A fractional step solution method for the unsteady incompressible navier-stokes equations in generalized coordinate systems

Rosenfeld, M.; Kwak, Dochan; Vinokur, Marcel

doi:10.1016/0021-9991(91)90139-c

Cited by 270 publications

(146 citation statements)

References 21 publications

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“…The equations are solved on a staggered curvilinear grid using a finite volume scheme, following the method described in Rosenfeld et al (1991). Time integration is performed with a second-order fractional step method: First, a provisional velocityû is computed and then a pseudo-pressure, ϕ, is used to correct the provisional velocity field so that the continuity equation is satisfied at each computational time step (Kim & Moin, 1985).…”

Section: Methodsmentioning

confidence: 99%

Direct numerical simulations of flow in realistic mouth–throat geometries

Nicolaou

Zaki

2013

Journal of Aerosol Science

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Section: Methodsmentioning

confidence: 99%

Direct numerical simulations of flow in realistic mouth–throat geometries

Nicolaou

Zaki

2013

Journal of Aerosol Science

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“…Stagerred grid strategies that employ the fully-transformed equations, albeit indirectly, and can be considered as hybrid techniques between the PT-1 and FT-1 formulations have been proposed and successfully applied in [19,20,11]. Methods in this category, which will be denoted here as FT-2 formulations, exploit the relationship between the volume fluxes and the Cartesian velocity components (see Eq.…”

Section: Overview Of Staggered Grid Formulations In Curvilinear Coordmentioning

confidence: 99%

“…For example, the V 1 volume flux is calculated by interpolating along the ξ 1 direction as follows: assuming the grid volumes centers along i direction is numbered from 1, 2, … i max , (19) Similarly the V 2 and V 3 volume fluxes are determined by interpolating along their respective grid lines (j and k lines, respectively). With all three volume fluxes known at the volume centers the three contravariant and Cartesian velocity components can be readily computed using Eq.…”

Section: Hybrid Staggered/non-staggered Approach In Curvilinear Coordmentioning

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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“…The objective is to provide an empirical view of the evolution of these instabilities and their breakdown to turbulence, in a canonical setting. The three-dimensional, incompressible Navier-Stokes equations are solved using the numerical algorithm described in Rosenfeld, Kwak & Vinokur (1991). The method is a fractional step formulation where the convective terms are treated explicitly using Adams-Bashforth time advancement; the diffusion and pressure terms are advanced by Crank-Nicolson and implicit Euler schemes, respectively.…”

Section: Direct Numerical Simulationsmentioning

confidence: 99%

Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

2011

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The secondary instability of a zero-pressure-gradient boundary layer, distorted by unsteady Klebanoff streaks, is investigated. The base profiles for the analysis are computed using direct numerical simulation (DNS) of the boundary-layer response to forcing by individual free-stream modes, which are low frequency and dominated by streamwise vorticity. Therefore, the base profiles take into account the nonlinear development of the streaks and mean flow distortion, upstream of the location chosen for the stability analyses. The two most unstable modes were classified as an inner and an outer instability, with reference to the position of their respective critical layers inside the boundary layer. Their growth rates were reported for a range of frequencies and amplitudes of the base streaks. The inner mode has a connection to the TollmienSchlichting (T-S) wave in the limit of vanishing streak amplitude. It is stabilized by the mean flow distortion, but its growth rate is enhanced with increasing amplitude and frequency of the base streaks. The outer mode only exists in the presence of finite amplitude streaks. The analysis of the outer instability extends the results of Andersson et al. (J. Fluid Mech. vol. 428, 2001, p. 29) to unsteady base streaks. It is shown that base-flow unsteadiness promotes instability and, as a result, leads to a lower critical streak amplitude. The results of linear theory are complemented by DNS of the evolution of the inner and outer instabilities in a zero-pressure-gradient boundary layer. Both instabilities lead to breakdown to turbulence and, in the case of the inner mode, transition proceeds via the formation of wave packets with similar structure and wave speeds to those reported by Nagarajan, Lele & Ferziger (J. Fluid Mech., vol. 572, 2007, p. 471).

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A fractional step solution method for the unsteady incompressible navier-stokes equations in generalized coordinate systems

Cited by 270 publications

References 21 publications

Direct numerical simulations of flow in realistic mouth–throat geometries

Direct numerical simulations of flow in realistic mouth–throat geometries

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

Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

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