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Research Papers: Flows in Complex Systems

Robust and Efficient Setup Procedure for Complex Triangulations in Immersed Boundary Simulations

[+] Author and Article Information
Jianming Yang

e-mail: jianming-yang@uiowa.edu

Frederick Stern

e-mail: frederick-stern@uiowa.edu
IIHR—Hydroscience and Engineering,
University of Iowa,
Iowa City, IA 52242

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering. Manuscript received November 12, 2012; final manuscript received June 11, 2013; published online August 7, 2013. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 135(10), 101107 (Aug 07, 2013) (11 pages) Paper No: FE-12-1570; doi: 10.1115/1.4024804 History: Received November 12, 2012; Revised June 11, 2013

Immersed boundary methods have been widely used for simulating flows with complex geometries, as quality boundary-conforming grids are usually difficult to generate for complex geometries, especially when motion and/or deformation is involved. A major task in immersed boundary simulations is to inject the immersed boundary information into the background Cartesian grid, such as the inside/outside status of a grid point with regard to the immersed boundary and the accurate subcell position of the immersed boundary for a grid point next to it. Complex geometries in immersed boundary methods can be conveniently represented with triangulated surfaces placed upon underlying Cartesian grids in a Lagrangian manner. Regular, intuitive implementations using triangulations can be error-prone and/or cumbersome in dealing with robustness issues. In addition, they can be prohibitively expensive for high resolution simulations with complex moving/deforming boundaries. In this paper, a simple, robust, and fast procedure is developed for setting up complex triangulations in immersed boundary simulations. Central to this setup procedure are a ray casting and closest surface point computation algorithms. Several illustrative examples, including high resolution cases with Cartesian grids of up to 2.1 × 109 points and triangulations of up to 1.3 × 106 surface elements, are performed to demonstrate the robustness and efficiency of our procedure.

Copyright © 2013 by ASME
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Figures

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Fig. 1

Flow chart for the present immersed boundary setup procedure

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Fig. 2

Immersed boundary treatment

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Fig. 3

Voronoi feature regions of a triangle. Region 1: triangle interior; Regions 2, 3, and 4: edges; Regions 5, 6, 7: vertices.

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Fig. 4

Ray casting and solid-grid configurations for the cube case

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Fig. 5

Ray casting and solid-grid configurations for the triangular bipyramid case

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Fig. 6

Triangulations of a unit sphere

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Fig. 7

CPU time for the ray casting step as a function of NP for all triangulations

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Fig. 8

CPU time for the ray casting step as a function of NF for all grids

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Fig. 9

CPU time for the ray casting step as a function of NP for all triangulations with the grid-based ray casting algorithm. Data from the triangulation-based algorithm are also shown (symbols of the same types and colors as in Fig. 7).

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Fig. 10

CPU time for the ray casting step as a function of NF for all grids with the grid-based ray casting algorithm. Data from the triangulation-based algorithm are also shown (symbols of the same types and colors as in Fig. 8).

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Fig. 11

CPU time for the step tagging inside/outside status of all grid points as a function of NP (with the finest triangulation). The straight line shows the third order slope.

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Fig. 12

CPU time for the step determining interface points as a function of NP (with the finest triangulation). The straight line shows the third order slope.

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Fig. 13

CPU time for the step indexing interface points as a function of NP (with the finest triangulation). The straight line shows the third order slope.

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Fig. 14

CPU time for the closest surface point computation step as a function of NP for all triangulations

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Fig. 15

CPU time for the closest surface point computation step as a function of NF for all grids

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Fig. 16

CPU time for the closest surface point computation step as a function of NP for all triangulations with the grid-based closest surface point computation algorithm. Data from the triangulation-based algorithm are also shown (symbols of the same types and colors as in Fig. 14).

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Fig. 17

CPU time for the closest surface point computation step as a function of NF for all grids with the grid-based closest surface point computation algorithm. Data from the triangulation-based algorithm are also shown (symbols of the same types and colors as in Fig. 15).

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Fig. 18

CPU time for the step constructing interpolation stencils as a function of NP (with the finest triangulation). The straight line shows the second order slope.

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