Ellipticity, accuracy, and convergence of the discrete Navier-Stokes equations

Armfield, S.W.

doi:10.1006/jcph.1994.1158

Cited by 53 publications

(25 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These are solved using an alternating-direction-implicit iterative method. The scheme is described in detail by Armfield (1991Armfield ( , 1994 and has been previously used for the simulation of buoyancy-dominated and stratified flows (Patterson & Armfield 1990;Armfield & Patterson 1992;Armfield & Debler 1993;Armfield 1994). …”

Section: Discretizationmentioning

confidence: 99%

Direct simulation of weak axisymmetric fountains in a homogeneous fluid

Lin

Armfield

2000

J. Fluid Mech.

View full text Add to dashboard Cite

The weak axisymmetric fountain that results from the injection of a dense fluid upwards into a large container of homogeneous fluid of lower density is studied numerically. Using a time-accurate finite volume code, the behaviour of fountains with both a uniform and a parabolic profile of the discharge velocity at the source has been investigated. The evolution of the transient fountain flow has been analysed and two distinct stages have been identified. The time series of the passage of the fountain front has been presented and the initial, temporary and final characteristic fountain heights have been determined and scaled with the Froude number at the source. At steady state, the final fountain height and the fountain width are found to be the height and horizontal length scales which provide the full parameterization of the flow in the fountain core. The vertical velocity and temperature on the symmetry axis have been scaled with the height scale and an explicit correlation is also obtained for the former. The radial distributions of both the vertical and horizontal velocities in the zone of self-similarity in the fountain core at steady state have been scaled with the two length scales and empirical correlations have been obtained.

show abstract

Section: Discretizationmentioning

confidence: 99%

Direct simulation of weak axisymmetric fountains in a homogeneous fluid

Lin

Armfield

2000

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…The right hand side is again, D(H(v n + 1 / 2 )) to second order in time and the pressure is again second order accurate in space and time. However the sparse 2L1x,2L1y spaced discretisation of the pressure Laplacian means that the grid scale pressure is un-coupled, and the discrete operator is non-elliptic [7,8]. This means that grid scale error in the pressure field can accumulate without bound, leading to a grid scale oscillation that may cause the solution to break down completely.…”

Section: Non-staggered Gridmentioning

confidence: 94%

“…This approach, which was first suggested by Rhie and Chow [6], has been used in equivalent forms in a number of schemes and has been defined as elliptic interpolation as it has effect of recovering the grid scale pressure ellipticity of the continuous equations [7,8]. The use of elliptic interpolation adds a divergence error of the form,…”

Section: Non-staggered Gridmentioning

confidence: 99%

A Parallel Non-Staggered Navier-Stokes Solver Implemented on a Workstation Cluster

Armfield

Morgan

Norris

et al. 2003

Computational Fluid Dynamics 2002

View full text Add to dashboard Cite

Abstract. Non-staggered, fractional step Navier-Stokes solvers are presented and analysed in comparison to a standard staggered solver. It is shown analytically that the non-staggered schemes have the same order of accuracy as the staggered scheme, although one of the schemes is non-elliptic in the pressure field at the grid scale. Numerical results are used to validate the analysis, with only the non-elliptic non-staggered scheme showing a reduced accuracy and efficiency compared to the staggered scheme. Details of a computer cluster built using Pentium 4 processors with a fast ethernet switch are presented. A serial benchmark demonstrates the excellent performance of the P4 for large array size compute intensive jobs, while both MPI and HPF coded parallel benchmarks show the effective parallel performance of the cluster.

show abstract

“…To enforce the continuity, the pressure correction method is used to construct a Poisson's equation which is solved using the preconditioned gmres method. Detailed descriptions of these schemes were given by Armfield [3,5] and the code has been previously used and validated for the simulation of a range of buoyancy dominated flows [11,1,2,9]. A nonuniform mesh is used allowing grid nodes to be concentrated in the region of C874 the heated wall and the upper and lower boundaries.…”

Section: Methodsmentioning

confidence: 99%

Natural convection flow of air in an inclined open cavity

Nateghi¹,

Armfield²

2004

ANZIAMJ

View full text Add to dashboard Cite

Consider natural convection flow in a two dimensional inclined open cavity for both transient and steady-state flow. The left hand vertical wall of cavity is heated and facing an opening. The top and bottom boundaries are insulated. Numerical solutions are obtained for the Navier-Stokes equations on a non-staggered grid using a finite volume scheme. Results are considered for a wide range of Rayleigh numbers varying from 10 5 to 10 10 with Prandtl number 0.7 and inclination angles from 10 • to 90 • . The flow is steady at the low Rayleigh number for all angles and becomes unsteady at the high Rayleigh number for all angles. The critical Rayleigh numbers for all angles are obtained and we show that the critical Rayleigh number decreases as the inclination angle increases.

show abstract

Ellipticity, accuracy, and convergence of the discrete Navier-Stokes equations

Cited by 53 publications

References 12 publications

Direct simulation of weak axisymmetric fountains in a homogeneous fluid

Direct simulation of weak axisymmetric fountains in a homogeneous fluid

A Parallel Non-Staggered Navier-Stokes Solver Implemented on a Workstation Cluster

Natural convection flow of air in an inclined open cavity

Contact Info

Product

Resources

About