulerian dis-As a consequence, complex interface structures and topocretization for interface problems. Several key steps in the implelogical changes can be captured quite naturally in two and mentation are addressed in detail. This new approach is then applied three dimensions; see, e.g., [4,26, 32, 33]. One difficulty to Hele-Shaw flow, an unstable flow involving two fluids with very different viscosity.