# 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:

- Univ. de Sao Paulo (Brazil). Inst. de Matematica e Estatistica
- 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}

}