Numerical simulation of thermally convective viscoplastic fluids by semismooth second order type methods

Journal of Non-Newtonian Fluid Mechanics

Volumn 193, Issue , 2013, Pages 43-48

  De Los Reyes, J C ^a   Gonzalez Andrade S ^a  

^a ESCUELA POLITÉCNICA NACIONAL   (Ecuador)

Author keywords

BDF methods; Semismooth Newton methods; Thermal convection; Viscoplastic fluids; Yield stress

Indexed keywords

BDF METHODS; COMPUTATIONAL EXPERIMENT; CONVECTION EFFECTS; COUPLED MODELS; DISCRETE SYSTEMS; DISCRETIZATIONS; GENERALIZED NEWTON METHOD; JACOBIANS; LOCAL REGULARIZATION; NONSMOOTH SYSTEMS; NUMERICAL APPROACHES; NUMERICAL SOLUTION; SECOND ORDERS; SEMISMOOTH; SEMISMOOTH NEWTON ALGORITHM; SEMISMOOTH NEWTON METHOD; THERMAL CONVECTIONS; TIME DISCRETIZATION; VISCOPLASTIC FLUID;

NEWTON-RAPHSON METHOD; PLASTIC FLOW; YIELD STRESS;

VISCOPLASTICITY;

EID: 84872904480     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2012.06.001     Document Type: Article

References (12)

1. Baker G.A., Dougalis V.A., Karakashian O.A. On a higher order accurate fully discrete Galerkin approximation to the Navier-Stokes equations. Math. Comput. 1982, 39:339-375.
2. Beverly C.R., Tanner R.I. Numerical analysis of three-dimensional Bingham plastic flow. J. Non-Newton. Fluid Mech. 1992, 42:85-115.
3. Dean E.J., Glowinski R., Guidoboni G. On the numerical simulation of Bingham visco-plastic flow: old and new results. J. Non-Newton. Fluid Mech. 2007, 142:36-62.
4. De los Reyes J.C., González S. Path following methods for steady laminar Bingham flow in cylindrical pipes. ESAIM: Math. Model. Numer. Anal. 2009, 43:81-117.
5. De los Reyes J.C., González Andrade S. Numerical simulation of two-dimensional Bingham fluid flow by semismooth Newton methods. J. Comput. Appl. Math. 2010, 235:11-32.
6. De los Reyes J.C., González Andrade S. A combined BDF-semismooth Newton approach for time-dependent Bingham flow. Numer. Methods Partial Diff. Eq. 2012, 28:834-860.
7. Glowinski R. Numerical Methods for Nonlinear Variational Problems 1984, Springer-Verlag, New York.
8. Glowinski R., Wachs A. On the numerical simulation of viscoplastic fluid flow. Handbook of Numerical Analysis 2011, vol. 16:483-717. Elsevier.
9. Hintermüller M., Ito K., Kunisch K. The primal-dual active set strategy as a semi-smooth Newton method. SIAM J. Opt. 2003, 13:865-888.
10. Muravleva E.A., Olshanskii M.A. Two finite-difference schemes for calculation of Bingham fluid flows in a cavity. Russ. J. Numer. Anal. Math. Modell. 2009, 23(6):615-634.
11. Vikhansky A. Thermal convection of a viscoplastic liquid with high Rayleigh and Bingham numbers. Phys. Fluids 2009, 21:103103.
12. Zhang J., Vola D., Frigaard I. Yield stress effects on Rayleigh-Bérnard convection. J. Fluid Mech. 2006, 566:389-419.