Arbitrary Lagrangian–Eulerian Numerical Prediction for Local Scour Caused by Turbulent Flows

Ushijima, Satoru

doi:10.1006/jcph.1996.0080

Cited by 22 publications

(10 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For the explicit method, the explicit boundary conditions in (7) (14) in the case of explicit boundary conditions. Finally, for the Crank-Nicolson method, we use (16) in the case of explicit boundary conditions.…”

Section: Model Problem and Discretizationmentioning

confidence: 99%

Stability of numerical schemes on staggered grids

Oishi

Cuminato²,

Yuan

et al. 2008

Numerical Linear Algebra App

View full text Add to dashboard Cite

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthermore, we consider the cases when both explicit and implicit approximations of the boundary conditions are employed. Why we choose to do this is clearly motivated and arises from solving fluid flow equations with free surfaces when the Reynolds number can be very small, in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t=nt rather than t=(n+1)t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar, thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally stable

show abstract

Section: Model Problem and Discretizationmentioning

confidence: 99%

Stability of numerical schemes on staggered grids

Oishi

Cuminato²,

Yuan

et al. 2008

Numerical Linear Algebra App

View full text Add to dashboard Cite

show abstract

“…Based on the well known MAC method [15], many numerical schemes have been developed with the objective of solving such flows. Examples of those numerical methods are: SMAC [3], GENSMAC [34], SIMAC [4], the methods of Ushijima [41], Kim and No [19], among others. More recently, improved variants have been developed: for instance, Sousa et al [32] used the MAC method for 3D multi-fluid flows with free surfaces (and interfaces); Ferreira et al [13] presented numerical simulations of turbulent free surface flows based on MAC techniques; Mangiavacchi et al [21] implemented an effective technique for dealing with axisymmetric and planar flows when surface tension is relevant; Ferreira et al [14] adapted the MAC method to calculate confined and free surface flows at both low and high Reynolds numbers.…”

Section: Free Surface Boundary Conditionsmentioning

confidence: 99%

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom–Pom model

Oishi

Martins

Tomé

et al. 2012

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

“…They also concluded that the vibrating pipe may induce a deeper scour hole than the fixed pipe. Ushijima [6] developed a numerical model based on the arbitrary Lagrangian-Eulerian formulation in order to predict local scour caused by turbulent flow. He concluded that his numerical results of sand bed profiles compared well with the experimental data.…”

Section: Introductionmentioning

confidence: 99%

A parallel three-dimensional scour model to predict flow and scour below a submarine pipeline

Alam

Cheng

2010

Open Physics

View full text Add to dashboard Cite

Abstract:A three-dimensional Lattice Boltzmann flow and scour model is developed to simulate time-dependent scour below a submarine pipeline. The proposed model presented in this paper is able to predict streamwise and spanwise propagations of scour with respect to lattice unit of time. It is evident from this study that the existence of a spiral vortex in the proximity of the span shoulder is quite noteworthy. It is revealed that the critical regime of the 2-D scour process is found to be up to one pipe diameter away in both directions from the middle of the unsupported length of pipelines. The equilibrium maximum scour depth and the shape of streamwise equilibrium scour hole compare well with the available experimental data. The speed of propagation of scour along the pipeline length maintains an almost constant rate, which is consistent with the experimental observations found in literature. In addition, it is seen that the scour slope at the shoulder region remains fairly constant throughout the whole scour process.

show abstract

Arbitrary Lagrangian–Eulerian Numerical Prediction for Local Scour Caused by Turbulent Flows

Cited by 22 publications

References 4 publications

Stability of numerical schemes on staggered grids

Stability of numerical schemes on staggered grids

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom–Pom model

A parallel three-dimensional scour model to predict flow and scour below a submarine pipeline

Contact Info

Product

Resources

About