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Title: An adaptive version of the Immersed Boundary Method

Abstract

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, progessively 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 self-adaptive 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.

Authors:
 [1]; ;  [2]
  1. Univ. de Sao Paulo (Brazil). Inst. de Matematica e Estatistica
  2. New York Univ., NY (United States). Courant Inst. of Mathematical Sciences
Publication Date:
Sponsoring Org.:
National Science Foundation, Washington, DC (United States); USDOE, Washington, DC (United States)
OSTI Identifier:
687484
DOE Contract Number:  
FG02-92ER25139
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 153; Journal Issue: 2; Other Information: PBD: 10 Aug 1999
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; 66 PHYSICS; MESH GENERATION; CALCULATION METHODS; FLUID MECHANICS; TWO-DIMENSIONAL CALCULATIONS; INCOMPRESSIBLE FLOW

Citation Formats

Roma, A.M., Peskin, C.S., and Berger, M.J. An adaptive version of the Immersed Boundary Method. United States: N. p., 1999. Web. doi:10.1006/jcph.1999.6293.
Roma, A.M., Peskin, C.S., & Berger, M.J. An adaptive version of the Immersed Boundary Method. United States. doi:10.1006/jcph.1999.6293.
Roma, A.M., Peskin, C.S., and Berger, M.J. Tue . "An adaptive version of the Immersed Boundary Method". United States. doi:10.1006/jcph.1999.6293.
@article{osti_687484,
title = {An adaptive version of the Immersed Boundary Method},
author = {Roma, A.M. and Peskin, C.S. and Berger, M.J.},
abstractNote = {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, progessively 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 self-adaptive 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.},
doi = {10.1006/jcph.1999.6293},
journal = {Journal of Computational Physics},
number = 2,
volume = 153,
place = {United States},
year = {1999},
month = {8}
}