Immersed boundary methods
TL;DR: The term immersed boundary (IB) method is used 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.
Abstract: 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
Citations
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TL;DR: A sharp interface immersed boundary method for simulating incompressible viscous flow past three-dimensional immersed bodies is described, with special emphasis on the immersed boundary treatment for stationary and moving boundaries.
1,013 citations
Cites background or methods from "Immersed boundary methods"
...Within the context of the categorization put forth by Mittal and Iaccarino [34], the current method employs a ‘‘discrete forcing” method wherein the effect of the immersed boundary is incorporated into the discretized governing equations....
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...As noted in [34], successful implementation of the cut-cell method to 3D geometries has not yet been accomplished....
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...This implies that the boundary conditions on the immersed boundary are imposed at the precise location of the immersed body and there is no spurious spreading of boundary forcing into the fluid as what usually occurs with diffuse interface methods [34]....
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...Immersed boundary methods can broadly be characterized under two categories [34]; first is the category of methods that employ ‘‘continuous forcing” wherein a forcing...
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...Within the context of the categorization put forth by Mittal and Iaccarino [34], the current method employs a ‘‘discrete forcing” method wherein the effect of...
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15 Nov 2004
TL;DR: In this paper, the authors provide an in-depth survey of arbitrary Lagrangian-Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical description and numerical implementation details.
Abstract: The aim of the present chapter is to provide an in-depth survey of arbitrary Lagrangian–Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical description and numerical implementation details. Applications are discussed in fluid dynamics, nonlinear solid mechanics and coupled problems describing fluid–structure interaction. The need for an adequate mesh-update strategy is underlined, and various automatic mesh-displacement prescription algorithms are reviewed. This includes mesh-regularization methods essentially based on geometrical concepts, as well as mesh-adaptation techniques aimed at optimizing the computational mesh according to some error indicator. Emphasis is then placed on particular issues related to the modeling of compressible and incompressible flow and nonlinear solid mechanics problems. This includes the treatment of convective terms in the conservation equations for mass, momentum, and energy, as well as a discussion of stress-update procedures for materials with history-dependent constitutive behavior.
Keywords:
ALE description;
convective transport;
finite elements;
stabilization techniques;
mesh regularization and adaptation;
fluid dynamics;
nonlinear solid mechanics;
stress-update procedures;
fluid–structure interaction
901 citations
TL;DR: In this article, a review of the recent progress in flapping wing aerodynamics and aeroelasticity is presented, where it is realized that a variation of the Reynolds number (wing sizing, flapping frequency, etc.) leads to a change in the leading edge vortex (LEV) and spanwise flow structures, which impacts the aerodynamic force generation.
877 citations
Cites background from "Immersed boundary methods"
...Suffice it to say, numerous computational techniquesbased moving meshes [122–124] or stationary meshes (cut cell or immersed boundary) [125,126] have been developed....
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TL;DR: A new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion, achieving second-order temporal accuracy and better than first-order spatial accuracy in L"2-norms for one- and two-dimensional test problems.
626 citations
Additional excerpts
...[33,27] should be consulted for additional IBMs....
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...Immersed boundary methods (IBMs) have gained popularity for their ability to handle moving or deforming bodies with complex surface geometry [33,27]....
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TL;DR: A review of linear instability analysis of flows over or through complex 2D and 3D geometries is presented in this article, where the authors make a conscious effort to demystify both the tools currently utilized and the jargon employed to describe them, demonstrating the simplicity of the analysis.
Abstract: This article reviews linear instability analysis of flows over or through complex two-dimensional (2D) and 3D geometries. In the three decades since it first appeared in the literature, global instability analysis, based on the solution of the multidimensional eigenvalue and/or initial value problem, is continuously broadening both in scope and in depth. To date it has dealt successfully with a wide range of applications arising in aerospace engineering, physiological flows, food processing, and nuclear-reactor safety. In recent years, nonmodal analysis has complemented the more traditional modal approach and increased knowledge of flow instability physics. Recent highlights delivered by the application of either modal or nonmodal global analysis are briefly discussed. A conscious effort is made to demystify both the tools currently utilized and the jargon employed to describe them, demonstrating the simplicity of the analysis. Hopefully this will provide new impulses for the creation of next-generation algorithms capable of coping with the main open research areas in which step-change progress can be expected by the application of the theory: instability analysis of fully inhomogeneous, 3D flows and control thereof.
