Finite Volume Simulation of Viscoelastic Flows in
General Orthogonal Coordinates
type de publication 
article dans une revue internationale avec comité de lecture 
date de publication 
2010 
auteur(s) 
Mompean Gilmar; Thais Laurent 
journal (abréviation) 
Mathematics and Computers in Simulation (Math Com) 
volume (numéro) 
80 (11) 
 
pages 
2185 – 2199 
résumé 
This work reports on numerical simulations of unsteady two and threedimensional viscoelastic flows in complex geometries. The NavierStokes solver is designed for general orthogonal grids in two dimensions and a Cartesian description in the spanwise direction. The conservation equations are written in primitive pressurevelocity variables, making use of the physical curvilinear lengths and contravariant velocities (Pope, J. Comp. Phys. 26, pp197217, 1978). The space discretization is finite volume, with the pressure at the center of the control volumes and the velocity components staggered at the center of the cell faces. The conservative advective terms are discretized with a quadratic upwind scheme (QUICK). The extra advective terms induced by coordinate curvature are treated explicitly as integral volumes evaluated at the cell centers. The time advancement of the solution follows from an explicit decoupling procedure (Harlow & Welch, Phys. Fluids 8, pp2182 2189, 1965). The AdamsBashforth level 2 scheme is used to evaluate advection, curvature and viscous terms. This discretization produces a symmetric and positive definite matrix for the pressure. The overall formulation is second order accurate in space, firstorder in time. To model the viscoelastic flow, the PTT (PhanThien Tanner) constitutive equation is considered. Results are presented for 2D and 3D configurations (flow past a cylinder and flow through a Ucurved channel), both presenting recirculations and secondary flows. This contribution demonstrates the versatility of the formulation for 2D and 3D flows with curved boundaries, and its easy implementation starting from a Cartesian description. 
mots clés 
finite volume; general orthogonal coordinates; unsteady viscoelastic; flow simulation; flow past a cylinder; flow inside a Ucurved channel 
lien 

Exporter la citation au format
CSV (pour Excel)
ou
BiBTeX (pour LaTeX).