The term “immersed boundary method” was first used in reference to a method developed by Peskin (1972) to simulate cardiac mechanics and associated blood flow. The distinguishing feature of this method was that the entire simulation was carried out on a Cartesian grid, which did not conform to the geometry of the heart, and a novel procedure was formulated for imposing the effect of the immersed boundary (IB) on the flow. Since Peskin introduced this method, numerous modifications and refinements have been proposed and a number of variants of this approach now exist. In addition, there is another class of methods, usually referred to as “Cartesian grid methods,” which were originally developed for simulating inviscid flows with complex embedded solid boundaries on Cartesian grids (Berger & Aftosmis 1998, Clarke et al. 1986, Zeeuw & Powell 1991). These methods have been extended to simulate unsteady viscous flows (Udaykumar et al. 1996, Ye et al. 1999) and thus have capabilities similar to those of IB methods. In this review, we use the term immersed boundary (IB) method to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries. Furthermore, this review focuses mainly on IB methods for flows with immersed solid boundaries. Application of these and related methods to problems with liquid-liquid and liquid-gas boundaries was covered in previous reviews by Anderson et al. (1998) and Scardovelli & Zaleski (1999). Consider the simulation of flow past a solid body shown in Figure 1a. The conventional approach to this would employ structured or unstructured grids that conform to the body. Generating these grids proceeds in two sequential steps. First, a surface grid covering the boundaries b is generated. This is then used as a boundary condition to generate a grid in the volume f occupied by the fluid. If a finite-difference method is employed on a structured grid, then the differential form of the governing equations is transformed to a curvilinear coordinate system aligned with the grid lines (Ferziger & Peric 1996). Because the grid conforms to the surface of the body, the transformed equations can then be discretized in the

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Immersed boundary methods

An immersed boundary method with direct forcing for the simulation of particulate flows

A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries

In this review, we present control methods for flow over a bluff body such as a circular cylinder, a 2D bluff body with a blunt trailing edge, and a sphere. We introduce recent major achievements in bluff-body flow controls such as 3D forcing, active feedback control, control based on local and global instability, and control with a synthetic jet. We then classify the controls as boundary-layer controls and direct-wake modifications and discuss important features associated with these controls. Finally, we discuss some other issues such as Reynolds-number dependence, the lowest possible drag by control, and control efficiency.

Control of Flow Over a Bluff Body

An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

An immersed-boundary finite-volume method for simulations of flow in complex geometries

A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids

Large eddy simulations of turbulent flow over a sphere are conducted at subcritical Reynolds numbers (Re=3700 and 104) based on the freestream velocity and sphere diameter. At Re=3700, the separating shear layer persists downstream to form a cylindrical vortex sheet and its instability becomes manifest at x≈2d. The flow right behind the sphere contains only a few vortices. On the other hand, at Re=104, the shear-layer instability occurs right behind the sphere in a form of vortex rings, and the flow becomes turbulent in the near wake. Therefore, at Re=104, the size of the recirculation region is smaller and the wake recovers more quickly than at Re=3700. At both Reynolds numbers, large-scale waviness of vortical structures is observed in the wake and the plane containing the large-scale waviness changes quasirandomly in time. This waviness is more pronounced at Re=104 than at Re=3700. The mechanism responsible for this large-scale waviness of vortical structures is shown to be closely associated with the ...

Vortical structures behind a sphere at subcritical Reynolds numbers

Numerical simulations are conducted for laminar flow past a sphere rotating in the streamwise direction, in order to investigate the effect of the rotation on the characteristics of flow over the sphere. The Reynolds numbers considered are Re = 100, 250 and 300 based on the free-stream velocity and sphere diameter, and the rotational speeds are in the range of 0 [les ] ω* [les ] 1, where ω* is the maximum azimuthal velocity on the sphere surface normalized by the free-stream velocity. At ω* = 0 (without rotation), the flow past the sphere is steady axisymmetric, steady planar-symmetric, and unsteady planar-symmetric, respectively, at Re = 100, 250 and 300. Thus, the time-averaged lift forces exerted on the stationary sphere are not zero at Re = 250 and 300. When the rotational speed increases, the time-averaged drag force increases for the Reynolds numbers investigated, whereas the time-averaged lift force is zero for all ω* > 0. On the other hand, the lift force fluctuations show a non-monotonic behaviour with respect to the rotational speed. At Re = 100, the flow past the sphere is steady axisymmetric for all the rotational speeds considered and thus the lift force fluctuation is zero. At Re = 250 and 300, however, the flows are unsteady with rotation and the lift force fluctuations first decrease and then increase with increasing rotational speed, showing a local minimum at a specific rotational speed. The vortical structures behind the sphere are also significantly modified by the rotation. For example, at Re = 300, the flows become ‘frozen’ at ω* = 0.5 and 0.6, i.e. the vortical structures in the wake simply rotate without temporal variation of their strength and the magnitude of the instantaneous lift force is constant in time. It is shown that the flow becomes frozen at higher rotational speed with increasing Reynolds number. The rotation speed of the vortical structures is shown to be slower than that of the sphere.

Laminar flow past a sphere rotating in the streamwise direction

Numerical simulations are conducted for laminar flow past a hemisphere up to Re=300 in order to investigate its characteristics. It is found that unlike steady flows significant differences exist between unsteady flows past a hemisphere and a sphere. First, in the case of time-periodic planar-symmetric flow, alternating vortex shedding takes place behind a hemisphere with zero mean lift force, while nonzero mean lift force occurs for flow over a sphere. Second, there exists a time-periodic asymmetric flow regime for flow past a hemisphere, but it does not exist for flow past a sphere. It is also found that for flow past a hemisphere, the onsets of axisymmetry breaking and unsteadiness take place at lower Reynolds numbers than those for flow past a sphere.

Dongjoo Kim

Papers

An immersed-boundary finite-volume method for simulations of flow in complex geometries

A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids

Vortical structures behind a sphere at subcritical Reynolds numbers

Laminar flow past a sphere rotating in the streamwise direction

Laminar flow past a hemisphere