Modeling a No-Slip Flow Boundary with an External Force Field

Goldstein, David J.; Handler, R.; Sirovich, Lawrence

doi:10.1006/jcph.1993.1081

Cited by 1,080 publications

(700 citation statements)

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“…This Poisson equation is solved with a highly efficient geometric multigrid method [3] which employs a Gauss-Siedel line-SOR smoother [38]. 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%

“…(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%

“…Immersed boundary methods can broadly be characterized under two categories [29]; first is the category of methods that employ "continuous forcing" wherein a forcing term is added to the continuous Navier-Stokes equations before they are discretized. Methods such as those of Peskin [36], Goldstein et al [13] and Saiki and Biringen [39] fall in this category.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Mittal

Dong

Bozkurttas

et al. 2008

Journal of Computational Physics

1,012

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

1,012

768

View full text Add to dashboard Cite

show abstract

“…To represent curved, no-slip walls in the uniform, cubic lattice, a forcing technique has been developed [22], based on a similar technique developed by Goldstein et al in the framework of spectral methods [23], and by Balaras [24], and Verzicco et al [25] for finite volume schemes (the latter authors call it the immersed boundary technique). In our forcing technique, the wall surface is represented by a large set of control points r j with a nearest neighbor distance slightly less than the lattice spacing.…”

Section: Simulation Proceduresmentioning

confidence: 99%

Simulations of confined turbulent vortex flow

Derksen

2005

Computers & Fluids

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Large-eddy simulations (LES) of the turbulent flow in a swirl tube with a tangential inlet have been performed. The geometry, and flow conditions were chosen according to an experimental study by [Escudier MP, Bornstein J, Zehnder N. Observations and LDA measurements of confined turbulent vortex flow. J Fluid Mech 1980;98:49-63]. Lattice-Boltzmann discretization was used to numerically solve the Navier-Stokes equations in the incompressible limit. Effects of spatial resolution and choices in subgridscale modeling were explicitly investigated with the experimental data set as the testing ground. Experimentally observed flow features, such as vortex breakdown and laminarization of the vortex core were well represented by the LES. The simulations confirmed the experimental observations that the average velocity profiles in the entire vortex tube are extremely sensitivity to the exit pipe diameter. For the narrowest exit pipe considered in the simulations, very high average velocity gradients are encountered. In this situation, the LES shows the most pronounced effects of spatial resolution and subgrid-scale modeling.

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“…The main concept of this particular numerical method is to impose an external force field at the fluid grid points adjacent to the solid boundary in the same manner as would the solid boundary. This branch of numerical methods was studied extensively for biological flow, multi-phase flow and problems with elastic boundary [6][7][8][9][10][11][12]. One of the major drawbacks of the immersed-boundary method is the smoothing of the external force field that could lead to smearing of interface information.…”

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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Modeling a No-Slip Flow Boundary with an External Force Field

Cited by 1,080 publications

References 0 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

Simulations of confined turbulent vortex flow

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

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