An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries

Ye, T.; Mittal, Rajat; Udaykumar, H. S.; Shyy, Wei

doi:10.1006/jcph.1999.6356

Cited by 657 publications

(486 citation statements)

References 42 publications

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“…Once the pressure correction is obtained, the pressure and velocity are updated as (11) (12) (13) These separately updated face-velocities satisfy discrete mass-conservation to machine accuracy and use of these velocities in estimating the non-linear convective flux in equation (3) leads to a more accurate and robust solution procedure. The advantage of separately computing the face-center velocities was initially proposed by Zang et al [53] and discussed in the context of the Cartesian grid methods in Ye et al [51].…”

Section: Governing Equations and Discretization Schemementioning

confidence: 99%

“…3 for a fresh cell, it can be seen that terms such as , , and are not readily available. In the context of fluid flow simulations, Ye et al [51] devised a simple and consistent methodology for this problem for their cut-cell based Cartesian grid method and we have adapted this same method for the current finite-difference based immersed boundary method. Referring to Fig.…”

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

Self Cite

968

754

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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

Self Cite

968

754

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show abstract

“…We set l = d = 1 and consider three, successively finer uniform grids: 33 3 , 65 3 and 129 3 . The performance of the iterative solver is measured through the convergence rate, which is defined as:…”

Section: Impulsively Started Pipe Flowmentioning

confidence: 99%

“…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

343

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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 fictitious domain method for lithosphere‐asthenosphere interaction: Application to periodic slab folding in the upper mantle

Cerpa

Hassani

Gerbault

et al. 2014

Geochem Geophys Geosyst

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We present a new approach for the lithosphere-asthenosphere interaction in subduction zones.The lithosphere is modeled as a Maxwell viscoelastic body sinking in the viscous asthenosphere. Both domains are discretized by the finite element method, and we use a staggered coupling method. The interaction is provided by a nonmatching interface method called the fictitious domain method. We describe a simplified formulation of this numerical technique and present 2-D examples and benchmarks. We aim at studying the effect of mantle viscosity on the cyclicity of slab folding at the 660 km depth transition zone. Such cyclicity has previously been shown to occur depending on the kinematics of both the overriding and subducting plates, in analog and numerical models that approximate the 660 km depth transition zone as an impenetrable barrier. Here we applied far-field plate velocities corresponding to those of the South-American and Nazca plates at present. Our models show that the viscosity of the asthenosphere impacts on folding cyclicity and consequently on the slab's dip as well as the stress regime of the overriding plate. Values of the mantle viscosity between 3 and 5 3 10 20 Pa s are found to produce cycles similar to those reported for the Andes, which are of the order of 30-40 Myr (based on magmatism and sedimentological records). Moreover, we discuss the episodic development of horizontal subduction induced by cyclic folding and, hence, propose a new explanation for episodes of flat subduction under the South-American plate.

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An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries

Cited by 657 publications

References 42 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

A fictitious domain method for lithosphere‐asthenosphere interaction: Application to periodic slab folding in the upper mantle

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