An Adaptive Version of the Immersed Boundary Method

✍ Scribed by Alexandre M Roma; Charles S Peskin; Marsha J Berger

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 244 KB
• Volume: 153
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1999.6293

✦ Synopsis

A computational setting for the Immersed Boundary Method employing an adaptive mesh refinement is presented. Enhanced accuracy for the method is attained locally by covering an immersed boundary vicinity with a sequence of nested, progressively finer rectangular grid patches which dynamically follow the immersed boundary motion. The set of equations describing the interaction between a nonstationary, viscous incompressible fluid and an immersed elastic boundary is solved by coupling a projection method, specially designed for locally refined meshes, to an implicit formulation of the Immersed Boundary Method. The main contributions of this work concern the formulation and the implementation of a multilevel selfadaptive version of the Immersed Boundary Method on locally refined meshes. This approach is tested for a particular two-dimensional model problem, for which no significant difference is found between the solutions obtained on a mesh refined locally around the immersed boundary, and on the associated uniform mesh, built with the resolution of the finest level.