Transient Start-up of Plane Poiseuille Flow
نویسندگان
چکیده
INTRODUCTION This article investigates various improvements to two existing finite volume (fv) algorithms, specifically constructed to solve transient viscoelastic flow problems. Here, we consider model problems to identify fundamental algorithmic advances. Two alternative fv-approaches are advocated and contrasted for their properties, a hybrid cell-vertex scheme and a cell-centred staggered-grid scheme. The former utilises fe-discretisation for momentum/continuity components and fv for constitutive equations. The latter cell-centred scheme is a pure fv-discretisation. Both schemes adopt a time-stepping solution approach to solve the velocity/stress problem in a coupled sense. The model problem selected for study is that of the transient start-up flow of an Oldroyd-B model fluid in a channel. This is a transient shear flow, so that inertia is unimportant. Here, one may solve for the transient evolution of velocity and/or stress, and compare results against the analytical solution available. For the cell-vertex scheme, attention is given to the consistent spatial discretisation of the stress-flux and source, both under the fluctuationdistributed (FD) contribution and the median-dualcell (MDC) counterpart. The latter is paramount to ensure stability of convergence in complex flows. A generalised finite volume update is proposed, that takes into account a consistent discretisation of the time term of the constitutive equation, whilst retaining the aforementioned spatial consistency. For the cell-centred scheme, improved methodology on area-weighting is considered attracting higher-orders of accuracy within a semiLagrangian implementation. A first-order variant of this scheme has already been established for complex flows [2].
منابع مشابه
Magnetohydrodynamic (MHD ) Plane Poiseuille Flow With Variable Viscosity and Unequal Wall Temperatures
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