Incompressible Fluid Dynamics: Some Fundamental Formulation Issues

Gresho, P. M.

doi:10.1146/annurev.fl.23.010191.002213

Cited by 360 publications

(230 citation statements)

References 0 publications

Supporting

Mentioning

226

Contrasting

Unclassified

Order By: Relevance

“…A 33 point equallength finite-difference grid in the vertical provided an economic compromise between the resolution needs of the boundary layers and those of the long-range fluxes. We worked with the equations of motion in their biharmonic form (1)- (3) rather than the more traditional streamfunction-vorticity formulation in order to avoid (a) inversion of the Poisson operator, and (b) difficulties arising from the coupling between the stream function and vorticity [12]. These are associated with the peculiar nature of the boundary conditions for the stream function • and the initial conditions on the vorticity w, which lacks boundary conditions [13].…”

Section: 0x104mentioning

confidence: 99%

Confined states in large-aspect-ratio thermosolutal convection

1998

View full text Add to dashboard Cite

Section: 0x104mentioning

confidence: 99%

Confined states in large-aspect-ratio thermosolutal convection

1998

View full text Add to dashboard Cite

“…In this case, the boundary conditions imposed at the top and the bottom are zero normal velocity (no-penetration) and zero normal derivative of the horizontal velocities (free-slip) and the scalar field χ (adiabatic). The Neumann boundary conditions for the Poisson equation for the pressure at the top and the bottom are then [26] ∂ p ∂z = 1 Re…”

Section: Numerical Algorithmsmentioning

confidence: 99%

Two-fluid formulation of the cloud-top mixing layer for direct numerical simulation

Mellado

Stevens

Schmidt

et al. 2010

Theor. Comput. Fluid Dyn.

View full text Add to dashboard Cite

A mixture fraction formulation to perform direct numerical simulations of a disperse and dilute two-phase system consisting of water liquid and vapor in air in local thermodynamic equilibrium using a twofluid model is derived and discussed. The goal is to understand the assumptions intrinsic to this simplified but commonly employed approach for the study of two-layer buoyancy reversing systems like the cloud-top mixing layer. Emphasis is placed on molecular transport phenomena. In particular, a formulation is proposed that recovers the actual nondiffusive liquid-phase continuum as a limiting case of differential diffusion. High-order numerical schemes suitable for direct numerical simulations in the compressible and Boussinesq limits are described, and simulations are presented to validate the incompressible approach. As expected, the Boussinesq approximation provides an accurate and efficient description of the flow on the scales (of the order of meters) that are considered.

show abstract

“…A discussion and analysis of the various forms of incompressible Navier-Stokes equations can be found for instance in [13,18,22]. Let Ω be a bounded domain in R 2 or R 3 , we assume that Ω contains regular obstacles the reunion of which is called Ω s .…”

Section: Preliminariesmentioning

confidence: 99%

Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations

Bruneau¹

2000

ESAIM: M2AN

View full text Add to dashboard Cite

Abstract.Non reflecting boundary conditions on artificial frontiers of the domain are proposed for both incompressible and compressible Navier-Stokes equations. For incompressible flows, the boundary conditions lead to a well-posed problem, convey properly the vortices without any reflections on the artificial limits and allow to compute turbulent flows at high Reynolds numbers. For compressible flows, the boundary conditions convey properly the vortices without any reflections on the artificial limits and also avoid acoustic waves that go back into the flow and change its behaviour. Numerical tests illustrate the efficiency of the various boundary conditions. Mathematics Subject Classification. 35Q30, 65C20, 65M99. Résumé. Leséquations de

show abstract

Incompressible Fluid Dynamics: Some Fundamental Formulation Issues

Cited by 360 publications

References 0 publications

Confined states in large-aspect-ratio thermosolutal convection

Confined states in large-aspect-ratio thermosolutal convection

Two-fluid formulation of the cloud-top mixing layer for direct numerical simulation

Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations

Contact Info

Product

Resources

About