Aboubacar, M.; Aguayo, J. P.; Phillips, P. M.; Phillips, T. N.; Tamaddon-Jahromi, H. R.; Snigerev, B. A.; Webster, M. F. Modelling pom-pom type models with high-order finite volume schemes. (English) Zbl 1088.76553 J. Non-Newton. Fluid Mech. 126, No. 2-3, 207-220 (2005). Summary: We are concerned with the numerical solution of viscoelastic flows using two contrasting high-order finite volume schemes. We take our earlier work for transient start-up flow in a channel and extend this beyond Oldroyd-B modelling to consider a different fluid model of the pom-pom class. This includes single extended form of the pom-pom model, comparing the results of two different finite volume schemes. The numerical techniques employed are time-stepping algorithms, one of hybrid finite element/volume type, the other of pure finite volume form. The pure finite volume scheme is a staggered-grid cell-centred scheme based on area-weighting and a semi-Lagrangian formulation. This may be implemented on structured or unstructured rectangular grids, utilising backtracking along the solution characteristics in time. For the hybrid scheme, we solve the momentum/continuity equations by a fractional-staged Taylor-Galerkin/pressure-correction procedure and invoke a cell-vertex finite volume scheme for the constitutive law. This draws upon fluctuation distribution schemes (upwinding), different combinations of ’flux’ and ’median-dual-cell’ spatial discretisations and time-term treatments. Here, unstructured and structured meshes may be used, based largely on triangular grids. A comparison of the two finite volume approaches is presented, concentrating upon the new features posed by the pom-pom class of models. Cited in 1 ReviewCited in 8 Documents MSC: 76M12 Finite volume methods applied to problems in fluid mechanics 76A10 Viscoelastic fluids Keywords:single extended pom-pom model; staggered-grid cell-centred scheme; Taylor-Galerkin pressure-correction procedure PDFBibTeX XMLCite \textit{M. Aboubacar} et al., J. Non-Newton. Fluid Mech. 126, No. 2--3, 207--220 (2005; Zbl 1088.76553) Full Text: DOI