Study of the effect of the non-orthogonality for non-staggered grids—the theory

Xu, Hao; Zhang, C.

doi:10.1002/(sici)1097-0363(19981215)28:9<1265::aid-fld726>3.0.co;2-1

Cited by 7 publications

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“…On the other hand, PICTURE assumption is correct over the whole domain resulting in a smooth solution. It was mentioned in a previous section that there are consistent schemes that can produce oscillations, now it is understood that these are partially linked 10 to the adequacy of the linearity assumption implicit in the derivation of the cell face velocity.…”

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confidence: 99%

“…Due to the wrong coupling between faces and nodes the results show a velocity field quite spiky. This is a clear example of a very simple flow in which both pressure and velocity behave erratically owing to the inconsistencies of the transient 10 We say 'partially linked' because there are other required interpolations in the u * e expression that can affect the amplitude of the oscillations, if any.…”

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Cell face velocity alternatives in a structured colocated grid for the unsteady Navier–Stokes equations

Pascau

2011

Numerical Methods in Fluids

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The use of a colocated variable arrangement for the numerical solution of fluid flow is becoming more and more popular due to its coding simplicity. The inherent decoupling of the pressure and velocity fields in this arrangement can be handled via a special interpolation procedure for the calculation of the cell face velocity named PWIM (Pressure Weighted Interpolation Method). In this paper a discussion on the alternatives to extend PWIM to unsteady flows is presented along with a very simple criterium to ascertain if a given interpolation practice will produce steady results that are relaxation dependent or time step dependent. Following this criterium it will be shown that some prior schemes presented as time step independent are actually not, although by using special interpolations can be readily adapted to be. A systematic way of deriving different cell face velocity expressions will be presented and new formulae free of ∆t dependence will be derived. Several computational exercices will accompany the theoretical discussion to support our claims.

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