Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations

Fadlun, E.A.; Verzicco, Roberto; Orlandi, P.; Mohd-Yusof, Jamaludin

doi:10.1006/jcph.2000.6484

Cited by 1,538 publications

(1,216 citation statements)

References 26 publications

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“…The above procedure is necessary to eliminate odd-even decoupling that usually occurs with non-staggered methods and which leads to large pressure variations in space. The second sub-step requires the solution of the pressure correction equation (9) which is solved with the constraint that the final velocity be divergence-free. This gives the following Poisson equation for the pressure correction (10) and a Neumann boundary condition imposed on this pressure correction at all boundaries.…”

Section: Governing Equations and Discretization Schemementioning

confidence: 99%

“…(24) is used as the velocity boundary condition in advancing the flow equations (Eqs. [3][4][5][6][7][8][9][10][11][12][13] which ensures that at the end of the time-step, the boundary and flow velocities are compatible. The general framework described above can therefore be considered as EulerianLagrangian, wherein the immersed boundaries are explicitly tracked as surfaces in a Lagrangian mode, while the flow computations are performed on a fixed Eulerian grid.…”

Section: Boundarymentioning

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: Governing Equations and Discretization Schemementioning

confidence: 99%

Section: Boundarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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%

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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“…In the IB approach, the presence of a solid boundary is replaced by suitable forcing conditions modeling the effect of the body on the flow. The IB technique was originally developed for incompressible flows [1,2,3,4,5] using non-uniform Cartesian grids to take advantage of simple numerical algorithms. Two of the authors have contributed to the extension of the IB method to the preconditioned compressible Navier-Stokes (NS) equations in order to solve complex flows at any value of the Mach number [6], and equipped it with a local mesh refinement procedure to resolve boundary layers and regions with high flow gradients (e.g., shocks) [7].…”

Section: Introductionmentioning

confidence: 99%

Simulation of hypersonic rarefied flows with the immersed-boundary method

Bruno

Palma

Tullio

2011

AIP Conference Proceedings

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Abstract. This paper provides a validation of an immersed boundary method for computing hypersonic rarefied gas flows. The method is based on the solution of the Navier-Stokes equation and is validated versus numerical results obtained by the DSMC approach. The Navier-Stokes solver employs a flexible local grid refinement technique and is implemented on parallel machines using a domain-decomposition approach. Thanks to the efficient grid generation process, based on the ray-tracing technique, and the use of the METIS software, it is possible to obtain the partitioned grids to be assigned to each processor with a minimal effort by the user. This allows one to by-pass the expensive (in terms of time and human resources) classical generation process of a body fitted grid. First-order slip-velocity boundary conditions are employed and tested for taking into account rarefied gas effects.

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Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations

Cited by 1,538 publications

References 26 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

Simulation of hypersonic rarefied flows with the immersed-boundary method

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