A high-order incompressible flow solver with WENO

Journal of Computational Physics

Volumn 228, Issue 7, 2009, Pages 2426-2442

  Zhang, Ju ^a   Jackson, Thomas L ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Incompressible; Methods: numerical; WENO scheme

Indexed keywords

COMPRESSIBILITY; CONVERGENCE OF NUMERICAL METHODS; NAVIER STOKES EQUATIONS; RUNGE KUTTA METHODS;

ARTIFICIAL COMPRESSIBILITY; ESSENTIALLY NON-OSCILLATORY; ESSENTIALLY NON-OSCILLATORY SCHEMES; FLOW SOLVER; HIGH-ORDER; HIGHER-ORDER; INCOMPRESSIBLE; INCOMPRESSIBLE (NAVIER )STOKES EQUATION; METHOD: NUMERICAL; WEIGHTED ESSENTIALLY NON-OSCILLATORY SCHEME;

INCOMPRESSIBLE FLOW;

EID: 60349095768     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.12.009     Document Type: Article

References (34)

1. Adams J. MUDPACK: multigrid fortran software for the efficient solution of linear elliptic partial differential equations. Appl. Math. Comput. 34 (1989) 113-146
2. Auteri F., Quartapelle L., and Vigevano L. Accurate ψ - ζ spectral solution of the singular driven cavity problem. J. Comput. Phys. 180 (2002) 597-615
3. Barragy E., and Carey G.F. Stream function-vorticity driven cavity solution using p finite elements. Comput. Fluids 26 5 (1997) 453-468
4. Bell J.B., Colella P., and Glaz H.M. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85 (1989) 257
5. Bijl H., and Wesseling P. A unified method for computing incompressible and compressible flows in boundary-fitted coordinates. J. Comput. Phys. 141 (1998) 153-173
6. Brown D.L., Cortez R., and Minion M.L. Accurate projection methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 168 (2001) 464-499
7. Chen Y.-N., Yang S.-C., and Yang J.-Y. Int. J. Numer. Meth. Fluids 31 (1999) 747-765
8. Chorin A.J. A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2 (1967) 12-26
9. Criminale W.O., Jackson T.L., and Joslin R.D. Theory and Computation in Hydrodynamic Stability (2003), Cambridge University Press
10. Culick F.E.C. Rotational axisymmetric mean flow and damping of acoustic waves in solid propellant rocket motors. AIAA J. 4 (1966) 1462-1464
11. E W., and Shu C.-W. A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow. J. Comput. Phys. 110 (1993) 39-46
12. W.E., and Liu J. Gauge method for viscous incompressible flows. Commun. Math. Sci. 1 (2003) 317-332
13. Ghia U., Ghia K.N., and Shin C.T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comput. Phys. 48 (1982) 387-411
14. Gresho P.M., and Chan S.T. On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly-consistent mass matrix: part 2: implementation. Int. J. Numer. Meth. Fluids 11 (1990) 621-659
15. Guermond J.L., Minev P., and Shen J. An overview of projection methods for incompressible flows. Comput. Meth. Appl. Mech. Eng. 195 (2006)
16. Harlow F.H., and Welch J.E. Numerical calculation of time-dependent viscous incompressible fluid with a free surface. Phys. Fluids 8 (1965) 2182
17. Henrick A.K., Aslam T.D., and Powers J.M. Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points. J. Comput. Phys. 207 (2005) 542-567
18. Hu F.Q., Hussaini M.Y., and Manthey J.L. Low-dissipation and -dispersion Runge-Kutta schemes for computational acoustics. J. Comput. Phys. 124 (1996) 177-191
19. Jiang G.S., and Shu C.-W. Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1996) 202
20. Kadioglu S.Y., Klein R., and Minion M.L. A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics. J. Comput. Phys. 227 (2008) 2012-2043
21. Karki K.C., and Patankar S.V. Pressure based calculation procedure for viscous flows at all speeds in arbitrary configurations. AIAA J. 27 (1989) 1167-1174
22. Moin P., and Kim J. On the numerical solution of time-dependent viscous incompressible fluid flows involving solid boundaries. J. Comput. Phys. 35 (1980) 381
23. Kim J., and Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59 (1985) 308-323
24. Lele S.K. Compact finite differences with spectral like resolution. J. Comput. Phys. 103 (1992) 16
25. C.L. Merkle, M. Athavale, Time-accurate Unsteady Incompressible Flow Algorithms Based on Artificial Compressibility, AIAA Paper 87-1137, 1987.
26. Morinishi Y., Lund T.S., Vasilyev O.V., and Moin P. Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 143 (1998) 90-124
27. Nagarajan S., Lele S.K., and Ferziger J.H. A robust high-order compact method for large eddy simulation. J. Comput. Phys. 191 (2003) 392
28. Orszag S.A., and Israeli M. Numerical simulation of viscous incompressible flows. Ann. Rev. Fluid Mech. 6 (1974) 281-318
29. Pandit S.K., Kalita J.C., and Dalal D.C. A transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular. J. Comput. Phys. 225 (2007) 1100-1124
30. Patankar S.V., and Spalding D.B. A calculation procedure for heat, mass, and momentum transfer in three-dimensional parabolic flow. Int. J. Heat Mass Trans. 15 (1972) 1787-1806
31. P. Venugopal, F.M. Najjar, R.D. Moser, DNS and LES computations of model solid rocket motors, AIAA paper 2000-3571, 2000.
32. Rogers S.E. Numerical solution of the incompressible Navier-Stokes equations (1990), NASA TM 102199, Ames Research Center, Moffett Field, CA
33. θ = 1410. J. Fluid Meek. 187 (1988) 61-98
34. Wu C.C. A high order WENO finite difference scheme for incompressible fluids and magnetohydrodynamics. Geophys. Astrophys. Fluid Dynam. 101 1 (2007) 37-61