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

An immersed boundary method for solving the Navier-Stokes and thermal energy equations is developed to compute the heat transfer over or inside the complex geometries in the Cartesian or cylindrical coordinates by introducing the momentum forcing, mass source/sink, and heat source/sink The present method is based on the finite volume approach on a staggered mesh together with a fractional step method The method of applying the momentum forcing and mass source/sink to satisfy the no-slip condition on the body surface is explained in detail in Kim, Kim and Choi (2001, Journal of Computational Physics) In this paper, the heat source/sink is introduced on the body surface or inside the body to satisfy the iso-thermal or iso-heat-flux condition on the immersed boundary The present method is applied to three different problems : forced convection around a circular cylinder, mixed convection around a pair of circular cylin-ders, and forced convection around a main cylinder with a secondary small cylinder The results show good agreements with those obtained by previous experiments and numerical simulations, verifying the accuracy of the present method

An Immersed-Boundary Finite-Volume Method for Simulation of Heat Transfer in Complex Geometries

Sources of spurious force oscillations from an immersed boundary method for moving-body problems

In this paper, we present a new passive control device for form-drag reduction in flow over a two-dimensional bluff body with a blunt trailing edge. The device consists of small tabs attached to the upper and lower trailing edges of a bluff body to effectively perturb a two-dimensional wake. Both a wind-tunnel experiment and large-eddy simulation are carried out to examine its drag-reduction performance. Extensive parametric studies are performed experimentally by varying the height and width of the tab and the spanwise spacing between the adjacent tabs at three Reynolds numbers of Re=u ∞ h/v=20000, 40000 and 80000, where u ∞ is the free-stream velocity and h is the body height. For a wide parameter range, the base pressure increases (i.e. drag reduces) at all three Reynolds numbers. Furthermore, a significant increase in the base pressure by more than 30 % is obtained for the optimum tab configuration. Numerical simulations are performed at much lower Reynolds numbers of Re = 320 and 4200 to investigate the mechanism responsible for the base-pressure increase by the tab. Results from the velocity measurement and numerical simulations show that the tab introduces the spanwise mismatch in the vortex-shedding process, resulting in a substantial reduction of the vortical strength in the wake and significant increases in the vortex formation length and wake width.

Drag reduction in flow over a two-dimensional bluff body with a blunt trailing edge using a new passive device

In the present study, the effects of the jet inflow conditions such as the initial momentum thickness (0) and background disturbances on the downstream evolution of a circular jet are investigated using large eddy simulation (LES). We consider four different initial momentum thicknesses, D/0 = 50, 80, 120 and 180, and three different Reynolds numbers, Re D = U J D/v = 3600, 10 4 and 10 5 , where Uj is the jet inflow velocity and D is the jet diameter. The present study shows that the jet characteristics significantly depend on both the initial momentum thickness and the Reynolds number. For all the Reynolds numbers considered in this study, vortex rings are generated at an earlier position with decreasing initial momentum thickness. In case of a relatively low Reynolds number of Re D = 3600, at smaller initial momentum thickness, early growth of the shear layer due to the early generation of vortex ring leads to the occurrence of large-scale coherent structures in earlier downstream locations, which results in larger mixing enhancement and more rapid increase in turbulence intensity. However, at a high Reynolds number such as Re D = 10 5 , with decreasing initial momentum thickness, rapid growth of the shear layer leads to the saturation of the shear layer and the generation of fine-scale turbulence structures, which reduces mixing and turbulence intensity. With increasing Re θ (= UjO/v), the characteristic frequency corresponding to the shear layer mode (St θ = fθ/U J ) gradually increases and reaches near 0.017 predicted from the inviscid instability theory. On the other hand, the frequency corresponding to the jet-preferred mode (St D = fD/Uj) varies depending on Re D and D/0. From a mode analysis, we show that, in view of the energy of the axial velocity fluctuations integrated over the radial direction, the double-helix mode (mode 2) becomes dominant past the potential core, but the axisymmetric mode (mode 0) is dominant near the jet exit. In view of the local energy, the disturbances grow along the shear layer near the jet exit: for thick shear layer, mode 0 grows much faster than other modes, but modes 0-3 grow almost simultaneously for thin shear layer. However, past the potential core, the dominant mode changes from mode 0 near the centreline to mode 1 and then to mode 2 with increasing radial direction regardless of the initial shear layer thickness.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112008004722

Jungwoo Kim

Papers

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

An Immersed-Boundary Finite-Volume Method for Simulation of Heat Transfer in Complex Geometries

Sources of spurious force oscillations from an immersed boundary method for moving-body problems

Drag reduction in flow over a two-dimensional bluff body with a blunt trailing edge using a new passive device

Large eddy simulation of a circular jet: effect of inflow conditions on the near field