Preconditioned Uzawa Algorithm for the Velocity-Pressure-Stress Formulation of Viscoelastic Flow Problems

Journal of Scientific Computing

Volumn 17, Issue 1-4, 2002, Pages 201-210

  Escriva, X ^a   Leriche, E ^b   Phillips, T N ^a  

^a ABERYSTWYTH UNIVERSITY   (United Kingdom)

^b EPFL   (Switzerland)

Author keywords

Oldroyd B fluid; Preconditioned; Spectral elements; Uzawa algorithm; Viscoelastic flow

Indexed keywords

ALGORITHMS; EQUATIONS OF MOTION; FLOW OF FLUIDS; GALERKIN METHODS; INCOMPRESSIBLE FLOW; ITERATIVE METHODS; NATURAL SCIENCES COMPUTING; PROBLEM SOLVING;

OLDROYD B FLUID; PRECONDITIONERS; SPECTRAL ELEMENTS; UZAWA ALGORITHM; VISCOELASTIC FLOW;

VISCOELASTICITY;

EID: 1942443584     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1015104815431     Document Type: Conference Paper

References (11)

1. Bramble, J. H., and Pasciak, J. E. (1997). Iterative techniques for time dependent Stokes problems. Math. Applic. 33, 13-30.
2. Cahouet, J., and Chabard, J.-P. (1988). Some fast 3D finite element solvers for the generalized Stokes problem. Internat. J. Numer. Methods Fluids 8, 869-895.
3. Chauvière, C., and Owens, R. G. (2001). A new spectral element method for the reliable computation of viscoelastic flow. J. Non-Newtonian Fluid Mech. 190, 3999-4018.
4. Deville, M., and Mund, E. (1985). Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning. J. Comput. Phys. 60, 517-533.
5. Dryja, M., and Widlund, O. B. (1994). Domain decomposition algorithms with small overlap. SIAM J. Sci. Comput. 15, 604-620.
6. Fischer, P. F., Miller, N. I., and Tufo, H. M. (2000). An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows. In Bjørstad, P., and Luskin, M. (eds.), Parallel Solution of Partial Differential Equations, Springer-Verlag, pp. 158-180.
7. Gerritsma, M. I., and Phillips, T. N. (1998). Discontinuous spectral element approximations for the velocity-pressure-stress formulation of the Stokes problem. Internat. J. Numer. Methods Engrg. 43, 1401-1419.
8. Gerritsma, M. I., and Phillips, T. N. (1999). Compatible spectral approximations for the velocity-pressure-stress formulation of the Stokes problem. SIAM J. Sci. Comput. 20, 1530-1550.
9. Karniadakis, G. E. M., Israeli, M., and Orszag, S. A. (1991). High order splitting methods for incompressible Navier-Stokes equations. J. Comput. Phys. 97, 414-443.
10. Maday, Y., Meiron, D., Patera, A. T., and Rønquist, E. M. (1993). Analysis of iterative methods for the steady and unsteady Stokes problem: Application to spectral element discretizations. SIAM J. Sci. Comput. 14, 310-337.
11. Maday, Y., Patera, A. T., and Rønquist, E. M. (1990). An operator-integration-factor splitting method for time dependent problems: Application to incompressible fluid flow. SIAM J. Sci. Comput. 5, 263-292.