A computational stream function method for two-dimensional incompressible viscous flows

International Journal for Numerical Methods in Engineering

Volumn 62, Issue 14, 2005, Pages 1950-1981

  Kobayashi, Marcelo H ^a   Pereira, Manuel C ^b  

^a University of Hawaii at Manoa   (United States)

^b INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Compact methods; Incompressible flows; Multigrid method; Newton Krylov matrix free method; Stream function

Indexed keywords

COMPUTER SIMULATION; FINITE DIFFERENCE METHOD; INCOMPRESSIBLE FLOW; INTEGRATION; NAVIER STOKES EQUATIONS; NUMERICAL METHODS; RUNGE KUTTA METHODS; VISCOUS FLOW;

AXISYMMETRIC-VISCOUS FLOWS; NON-STATIONARY FLOWS; STREAM FUNCTION EQUATIONS; TWO-DIMENSIONAL INCOMPRESSIBLE VISCOUS FLOW;

COMPUTATIONAL METHODS;

INCOMPRESSIBLE FLOW; MATHEMATICAL METHOD; NAVIER-STOKES EQUATIONS; TWO-DIMENSIONAL FLOW; VISCOUS FLOW;

EID: 15844377785     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1255     Document Type: Article

References (47)

1. Girault V, Raviart P. Finite Element Methods for Navier-Stokes Equations. Springer: Berlin, 1986.
2. Chorin AJ. A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics 1967; 2:12-26.
3. Rogers S, Kuak D, Kiris C. Steady and unsteady solutions of the incompressible Navier-Stokes equations. AIAA Journal 1991; 29 4):603-610.
4. Harlow FH, Welch JE. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. The Physics of Fluids 1965; 8(12):2182-2189.
5. Wilson RV, Demuren AO, Carpenter MH. Higher-order compact schemes for numerical simulation of incompressible flows. ICASE Report 98-13, ICASE, Langley Research Center, 1998.
6. Chorin AJ. Numerical solution of the Navier-Stokes equations. Mathematics of Computation 1968; 22: 745-762.
7. Chorin AJ. On the convergence of discrete approximations of the Navier-Stokes equations. Mathematics of Computation 1969; 23 341-353.
8. Bell JB, Colella P, Glaz HM. A second-order projection method for the incompressible Navier-Stokes equations. Journal of Computational Physics 1989; 85:257-283.
9. Kobayashi MH, Pereira JMC, Pereira JCF. A conservative finite-volume 2nd order accurate projection method on hybrid unstructured grids. Journal of Computational Physics 1999; 150(1):40-75.
10. Patankar SV, Spalding DB. A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows. International Journal of Heat and Mass Transfer 1972; 15:1787-1806.
11. Issa RI. Solution of the implicitly discretized fluid flow equations by operator splitting. Journal of Computational Physics 1985; 62 40-62.
12. Galpin PF, van Doormaal JP, Raithby GD. Solution of the incompressible mass and momentum equations by application of the coupled equation line solver. International Journal for Numerical Methods in Fluids 1985; 5:615-625.
13. Caseiras CP. Desarrollo de métodos de volúmenes finitos para la resolución de las equaciones de Navier-Stokes incompressibles, Ph.D. Thesis, Centro Politécnico de la Universidad de Zaragoza, October 1994.
14. Saad Y. Schultz MH. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 1986; 3:856-869.
15. van der Vorst HA. BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 1992; 13:631-644.
16. Saad Y. A flexible inner-outer preconditioned GMRES algorithm. SIAM Journal on Scientific and Statistical Computing 1993; 14 2):461-469.
17. Roache PJ. Computational Fluid Dynamics. Hermosa: Albuquerque, NM, 1976.
18. Spotz WF, Carey GF. High-order compact scheme for the steady stream-function vorticity equations. International Journal for Numerical Methods in Engineering 1995; 38(20):3497-3512.
19. Weiman E, Liu J-G. Essentially compact schemes for unsteady viscous incompressible flows. Journal of Computational Physics 1996; 126:122-138.
20. Auteri F, Quartapelle L. Galerkin spectral method for the vorticity and stream function equations. Journal of Computational Physics 1999; 149:306-332.
