An Immersed-Boundary Finite-Volume Method for Simulations of Flow in Complex Geometries

Kim, Jung-Woo; Kim, Dongjoo; Choi, Haecheon

doi:10.1006/jcph.2001.6778

Cited by 993 publications

(662 citation statements)

References 15 publications

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“…Once the BI and the corresponding IP have been identified, a tri-linear interpolant of the following form is used to express the value of a generic variable (say ϕ) in the region between the eight nodes surrounding the image-point: (14) The eight unknown coefficients can be determined in terms of the variable values of the eight surrounding nodes (15) where (16) is the vector containing the eight unknown coefficients and (17) are the values of the variables at the eight surrounding points. Furthermore, [V ] is the Vandermonde matrix [38] corresponding to the trilinear interpolation scheme shown in Eq.…”

Section: Ghost-cell Formulation-mentioning

confidence: 99%

“…These include methods of Udaykumar et al [44], Ye et al [51], Fadlun et al [9], Kim et al [16], Gibou et al [12], You et al [52], Balaras [2], Marella et al [22], Ghias et al [11] and others. The key advantage of the first category of methods is that they are formulated relatively independent of the spatial discretization and therefore can be implemented into an existing Navier-Stokes solver with relative ease.…”

Section: Introductionmentioning

confidence: 99%

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

Mittal

Dong

Bozkurttas

et al. 2008

Journal of Computational Physics

996

768

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A sharp interface immersed boundary method for simulating incompressible viscous flow past threedimensional immersed bodies is described. The method employs a multi-dimensional ghost-cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three-dimensional, stationary, moving and/or deforming bodies. The complex immersed surfaces are represented by grids consisting of unstructured triangular elements; while the flow is computed on non-uniform Cartesian grids. The paper describes the salient features of the methodology with special emphasis on the immersed boundary treatment for stationary and moving boundaries. Simulations of a number of canonical two-and three-dimensional flows are used to verify the accuracy and fidelity of the solver over a range of Reynolds numbers. Flow past suddenly accelerated bodies are used to validate the solver for moving boundary problems. Finally two cases inspired from biology with highly complex three-dimensional bodies are simulated in order to demonstrate the versatility of the method.

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Section: Ghost-cell Formulation-mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Mittal

Dong

Bozkurttas

et al. 2008

Journal of Computational Physics

996

768

View full text Add to dashboard Cite

show abstract

“…The former methods are known as immersed boundary formulations and tend to smear a solid boundary across few grid nodes due to the discrete delta function formulation they employ to introduce the effect of the boundary on the equations of motion [2]. The latter class of methods, on the other hand, treats solid boundaries as sharp interfaces utilizing either Cartesian, cut-cell formulations [3,4] or hybrid Cartesian/Immersed Boundary (HCIB) approaches (see [5,6,1,7] among others)-the reader is referred to [8,9] for more detailed discussion of this class of methods. Regardless on whether a diffused or a sharp interface formulation is employed, however, all available non-boundary conforming methods solve the Navier-Stokes equations in a background coordinate-conforming mesh, such as a Cartesian (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…[1]) or a cylindrical (e.g. [6]) mesh. This is an inherent feature of such methods as their derivation is motivated by the need to avoid constructing a curvilinear, boundary conforming mesh, which for arbitrarily complex boundaries could be difficult if not impossible to construct.…”

Section: Introductionmentioning

confidence: 99%

A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries

Sotiropoulos

2007

Journal of Computational Physics

352

348

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A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [1]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow through a mechanical, bileaflet heart valve mounted in a model straight aorta with an anatomical-like triple sinus.

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“…They proposed a direct forcing approach such that the desired velocity distribution on the immersed boundary is satisfied explicitly. Various formulations for the direct forcing approach have been developed subsequently [15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Implicit Virtual Boundary Method for Moving Boundary Problems on Non-Staggered Cartesian Patch Grids

2017

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A simple numerical method is proposed in the paper for fluid flow around a moving boundary of irregular shape. The unsteady term is discretized with the implicit scheme such that large time step is allowed. All of the computations are performed on non-staggered Cartesian grid system. Fine Cartesian patch grid system covering the moving object is employed to resolve the solution around the solid body. A closed curve defined by connecting the solid grid points adjacent to the solid-liquid interface is referred to as virtual boundary. The narrow irregular strip of solid between the virtual boundary and the actual solid-fluid interface is called pseudo-fluid. The general fluid region consisting of both fluid and pseudo-fluid is a regular domain that can be efficiently solved with conventional numerical method. In this connection, external force is imposed at each fluid grid point adjacent to the solid-fluid interface to compensate for the numerical error arising from the assumption of pseudo-fluid. The solution procedure is iterated until the required external force converges. Accuracy of the new numerical method is validated through three test problems. The numerical method then is used to investigate the flow induced by the flapping wings of a tethered dragonfly in literature. The corresponding CFL numbers of the four examples are infinity, 20, 100, and 3.29.

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An Immersed-Boundary Finite-Volume Method for Simulations of Flow in Complex Geometries

Cited by 993 publications

References 15 publications

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

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

A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries

Implicit Virtual Boundary Method for Moving Boundary Problems on Non-Staggered Cartesian Patch Grids

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