A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries

Udaykumar, H. S.; Mittal, Rajat; Rampunggoon, P.; Khanna, Anupam

doi:10.1006/jcph.2001.6916

Cited by 457 publications

(307 citation statements)

References 60 publications

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“…For sharp interface methods, one issue encountered with moving boundaries is the so called "fresh-cell" problem [44,45]. This refers to the situation where a cell that is in the solid at one time step, emerges into the fluid at the next time-step due to boundary motion.…”

Section: Boundarymentioning

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

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1,014

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: Boundarymentioning

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

Self Cite

1,014

768

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“…The implicitly filtered LES momentum and continuity equations for incompressible flow were solved over a general non-orthogonal, boundary-fitted, multi-block finitevolume mesh, supplemented by the immersed boundary method (Udaykumar et al 2001) to cater specifically to the complexities posed by the round orifices and the cavities. In total, the default mesh covering the duct-flow domain contained around 11 million nodes, while each cavity was meshed with a further 0.8 million nodes.…”

Section: The Computational Approachmentioning

confidence: 99%

The interaction of round synthetic jets with a turbulent boundary layer separating from a rounded ramp

Lardeau

Leschziner

2011

J. Fluid Mech.

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A computational large eddy simulation (LES) study is presented of the interaction between a turbulent boundary layer separating from a rounded ramp in a duct and a pair of spanwise-periodic, round synthetic jets, actuated upstream of the nominal separation line. Several scenarios are considered, for different injection angles and velocity ratios. In all cases, the actuation frequency corresponds to the sheddinginstability mode of the separated shear layer. Experimental data, available for both the baseline flow and one actuated configuration, are used to verify the validity of the computational solutions. The analysis includes a separation of coherent and stochastic contributions to the time-averaged statistics of the auto-and cross-correlations of the fluctuations. The control authority is examined by reference to the effects of the actuation on the size of the separated zone, the momentum thickness of the boundary layer, the velocity field, various turbulence quantities and phase-averaged properties. The study demonstrates that the principal aspect of the interaction, at mean-flow level, is an increase in mixing provoked by the formation of strong streamwise vortices away from the wall, the induction of much weaker streamwise vortices close to the wall, and the extra production of stochastic turbulence caused by unsteady straining. The coherent stresses arising from the periodic perturbations are high -typically 5 times the levels of the unperturbed flow -but only within about 5-7 diameters of the jet orifice, and 2 orifice diameters on each side of the jet, and these are dominant primarily in the outer parts of the boundary layer. Stochastic turbulence is also elevated, but more modestly. The global effect of the actuation is a reduction of 10-20 % in the length of the separated region and 20-40 % in the thickness of the reverse-flow layer, depending on the actuation scheme, counter-flow actuation being the most effective. This reduction is mainly associated with a delay in separation. These results highlight the need for synthetic jets to be placed close to the separation zone and for the inter-jet distance to be of order 5 or lower to achieve a high level of separation-control authority.

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“…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

358

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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A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries

Cited by 457 publications

References 60 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

The interaction of round synthetic jets with a turbulent boundary layer separating from a rounded ramp

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

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