21. Spotz WF. Accuracy and performance of numerical wall boundary conditions for steady, 2D, incompressible stream-function vorticity. International Journal for Numerical Methods in Fluids 1998; 28 737-757.
22. Stokes GG. On the effect of internal friction of fluids on the motion of pendulums. Transactions of the Cambridge Philosophical Society 1850; 9:8-106.
23. Basset AB. On the motion of a sphere in a viscous liquid. Philosophical Transactions of the Royal Society of London A 1888; 179:43-63.
24. Blasius H. Grenzschichten in flüssigkeiten mit kleiner reibung. Zeitschrift für Mathematik und Physik 1908; 56:1-37.
25. Liao S-J. An analytic approximation of the drag coefficient for the viscous flow past a sphere. International Journal of Non-linear Mechanics 2002; 37(1):1-18.
26. Kupferman R. A central-difference scheme for a pure stream function formulation of incompressible viscous flows. SIAM Journal of Scientific Computing 2001; 23(1):1-18.
27. Bubnovich VI, Rosas CE, Moraga NO. A stream function implicit finite difference scheme for 2D incompressible flows of Newtonian fluids. International Journal for Numerical Methods in Engineering 2002; 53:2163-2184.
28. Lele SK. Compact finite-difference schemes with spectral-like resolution. Journal of Computational Physics 1992; 103:16-42.
29. Kobayashi MH. On a class of Padé finite volume methods. Journal of Computational Physics 1999; 156(1):137-180.
30. Knoll DA, McHugh PR, Keyes DE. Newton-Krylov methods for low Mach number compressible combustion. AIAA Journal 1996; 34:961-967.
31. Johnson RW, McHugh PR, Knoll DA. High-order scheme implementation using Newton-Krylov solution methods. Numerical Heat Transfer, Part B 1997; 31:295-312.
32. Knoll DA. An improved convection scheme applied to recombining divertor plasma flows. Journal of Computational Physics 1998; 142 473-488.
33. Kelley CT, Keyes DE. Convergence analysis of pseudo-transient continuation. SIAM Journal of Numerical Analysis 1998; 35 508-523.
34. Knoll DA, Rider WJ. A multigrid preconditioned Newton-Krylov method. SIAM Journal of Scientific Computing 2000; 21:691-710.
35. Knoll DA, Mousseau VA. On Newton-Krylov multigrid methods for the incompressible Navier-Stokes equations. Journal of Computational Physics 2000; 163:262-267.
36. Pereira JMC, Kobayashi MH, Pereira JCF. A fourth-order-accurate finite volume compact method for the incompressible Navier-Stokes solutions. Journal of Computational Physics 2001; 167:217-243.
37. Marques NPC. Métodos implícitos sem matriz para a resolução das equações de Euler e Navier-Stokes. Ph.D. Thesis, Instituto Superior Técnico, Lisbon, Portugal, 2002.
38. Carpenter MH, Gottlieb D, Abarbanel S. The stability of numerical boundary treatments for compact high-order finite-difference schemes. Journal of Computational Physics 1993; 108:272-295.
39. Temam R. Navier-Stokes Equations: Theory and Numerical Analysis (3rd edn). Elsevier: Amsterdam, 1984.
40. Shih TM, Tan CH, Hwang BC. Effects of grid staggering on numerical schemes. International Journal for Numerical Methods in Fluids 1989; 9:193-212.
41. Slezkin NA. On an exact solution of the equations of viscous flows. Uchenye Zapiski Moskovskogo Gosudarstvennogo Universiteta 1934; 2 1.
42. Sherman FS. Viscous Flow, McGraw-Hill Series in Mechanical Engineering. McGraw-Hill: New York, 1990.
43. Botella O, Peyret R. Benchmark spectral results on the lid-driven cavity flow. Computers and Fluids 1998; 27(4):421-433.
44. Castleman RA. The resistance to the steady motion of small spheres in fluids. Technical Note 231, NACA, Washington, February 1926.
45. Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. Springer: New York, 1988.
46. Lang S. Differential and Riemannian Manifolds (3rd edn), vol. 160, Graduate Texts in Mathematics. Springer: New York, 1995.
47. Abraham R, Marsden JE, Ratiu T. Manifolds, Tensor Analysis, and Applications (2nd edn), vol. 75, Applied Mathematical Sciences. Springer: New York, 1988.