599 citations
References
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TL;DR: In this paper, a finite-difference method for solving the time-dependent Navier-Stokes equations for an incompressible fluid is introduced, which is equally applicable to problems in two and three space dimensions.
Abstract: A finite-difference method for solving the time-dependent Navier- Stokes equations for an incompressible fluid is introduced. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Test problems are solved, and an ap- plication to a three-dimensional convection problem is presented.
4,991 citations
"Immersed boundary methods" refers methods in this paper
...A number of numerical integration schemes such as fractional-step (Chorin 1968) and SIMPLE (Patankar 1980) also explicitly derive and solve a Poisson equation for pressure, which, depending on the particular implementation, also requires appropriate boundary conditions....
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TL;DR: In this paper, the viscous force exerted by a flowing fluid on a dense swarm of particles is described by a modification of Darcy's equation, which was necessary in order to obtain consistent boundary conditions.
Abstract: A calculation is given of the viscous force, exerted by a flowing fluid on a dense swarm of particles. The model underlying these calculations is that of a spherical particle embedded in a porous mass. The flow through this porous mass is decribed by a modification of Darcy's equation. Such a modification was necessary in order to obtain consistent boundary conditions. A relation between permeability and particle size and density is obtained. Our results are compared with an experimental relation due to Carman.
2,519 citations
TL;DR: In this paper, a method to simulate unsteady multi-fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described.
2,340 citations
"Immersed boundary methods" refers background or methods in this paper
...Consequently, many of the applications of these methods are found in biological (Beyer & Leveque 1992, Fauci & McDonald 1994, Peskin 1981) and multiphase flows (Unverdi & Tryggvason 1992) where elastic boundaries abound....
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...…this category have been successfully used for a wide variety of problems including cardiac mechanics (Peskin 1981), cochlear dynamics (Beyer 1992), aquatic animal locomotion (Fauci & McDonald 1994), bubble dynamics (Unverdi & Tryggvason 1992), and flow past flexible filaments (Zhu & Peskin 2003)....
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TL;DR: In this paper, the authors consider the formation of droplet clouds or sprays that subsequently burn in combustion chambers, which is caused by interfacial instabilities, such as the Kelvin-Helmholtz instability.
Abstract: The numerical simulation of flows with interfaces and free-surface flows is a vast topic, with applications to domains as varied as environment, geophysics, engineering, and fundamental physics. In engineering, as well as in other disciplines, the study of liquid-gas interfaces is important in combustion problems with liquid and gas reagents. The formation of droplet clouds or sprays that subsequently burn in combustion chambers originates in interfacial instabilities, such as the Kelvin-Helmholtz instability. What can numerical simulations do to improve our understanding of these phenomena? The limitations of numerical techniques make it impossible to consider more than a few droplets or bubbles. They also force us to stay at low Reynolds or Weber numbers, which prevent us from finding a direct solution to the breakup problem. However, these methods are potentially important. First, the continuous improvement of computational power (or, what amounts to the same, the drop in megaflop price) continuously extends the range of affordable problems. Second, and more importantly, the phenomena we consider often happen on scales of space and time where experimental visualization is difficult or impossible. In such cases, numerical simulation may be a useful prod to the intuition of the physicist, the engineer, or the mathematician. A typical example of interfacial flow is the collision between two liquid droplets. Finding the flow involves the study not only of hydrodynamic fields in the air and water phases but also of the air-water interface. This latter part
1,949 citations
"Immersed boundary methods" refers methods in this paper
...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)....
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TL;DR: Issues including sharp-interface analyses that relate these models to the classical free-boundary problem, computational approaches to describe interfacial phenomena, and models of fully miscible fluids are addressed.
Abstract: We review the development of diffuse-interface models of hydrodynamics and their application to a wide variety of interfacial phenomena. These models have been applied successfully to situations in which the physical phenomena of interest have a length scale commensurate with the thickness of the interfacial region (e.g. near-critical interfacial phenomena or small-scale flows such as those occurring near contact lines) and fluid flows involving large interface deformations and/or topological changes (e.g. breakup and coalescence events associated with fluid jets, droplets, and large-deformation waves). We discuss the issues involved in formulating diffuse-interface models for single-component and binary fluids. Recent applications and computations using these models are discussed in each case. Further, we address issues including sharp-interface analyses that relate these models to the classical free-boundary problem, computational approaches to describe interfacial phenomena, and models of fully miscible fluids.
1,948 citations