Analysis of semi-staggered finite-difference method with application to Bingham flows

Computer Methods in Applied Mechanics and Engineering

Volumn 198, Issue 9-12, 2009, Pages 975-985

  Olshanskii, Maxim A ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Bingham fluid; Iterative methods; Semi staggered grid; Stabilized discretization; Stokes problem; Visco plastic flow

Indexed keywords

DIFFERENCE EQUATIONS; FINITE DIFFERENCE METHOD; INCOMPRESSIBLE FLOW; NUMERICAL ANALYSIS; PLASTIC FLOW; POLYNOMIAL APPROXIMATION;

BINGHAM FLUID; SEMI-STAGGERED GRID; STABILIZED DISCRETIZATION; STOKES PROBLEM; VISCO-PLASTIC FLOW;

ITERATIVE METHODS;

EID: 58349113744     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.11.010     Document Type: Article

References (37)

1. Barragy E., and Carey G.F. Stream function-vorticity driven cavity solution using p finite elements. Comput. Fluids 26 (1997) 453-468
2. Barton I.E., and Kirby R. Finite difference scheme for the solution of fluid problems on non-staggered grids. Int. J. Numer. Methods Fluids 33 (2000) 939-959
3. Becker R., and Braak M. A finite element pressure gradient stabilization for the Stokes equations. Calcolo 28 (2001) 173-179
4. Benzi M., Golub G.H., and Liesen J. Numerical solution of saddle point problems. Acta Numer. 14 (2005) 1-137
5. Bercovier M., and Engelman M. A finite element method for incompressible non-newtonian flows. J. Comput. Phys. 36 (1980) 313-326
6. Berrone S. Adaptive discretization of the Navier Stokes equations by stabilized finite element methods. Comput. Methods Appl. Mech. Engrg. 190 (2001) 4435-4455
7. Boland J.M., and Nicolaides R.A. On the stability of bilinear-constant velocity-pressure finite elements. Numer. Math. 44 (1984) 219-222
8. Botella O., and Peyret R. Benchmark spectral results on the lid-driven cavity flow. Comput. Fluids 27 (1998) 421-433
9. Bochev P.B., Dohrmann C.R., and Gunzburger M.D. Stabilization of low-order mixed finite elements for the Stokes equations. SIAM J. Numer. Anal. 44 (2006) 82-101
10. Brezzi F., and Fortin M. Mixed and Hybrid Finite Element Methods (1991), Springer, New York
11. Brezzi F., and Pitkaranta J. On the stabilization of Finite Element approximations of the Stokes problem. In: Hackbush W. (Ed). Efficient Solutions of Elliptic Systems. Notes on Numerical Fluid Mechanics vol. 10 (1984), Vieweg, Braunschweig 11-19
12. Churbanov A.G., Pavlov A.N., and Vabishchevich P.N. Operator-splitting methods for the incompressible Navier-Stokes equations on non-staggered grids. Part 1: First-order schemes. Int. J. Numer. Meth. Fluids 21 (1995) 617-640
13. Dean E.J., Glowinski R., and Guidoboni G. On the numerical simulation of Bingham visco-plastic flow: old and new results. J. Non-Newton. Fluid Mech. 142 (2007) 36-62
14. Duvaut G., and Lions J.L. Inequalities in Mechanics and Physics (1976), Springer
15. Elias R.N., Martins M.A.D., and Coutinho A.L.G.A. Parallel edge-based solution of viscoplastic flows with the SUPG/PSPG formulation. Comput. Mech. 38 (2006) 365-381
16. Elman H.C., Silvester D.J., and Wathen A.J. Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics. Numerical Mathematics and Scientific Computation (2005), Oxford University Press, Oxford, UK
17. Fortin M., Peyret R., and Temam R. Resolution numerique des equations de Navier-Stokes pour un fluide incompressible. J. Mech. 10 (1971) 357-390
18. Glowinski R., Lions J.L., and Tremolieres R. Numerical Analysis of Variational Inequalities. Studies in Mathematics and its Applications vol. 8 (1981), North-Holland, Amsterdam
19. Glowinski R. Numerical Methods for Nonlinear Variational Problems (1984), Springer-Verlag, New York
20. Franca L.P., and Stenberg R. Error analysis of some Galerkin least-squares methods for the elasticity equations. SIAM J. Numer. Anal. 28 (1991) 1680-1697
21. Hackbusch W. Iterative Solution of Large Sparse Systems of Equations (1994), Springer, New York
22. Mitsoulis E., and Zisis Th. Flow of Bingham plastics in a lid-driven cavity. J. Non-Newton. Fluid Mech. 101 (2001) 173-180
23. Muravleva E.A., and Olshanskii M.A. Two finite-difference schemes for the Bingham cavity flows. Rus. J. Numer. Anal. Math. Model. 23 (2008) 615-634
24. Layton W. Model reduction by constraints and an induced pressure stabilization. J. Numer. Linear Alg. Appl. 12 (2005) 547-562
25. Ouazzi A., Turek S., and Hron J. Finite element methods for the simulation of incompressible powder flow. Commun. Numer. Meth. Engrg. 21 (2005) 581-596
26. Olshanskii M.A., and Vassilevski Yu.V. Pressure Schur complement preconditioners for the discrete Oseen problem. SIAM J. Sci. Comput. 29 (2007) 2686-2704
27. Pacheco J.R., Pacheco-Vega A., Rodic T., and Peck R.E. Numerical simulations of heat transfer and fluid flow problems using an immersed boundary method on non-staggered grids. Numer. Heat Transfer, Part B 48 (2005) 1-24
28. Papanastasiou T.C. Flows of materials with yield. J. Rheol. 31 (1987) 385-404
29. Patankar S.V. Numerical Heat Transfer and Fluid Flow (1980), Hemisphere, Washington, DC
30. Peters J., Reichelt V., and Reusken A. Fast iterative solvers for discrete Stokes equations. SIAM J. Sci. Comput. 27 (2005) 646-666
31. Sanchez F.J. Application of a first-order operator splitting method to Bingham fluid flow simulation. Comput. Math. Appl. 36 (1998) 71-86
32. Sahin M., and Wilson H.J. A semi-staggered dilation-free finite volume method for the numerical solution of viscoelastic fluid flows on all-hexahedral elements. J. Non-Newton. Fluid Mech. 147 (2007) 79-91
33. Shyy W., and Vu T.C. On the adoption of velocity variable and grid system for fluid flow computation in curvilinear coordinates. J. Comput. Phys. 92 (1991) 82-105
34. Stenberg R. Error analysis of some finite element methods for the Stokes problem. Math. Comput. 54 (1990) 495-508
35. Vola D., Boscardin L., and Latche J.C. Laminar unsteady flows of Bingham fluids: a numerical strategy and some benchmark results. J. Comput. Phys. 187 (2003) 441-456
36. Wendl M.C., and Agarawal R.K. Mass conservation and the accuracy of non-staggered grid incompressible flow schemes. In: Hafez M.M. (Ed). Numerical Simulations of Incompressible Flows (2003), World Scientific
37. Ye T., Mittal R., Udaykumar H.S., and Shyy W. An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J. Comput. Phys. 156 (1999) 209-240