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Special Section Articles

Adaptive Mesh Refinement for Immersed Boundary Methods

[+] Author and Article Information
Marcos Vanella

Post Doctoral Scientist
Department of Mechanical and
Aerospace Engineering,
The George Washington University,
Washington, DC 20052
e-mail: mvanella@gwu.edu

Antonio Posa

Post Doctoral Scientist
Department of Mechanical and
Aerospace Engineering,
The George Washington University,
Washington, DC 20052
e-mail: aposa@gwu.edu

Elias Balaras

Professor
Department of Mechanical and
Aerospace Engineering,
The George Washington University,
Washington, DC 20052
e-mail: balaras@gwu.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 12, 2013; final manuscript received December 5, 2013; published online February 28, 2014. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 136(4), 040909 (Feb 28, 2014) (9 pages) Paper No: FE-13-1151; doi: 10.1115/1.4026415 History: Received March 12, 2013; Revised December 05, 2013

Immersed boundary methods coupled with adaptive mesh refinement (AMR) are a powerful tool to solve complex viscous incompressible flow problems, especially in the presence of moving and deforming boundaries. Immersed boundary methods have been traditionally used in the framework of fractional step formulations for temporal integration and are generally coupled to logically structured grids, where the elliptic problem for the pressure is solved using fast solution techniques. In many situations, especially at large Reynolds numbers, adaptive clustering of fluid grid points on large gradient regions is desirable. This article gives an overview of currently available AMR tools, with an emphasis on block structured grids that are a natural fit to immersed boundary methods, and discusses future trends.

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Figures

Grahic Jump Location
Fig. 1

Eulerian and Lagrangian meshes: ΩS, solid region; Ωf, fluid region. Each marker point ml is related to a stencil of Eulerian points eij (♦).

Grahic Jump Location
Fig. 2

Direct forcing strategies: (a) Eulerian forcing and (b) Lagrangian forcing

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Fig. 3

Detail of the computational grid (r-z plane) near the immersed boundary

Grahic Jump Location
Fig. 4

Distribution of the pressure coefficient along the surface of a sphere for Re = 100: ---, immersed boundary method with Lagrangian forcing; ---, immersed boundary method with Eulerian forcing; ×, body-fitted results by Johnson [45]; and •, body-fitted results by Tomboulides and Orszag [46]

Grahic Jump Location
Fig. 5

Spanwise vorticity field for the flow around a sphere at Re = 100. Isolines on a meridian plane from a simulation using the IB method with the Lagrangian forcing (top) and Eulerian forcing (bottom).

Grahic Jump Location
Fig. 6

Distribution of the pressure coefficient on the surface of a sphere for Re=300. Average in time and along the azimuthal direction: ---, immersed boundary method with Lagrangian forcing; ---, immersed boundary method with Eulerian forcing; and •, body-fitted results by Lee [50].

Grahic Jump Location
Fig. 7

Distribution of the skin-friction coefficient on the surface of a sphere for Re = 300. See the caption of Fig. 6 for symbols/lines.

Grahic Jump Location
Fig. 8

Patch-based composite grid mesh in two dimensions; refinement is achieved by creating rectangular grid patches ΩLev,κ, κ=1,..., pLev at a higher refinement level. The number of cells on each direction for each patch is variable; in general, a factor of the underlying parent cells. Three refinement levels are used.

Grahic Jump Location
Fig. 9

Block-structured mesh in two dimensions; refinement is achieved by bisecting blocks in the two dimensions generating four blocks at a higher refinement level. Each grid-block ΩLev,κ contains 4 × 4 cells. Three levels of refinement are used. The tree structure of the mesh by refinement level is seen on the right.

Grahic Jump Location
Fig. 10

S-AMR block distribution in the vicinity of the cylinder. The mesh contains 744 leaf-blocks with 162 cells each.

Grahic Jump Location
Fig. 11

CD and CL for the flow around the oscillating cylinder at Re=185: ---, nonadaptive S-AMR mesh; and ×, adaptive S-AMR computation with grid motion every 10 time steps (sub-sampled)

Grahic Jump Location
Fig. 12

Vorticity isolines for the flow around the oscillating cylinder at Re=185. (a) and (c) centered location, t = 30/f0; and (b) and (d) extreme upper location. The left part is the fixed S-AMR grid and the right part is the time adapted S-AMR grid.

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