An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction

Barad, Michael F.

Brehm, Christoph

Kiris, Cetin C.

NASA Technical Reports Server

Ninth International Conference on
Computational Fluid Dynamics (ICCFD9),
Istanbul, Turkey, July 11-15, 2016
ICCFD9-xxxx
Solving Fluid Structure Interaction Problems with an
Immersed Boundary Method
Michael F. Barad1, Christoph Brehm2, and Cetin C. Kiris1
1 Computational Aerosciences Branch, NASA Ames Research Center, Moﬀett Field, CA, USA
2 Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, USA
Corresponding author: michael.f.barad@nasa.gov
Abstract: An immersed boundary method for the compressible Navier-Stokes equations can be
used for moving boundary problems as well as fully coupled ﬂuid-structure interaction is presented.
The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerody-
namics (LAVA) framework, based on the locally stabilized immersed boundary method previously
presented by the authors, is extended to account for unsteady boundary motion and coupled to
linear and geometrically nonlinear structural ﬁnite element solvers. The approach is validated for
moving boundary problems with prescribed body motion and fully coupled ﬂuid structure interac-
tion problems.
Keywords: Immersed Boundary Method, Higher-Order Finite Diﬀerence Method, Fluid Structure
Interaction.
1 Introduction
Immersed Boundary Methods (IBMs) have been developed for many years and have appeared in various
forms since they were ﬁrst introduced by Peskin[1, 2] (see for example Goldstein et al.[3], LeVeque and Li[4],
Wiegmann and Bube[5], Linnick and Fasel[6], Johansen and Collela[7], Mittal and Iaccarino[8], Zhong[9],
Duan et al.[10] and many others). These methods were ﬁrst introduced as a nontraditional approach for
numerically solving initial/boundary-value problems for complex geometries on Cartesian meshes and have
matured to become increasingly important for a wide range of applications[11, 12, 13]. One of the key
advantages of immersed boundary methods is that the computational meshes can be automatically generated
starting from a water tight surface triangulation independent of the complexity of the geometry. For highly
complex geometries, which are relevant for many ﬁelds of science and engineering, the process of generating
a high-quality grid is extremely time consuming. For ﬂows containing moving boundaries or ﬂuid structure
interaction (FSI), immersed boundary methods can dramatically simplify the numerical solution procedure
by solving the governing equations on stationary, non-deforming Cartesian grids. In contrast, conventional
body-ﬁtted grid approaches are confronted with immense diﬃculties in the solution procedure, especially for
ﬂuid-structure interaction problems involving large relative boundary motions/deformations, in which the
grids must be deformed and may become tangled.
2 Scope of Work
The ﬁnal paper will discuss all aspects of coupling the high-order accurate compressible Navier-Stokes solver
with a structural linear and geometrically nonlinear structural Finite Element Solver (FEM) solver. The
development of these FSI capabilities are part of the overall Launch Ascent and Vehicle Aerodynamics
(LAVA) framework[11] that is being developed by the authors at NASA Ames Research center.
1
https://ntrs.nasa.gov/search.jsp?R=20160008993 2019-08-31T02:02:16+00:00Z
irregular pnt.
cloud 1 pnt.
cloud 2 pnt.
cloud 3 pnt.
x−rays in x−dir.
x−rays in y−dir.
pierce pnt.
(a) (b) (c)
Figure 1: (a) Cloud selection process for the boundary extrapolation stencil, (b) illustration of x-ray algorithm
used for in-out testing and (c) freshly cleared cells after moving the immersed boundary in the time interval
[tn,tn+1].
Some of the key challenges for simulating FSI problems with an immersed boundary method is the
treatment of thin geometries, accounting for the thin boundary layer near the geometry, and dealing with
the moving boundary. The treatment of the thin geometry aﬀects the cloud selection process for the boundary
condition extrapolation stencil since the current sharp immersed boundary method does not utilize ghost
cells. The algorithm ensures that points are only selected for the point cloud if they reside on the same side
of the boundary as the irregular grid point (i.e. points adjoining the boundary). Figure 1a schematically
illustrates the cloud selection process at an irregular grid point. First, all irregular grid points compute their
base clouds while the base clouds for the regular grid points are assumed to contain the direct neighbors,
i.e., (i ± 1,j,k), (i,j ± 1,k), and (i,j,k ± 1). Then the point cloud at the irregular grid point is gradually
extended by adding the base clouds from the valid neighbors. To incorporate the eﬀect of the thin boundary
layers, a wall modeling approach was chosen. This wall modeling approach was ﬁrst successfully used to
simulate the ﬂow around the partially dressed landing gear for the AIAA Workshop on Benchmark problems
for Airframe Noise Computations (BANC). A detailed discussion of this approach will be presented in Brehm
et al.[14]. There are two additional challenges that had to be addressed in particular for moving geometries:
(1) speeding up the geometry queries and regeneration of irregular stencils after moving the geometry and
(2) the treatment of Freshly Cleared Cells (FCC). An x-ray algorithm, as visualized in Figure 1b, is used
for inside-outside (in-out) testing. Parallel geometry kernels were implemented to allow fast in-out testing
and exact computation of the distance from the irregular grid points to the surface triangulation (including
point to plane and point to edge cases). An optimized Boundary Volume Hierarchy (BVH) based x-ray
algorithm employing multi-resolution binning was developed for this purpose. Figure 1c displays some FCCs
after moving the immersed boundary in the time interval [tn,tn+1]. Since the FCCs do not contain a valid
time history, their state vector is initialized by interpolation considering the boundary condition and valid
grid points (not including other FCC) in the neighborhood of the FCC. Some more advanced strategies
for updating the FCCs similar to what has been discussed in Brehm and Fasel[15] for the incompressible
Navier-Stokes equations are still being explored.
3 Outlook
First, the immersed boundary method by Brehm et al.[16, 17] is described and the necessary additions
to eﬃciently capture unsteady body motion are introduced. Next, the structural Finite Element Solver
(FEM) solver is introduced and its implementation is validated for simple static deformation and vibration
problems. The validation section starts with moving boundary problems of prescribed motion. Finally, two
examples of fully coupled ﬂuid structure interaction problems are discussed. Experimental data is available
for comparison for all moving boundary and fully coupled ﬂuid structure interaction validation problems.
2
References
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Solving Fluid Structure Interaction Problems with an Immersed Boundary Method

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